WO2020042696A1 - Device and method for compensating for error of moving-base rotating-accelerometer gravity gradiometer - Google Patents

Device and method for compensating for error of moving-base rotating-accelerometer gravity gradiometer Download PDF

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WO2020042696A1
WO2020042696A1 PCT/CN2019/089302 CN2019089302W WO2020042696A1 WO 2020042696 A1 WO2020042696 A1 WO 2020042696A1 CN 2019089302 W CN2019089302 W CN 2019089302W WO 2020042696 A1 WO2020042696 A1 WO 2020042696A1
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motion error
module
linear motion
angular
gradient
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PCT/CN2019/089302
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French (fr)
Chinese (zh)
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蔡体菁
喻名彪
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东南大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V13/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices covered by groups G01V1/00 – G01V11/00

Definitions

  • the invention relates to an error compensation device and method of a moving base rotary accelerometer gravity gradient meter, and belongs to the technical field of precision measurement.
  • Moving base gravity gradient exploration is a low-cost, high-efficiency gravity gradient exploration method; it is currently the most advanced gravity field exploration method in the world.
  • Gravity gradient data is widely used in geological analysis, gravity field modeling, high-precision navigation, and resource exploration.
  • Gravity gradient instrument has extremely important national defense and civilian value.
  • the gravity gradient instruments under research at home and abroad mainly include cold atom gravity gradient instrument, superconducting gravity gradient instrument, MEMS gravity gradient instrument and so on.
  • Gravity gradiometers that have been put into commercial use abroad mainly include rotary accelerometer gravity gradient meters and rotary superconducting accelerometer gravity gradient meters. The prototype of China's gravity gradient instrument is under development.
  • the invention provides a device and method capable of real-time compensating the linear motion error, angular motion error, and self-gradient of a gravity gradient instrument.
  • the present invention provides a moving base rotary accelerometer gravity gradient meter error compensation device capable of feedback compensation of the acceleration, angular motion, and self-gradient output measurement errors caused by the gravity gradient meter, which can suppress environments such as temperature and electromagnetic fields
  • the influence of factors on the error transfer coefficient can also avoid overvoltage saturation and overvoltage damage of the front-end signal conditioning circuit of the gravity gradient instrument caused by the acceleration, angular velocity, and angular acceleration of the gravity gradient instrument.
  • the invention also provides a method for compensating for the error of the gravimetric gradient accelerometer of the moving base rotary accelerometer which has the above effects and solves the above problems.
  • the error compensation device of the gravity base of the moving base rotary accelerometer of the present invention includes:
  • a reference signal generating module for generating a quadrature amplitude modulation carrier
  • a self-gradient compensation signal generating module for generating a self-gradient compensation signal in real time
  • An angular motion error compensation signal generating module for generating a gravity gradient instrument angular motion error compensation signal in real time and detecting a centrifugal gradient of the gravity gradient instrument;
  • An angular motion error transfer coefficient processing module for fine-tuning the angular motion error transfer coefficient in real time
  • a linear motion error compensation signal generating module for generating a linear motion error compensation signal of the gravity gradient instrument in real time
  • Linear motion error transfer coefficient processing module for fine-tuning the linear motion error transfer coefficient in real time
  • a gravity gradient accelerometer signal processing module for summing and subtracting output signals of accelerometers mounted on a rotating disc
  • Accelerometer scaling coefficient adjustment module for adjusting the accelerometer scaling coefficient in real time
  • Compensation operation module for compensating the gravity gradient signal including angular motion error, linear motion error, and self-gradient;
  • a gravity gradient signal recovery module for demodulating and outputting a gravity gradient signal from a compensated gravity gradient instrument signal
  • the output of the reference signal generation module is connected to the inputs of a self-gradient compensation signal generation module, an angular motion error compensation signal generation module, and a linear motion error compensation signal generation module; the self-gradient compensation signal generation module and angular motion error compensation signal generation
  • the output of the module, the linear motion error compensation signal generation module, the gravity gradient accelerometer signal processing module is connected to the input of the compensation operation module; the output of the compensation operation module is connected to the accelerometer scale coefficient adjustment module, the angular motion error transfer coefficient
  • the output of the module is connected to the input of the angular motion error compensation signal generating module; the output of the accelerometer scale coefficient adjustment module is connected to the input of the gravity gradient accelerometer signal processing module.
  • the reference signal generating module includes a gravity gradient instrument rotating disc axis encoder and a signal generator; the gravity gradient instrument rotating disc axis encoder detects a phase angle of the rotation of the gravity gradient instrument disc.
  • ⁇ t the signal generator according to the phase angle ⁇ t, quadrature amplitude modulation carrier wave generating sin ⁇ t, sin2 ⁇ t, cos ⁇ t , cos2 ⁇ t;
  • the angular motion error transfer coefficient processing module includes an angular motion error transfer coefficient initial value setting module and an angular motion error transfer coefficient adjustment module, and the angular motion error transfer coefficient initial value setting module is used to set Initial value of angular motion error transfer coefficient:
  • the angular motion error transfer coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient meter signal, and fine-tunes the angular motion error transfer coefficient.
  • the angular motion error transfer coefficient processing module has two working modes, an adjustment mode and a non-slot mode. When working in the adjustment mode, the angular motion error transmission coefficient is adjusted in real time; when working in the non-adjustment mode, the angular motion error transmission system remains unchanged.
  • the angular motion error compensation signal generation module includes an angular motion error transfer coefficient input module, an angular motion detection module, a reference signal input module, an angular motion compensation signal generation module, and a centrifugal gradient detection module;
  • the angular motion error transfer coefficient input module is used to input the angular motion error transfer coefficient;
  • the reference signal input module is used to input a quadrature amplitude modulation carrier;
  • the angular motion detection module includes an angular rate sensor and a low-pass filter,
  • the angular rate sensor is used to detect the angular motion of the gravity gradient instrument;
  • the angular rate sensor is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and measures the angular velocity ⁇ x , ⁇ y , ⁇ z of the coordinate system And angular accelerations ⁇ ax , ⁇ ay , ⁇ az ;
  • the low-pass filter filters high-frequency noise in angular velocity and angular acceleration signals;
  • the angular motion compensation signal generation module modulates the carrier and angular motion according to orthogonal amplitudes
  • the centrifugal gradient detection module has two working modes, calibration mode and non-calibration mode.
  • the calibration mode the centrifugal gradient detection unit outputs the detected centrifugal gradient. There is no output from the centrifugal gradient detection unit in non-calibration mode.
  • the angular motion error compensation signal generating module has three working modes, non-compensation mode, normal mode, and calibration mode; in non-compensation mode, the generated angular motion error compensation signal C A (t )for:
  • the generated angular motion error compensation signal C A (t) is:
  • sin2 ⁇ t , cos2 ⁇ t , sin ⁇ t , and cos ⁇ t are quadrature amplitude modulation carriers of the input angular motion error compensation signal generation module at time t;
  • ⁇ x (t), ⁇ y (t), ⁇ z (t), ⁇ ax (t), ⁇ ay (t), ⁇ az (t) represents the angular motion signal of the input angular motion error compensation signal generation module at time t.
  • the linear motion error transfer coefficient processing module includes a linear motion error transfer coefficient initial value setting module and a linear motion error transfer coefficient adjustment module, and the linear motion error transfer coefficient initial value setting module is used to set Initial value of linear motion error transfer coefficient:
  • the linear motion error transfer difference coefficient adjustment module generates an adjustment amount and fine-tunes the linear motion error transfer coefficient according to the feedback-compensated gravity gradient instrument signal;
  • the linear motion error transfer coefficient processing module has two working modes, adjustment mode and non-slot Mode, when working in the adjustment mode, adjust the linear motion error transfer coefficient in real time; when working in the non-adjustment mode, the linear motion error transmission system remains unchanged.
  • the linear motion error compensation signal generating module includes a linear motion detection module, a linear motion error transfer coefficient input module, a reference signal input module, and a linear motion compensation signal generating module.
  • the linear motion detection module includes An accelerometer and a low-pass filter are used to detect the acceleration of the gravity gradient instrument; the accelerometer is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument to measure the acceleration a x ay , az ; the low-pass filter filters high-frequency noise in the acceleration signal; the linear motion error transfer coefficient input module is used to input the linear motion error transfer coefficient; and the reference signal generation module is used to An orthogonal amplitude modulation carrier is input; the linear motion compensation signal generating module generates a linear motion error compensation signal according to the input orthogonal amplitude modulation carrier, acceleration signal, and linear motion error transfer coefficient.
  • the linear motion error compensation signal generating module has two working modes: non-compensation mode and compensation mode; in non-compensation mode, the linear motion compensation signal C L (t) is
  • the generated linear motion compensation signal C L (t) is:
  • sin2 ⁇ t , cos2 ⁇ t , sin ⁇ t , and cos ⁇ t are quadrature amplitude modulation carriers of the input line motion error compensation signal generation module at time t;
  • a x (t), a y (t), a z (t) represents the acceleration signal of the input linear motion error compensation signal generation module at time t.
  • the compensation operation module generates the linear motion error compensation signal and the angular motion error compensation signal generation module generated from the self-gradient compensation signal output by the self-gradient compensation signal generation module, the linear motion error compensation signal generated by the linear motion error compensation signal generation module, and the angular motion error compensation signal generation module.
  • the angular motion error compensation signal is used to compensate the output of the self-gradient error, linear motion error, and angular motion error generated by the gravity gradient accelerometer signal processing module.
  • the method for compensating the error of a gravity accelerometer of a rotating base rotary accelerometer of the present invention includes the following steps:
  • Represents the linear motion error transfer coefficient at time t Represents the coefficient of linear motion error transmission at time t-1;
  • g c (t-1) represents the signal of the gravity gradient instrument after compensation at time t-1;
  • F 1 (g c (t-1)) is the transmission of linear motion error at time t Coefficient of fine-tuning, which is a function of g c (t-1);
  • Represents the angular motion error transfer coefficient at time t Represents the angular motion error transfer coefficient at time t-1;
  • g c (t-1) represents the gravimetric gradient signal after compensation at time t-1;
  • F 2 (g c (t-1)) represents the angular motion error transfer at time t Coefficient fine-tuning amount, which is a function of g c (t-1);
  • linear motion error transfer coefficient at time t 0 Angular motion error transfer coefficient All obtained through calibration;
  • I the attitude angle of the gravity gradient instrument at time t
  • P is a parameter of the self-gradient model
  • g c (t) g (t) -C L (t) -C sg (t) -C A (t)
  • g c (t) is the gravity gradient instrument signal after compensation at time t
  • g (t) is the gravity gradient instrument signal including linear motion error, angular motion error, and self-gradient at time t
  • C L (t) is time t
  • C sg (t) is a self-gradient compensation signal
  • C A (t) is an angular motion error compensation signal.
  • the acceleration, angular velocity, and angular acceleration of the gravity gradient instrument are caused.
  • the output of the gravity gradient instrument causes measurement error.
  • the linear motion error transfer coefficient and angular motion error transfer coefficient of the gravity gradient instrument are easily affected by environmental factors such as temperature and electromagnetic field.
  • acceleration, angular velocity, and angular acceleration of the gravity gradient instrument can cause overvoltage saturation or damage of the overvoltage of the signal conditioning circuit at the front end of the gravity gradient instrument.
  • the present invention has the following advantages:
  • the invention is the first time to provide a real-time compensation device and method for linear motion error, angular motion error, and self-gradient compensation of a rotary accelerometer gravity gradient instrument.
  • the present invention provides a device and method capable of real-time compensation for linear motion error, angular motion error, and self-gradient of a gravity gradient instrument. It fine-tunes the angular motion error transfer coefficient and linear motion error in real time based on the feedback compensated gravity gradient instrument signal.
  • the transfer coefficient and accelerometer scaling coefficient can offset the effects of environmental factors such as temperature and magnetic field on the gravity gradient instrument's linear motion error transfer coefficient, angular motion error transfer coefficient, and scale factor, and can compensate the gravity gradient instrument's linear motion.
  • Angular motion, self-gradient measurement error improve the measurement accuracy of gravity gradient instrument.
  • the quadrature amplitude modulation of the linear motion error, angular motion error, and self-gradient signal of the gravity gradient instrument is directly compensated for the signal before the demodulation of the gravity gradient instrument, so it can also solve the problems caused by the acceleration and angular velocity of the gravity gradient instrument.
  • the front-end signal conditioning circuit is over-saturated and over-voltage damaged.
  • FIG. 1 is a schematic diagram of a rotary accelerometer gravity gradient meter error real-time compensation device.
  • FIG. 1 Schematic diagram of the reference signal generation module.
  • FIG. 3 is a schematic diagram of a linear motion error transfer coefficient processing module and an angular motion error transfer coefficient processing module.
  • FIG. 4 is a schematic diagram of an angular motion error compensation signal generating module and a linear motion error compensation signal generating module.
  • Figure 5 Schematic diagram of angular velocity rate sensor and accelerometer installation.
  • an error compensation device of a moving base rotary accelerometer gravity gradient instrument of the present invention includes: a reference signal generating module for generating a quadrature amplitude modulation carrier; and a self-gradient for generating a self-gradient compensation signal in real time.
  • an angular motion error compensation signal generation module for generating a gravity gradient instrument angular motion error compensation signal in real time, this module can also detect the sensitive centrifugal gradient of the gravity gradient instrument; used to fine-tune the angle of the angular motion error transfer coefficient in real time
  • Motion error transfer coefficient processing module linear motion error compensation signal generation module for generating a gravity gradient linear motion error compensation signal in real time
  • linear motion error transfer coefficient processing module for fine-tuning the linear motion error transfer coefficient in real time
  • a gravity gradient accelerometer signal processing module for summing and subtracting the output signals of accelerometers on a rotating disc; an accelerometer scaling coefficient adjusting module for adjusting the accelerometer scaling coefficients in real time;
  • Motion error, linear motion error, gravity gradient signal from gradient Compensation calculation module for line compensation; a gravity gradient signal recovery module for demodulating and outputting a gravity gradient signal from a compensated gravity gradient instrument signal;
  • the output of the reference signal generation module is connected to the inputs of a self-gradient compensation signal generation module, an angular motion error compensation signal generation module, and a linear motion error compensation signal generation module; the self-gradient compensation signal generation module and angular motion error compensation signal generation
  • the output of the module, the linear motion error compensation signal generation module, the gravity gradient accelerometer signal processing module is connected to the input of the compensation operation module; the output of the compensation operation module is connected to the accelerometer scale coefficient adjustment module, the angular motion error transfer coefficient
  • the output of the module is connected to the input of the angular motion error compensation signal generating module; the output of the accelerometer scale coefficient adjustment module is connected to the input of the gravity gradient accelerometer signal processing module.
  • the reference signal generating module includes a gravity gradient instrument rotating disc axis encoder and a signal generator; the gravity gradient instrument rotating disc axis encoder detects a phase angle ⁇ t of the rotation of the gravity gradient instrument disc. , the signal generator phase angle ⁇ t, quadrature amplitude modulation carrier wave generating sin ⁇ t, sin2 ⁇ t, cos ⁇ t , cos2 ⁇ t according to;
  • the angular motion error transfer coefficient processing module is composed of an angular motion error transfer coefficient initial value setting module and an angular motion error transfer coefficient adjustment module; the angular motion error transfer coefficient initial value setting module , Used to set the initial value of the angular motion error transfer coefficient:
  • the angular motion error transmission difference coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient instrument signal to fine-tune the angular motion error transmission coefficient;
  • the angular motion error transmission coefficient processing module has two working modes, adjustment mode and non-regular In joint mode, the angular motion error transfer coefficient is adjusted in real time when working in the adjustment mode; when working in non-adjustment mode, the angular motion error transmission system remains unchanged.
  • the angular motion error compensation signal generation module is composed of an angular motion error transfer coefficient input module, an angular motion detection module, a reference signal input module, an angular motion compensation signal generation module, and a centrifugal gradient detection module.
  • the angular motion error transfer coefficient input module is used to input the angular motion error transfer coefficient;
  • the reference signal input module is used to input the quadrature amplitude modulation carrier;
  • the angular motion detection module is composed of an angular rate sensor and a low-pass filter; It is used to detect the angular motion of the gravity gradient instrument; as shown in FIG.
  • the angular rate sensor is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and measures the angular velocity of the coordinate system of the gravity gradient instrument.
  • the low-pass filter filters high-frequency noise in angular velocity and angular acceleration signals;
  • the angular motion error generation module is based on orthogonality Amplitude modulation carrier, angular motion error transfer coefficient, angular acceleration, angular velocity, generating angular motion error compensation signals;
  • the centrifugal gradient detection module has two working modes , Calibration mode and a non-calibration mode, the calibration mode, the centrifugal gradient centrifugation gradient detection unit outputs the detection, in a non-calibration mode, no output centrifugation gradient detection means;.
  • the angular motion error compensation signal generating module has three working modes, non-compensation mode, normal mode, and calibration mode.
  • non-compensation mode the angular motion error compensation signal C A (t) is:
  • the generated angular motion error compensation signal C A (t) is:
  • sin2 ⁇ t , cos2 ⁇ t , sin ⁇ t , and cos ⁇ t are quadrature amplitude modulation carriers of the input angular motion error compensation signal generation module at time t;
  • ⁇ x (t), ⁇ y (t), ⁇ z (t), ⁇ ax (t), ⁇ ay (t), ⁇ az (t) represents the angular motion signal of the input angular motion error compensation signal generation module at time t;
  • the linear motion error transfer coefficient processing module is composed of a linear motion error transfer coefficient initial value setting module and a linear motion error transfer coefficient adjustment module; the linear motion error transfer coefficient initial value setting module , Set the initial value of the linear motion error transfer coefficient:
  • the linear motion error transmission difference coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient instrument signal to fine-tune the linear motion error transmission coefficient;
  • the linear motion error transmission coefficient processing module has two working modes, adjustment mode and non-regular In joint mode, the linear motion error transmission coefficient is adjusted in real time when working in the adjustment mode; when working in non-adjustment mode, the linear motion error transmission system remains unchanged;
  • the linear motion error compensation signal generating module is composed of a linear motion detection module, a linear motion error transfer coefficient input module, and a reference signal input module.
  • the linear motion detection module is composed of an accelerometer, low A pass filter is used to detect the acceleration of the gravity gradient instrument; as shown in FIG.
  • the accelerometer is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and Acceleration a x , a y , a z ;
  • the low-pass filter filters high-frequency noise in acceleration signals;
  • the linear motion error transfer coefficient input module is used to input linear motion error transfer coefficients;
  • the reference signal The generating module is configured to input a quadrature amplitude modulation carrier; the linear motion compensation signal generating module generates a linear motion error compensation signal according to the input quadrature amplitude modulation carrier, an acceleration signal, and a linear motion error transfer coefficient.
  • the linear motion error compensation signal generating module has two working modes: non-compensated mode and compensation mode; in non-compensated mode, the generated linear motion compensation signal C L (t) is:
  • the generated linear motion compensation signal C L (t) is:
  • sin2 ⁇ t , cos2 ⁇ t , sin ⁇ t , and cos ⁇ t are quadrature amplitude modulation carriers of the input line motion error compensation signal generation module at time t;
  • a x (t), a y (t), a z (t) represents the acceleration signal of the input linear motion error compensation signal generation module at time t.
  • the compensation operation module According to the self-gradient compensation signal output from the self-gradient compensation signal generating module, the linear motion error compensation signal generated by the linear motion error compensation signal generating module, and the angular motion error compensation signal generated by the angular motion error compensation signal generating module, Compensate the output containing the self-gradient error, linear motion error, and angular motion error produced by the gravity gradient accelerometer signal processing module;
  • a method for compensating the error of a gravity accelerometer of a rotating base rotary accelerometer includes the following steps:
  • Represents the linear motion error transfer coefficient at time t Represents the coefficient of linear motion error transmission at time t-1;
  • g c (t-1) represents the signal of the gravity gradient instrument after compensation at time t-1;
  • F 1 (g c (t-1)) is the transmission of linear motion error at time t Coefficient of fine-tuning, which is a function of g c (t-1);
  • Represents the angular motion error transfer coefficient at time t Represents the angular motion error transfer coefficient at time t-1;
  • g c (t-1) represents the gravimetric gradient signal after compensation at time t-1;
  • F 2 (g c (t-1)) represents the angular motion error transfer at time t Coefficient fine-tuning amount, which is a function of g c (t-1);
  • linear motion error transfer coefficient at time t 0 Angular motion error transfer coefficient Obtained through calibration;
  • I the attitude angle of the gravity gradient instrument at time t
  • P is a parameter of the self-gradient model
  • g c (t) g (t) -C L (t) -C sg (t) -C A (t)
  • g c (t) is the gravity gradient instrument signal after compensation at time t
  • g (t) is the gravity gradient instrument signal including linear motion error, angular motion error, and self-gradient at time t
  • C L (t) is time t Linear motion error compensation signal
  • C sg (t) is a self-gradient compensation signal
  • C A (t) is an angular motion error compensation signal

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Abstract

Disclosed are a device and method for compensating for an error of a moving-base rotating-accelerometer gravity gradiometer. A signal of the gravity gradiometer before demodulation is compensated by calculating an angular motion error, a linear motion error, and a self-gradient of the gravity gradiometer according to the detected angular motion, linear motion, attitude angle of the gravity gradiometer, and based on an analytic model and a self-gradient model of the gravity gradiometer, and performing quadrature amplitude modulation of the angular motion error, the linear motion error, and the self-gradient. The present invention not only compensates for the angular motion error, the linear motion error, and the self-gradient in an output signal of the gravity gradiometer, but also solves the problems of over-voltage damage and over-voltage saturation of a conditioning circuit at a front end of the gravity gradiometer caused by the angular motion, the linear motion, and the self-gradient of the gravity gradiometer. The compensated signal of the gravity gradiometer is used to feedback and regulate a linear motion error transfer coefficient, an angular motion error transfer coefficient, and an accelerometer scale coefficient, and the influence of environmental factors, such as the temperature and magnetic fields, on the error transfer coefficients of the gravity gradiometer can be offset.

Description

一种动基座旋转加速度计重力梯度仪误差补偿装置及方法Device and method for compensating error of rotating base accelerometer gravity gradient instrument 技术领域Technical field
本发明涉及一种动基座旋转加速度计重力梯度仪误差补偿装置及方法，属于精密测量技术领域。The invention relates to an error compensation device and method of a moving base rotary accelerometer gravity gradient meter, and belongs to the technical field of precision measurement.
背景技术Background technique
动基座重力梯度勘探是一种低成本、高效率的重力梯度勘探方法；是目前世界上最先进的重力场勘探方式。重力梯度数据广泛应用于地质分析、重力场建模、高精度导航、资源勘探等。重力梯度仪具有极其重要的国防、民用价值。目前国内外在研的重力梯度仪主要有冷原子重力梯度仪、超导重力梯度仪、MEMS重力梯度仪等。国外已经投入商业应用的重力梯度仪主要有旋转加速度计重力梯度仪及旋转超导加速度计重力梯度仪。我国的重力梯度仪样机正处于研制中。Moving base gravity gradient exploration is a low-cost, high-efficiency gravity gradient exploration method; it is currently the most advanced gravity field exploration method in the world. Gravity gradient data is widely used in geological analysis, gravity field modeling, high-precision navigation, and resource exploration. Gravity gradient instrument has extremely important national defense and civilian value. At present, the gravity gradient instruments under research at home and abroad mainly include cold atom gravity gradient instrument, superconducting gravity gradient instrument, MEMS gravity gradient instrument and so on. Gravity gradiometers that have been put into commercial use abroad mainly include rotary accelerometer gravity gradient meters and rotary superconducting accelerometer gravity gradient meters. The prototype of China's gravity gradient instrument is under development.
在动基座重力梯度勘探时，由于重力梯度仪内部的加速度计存在安装误差、加速度计一阶、高阶标度系数不匹配、电路增益不匹配等，导致重力梯度仪的加速度，角速度，角加速度传递到重力梯度仪的输出，造成测量误差。同时重力梯度仪线运动、自梯度、角运动会引起重力梯度仪前端信号调理电路过电压饱和或损坏。本发明提供一种能够实时补偿重力梯度仪线运动误差、角运动误差、自梯度的装置及方法，目前没有关于重力梯度仪线运动误差、角运动误差实时补偿装置及技术的公开的报道。During gravity gradient exploration of the moving base, due to installation errors, accelerometer first-order, high-order scale coefficient mismatch, and circuit gain mismatch in the accelerometer inside the gravity gradient instrument, the acceleration, angular velocity, and angular acceleration of the gravity gradient instrument are caused. To the output of the gravity gradient instrument, causing measurement errors. At the same time, the line motion, self-gradient, and angular motion of the gravity gradient instrument can cause overvoltage saturation or damage of the signal conditioning circuit at the front of the gravity gradient instrument. The invention provides a device and method capable of real-time compensating the linear motion error, angular motion error, and self-gradient of a gravity gradient instrument. Currently, there are no published reports about the linear motion error, angular motion error real-time compensation device and technology of the gravity gradient instrument.
发明内容Summary of the Invention
技术问题：本发明提供一种能够反馈补偿重力梯度仪的加运动、角运动、自梯度引起的输出测量误差的动基座旋转加速度计重力梯度仪误差补偿装置，既能抑制温度、电磁场等环境因素对误差传递系数的影响，同时还能避免重力梯度仪的加速度、角速度、角加速度引起的重力梯度仪前端信号调理电路过电压饱和及过电压损坏。本发明同时提供一种具有以上效果、解决了以上问题的动基座旋转加速度计重力梯度仪误差补偿方法。Technical problem: The present invention provides a moving base rotary accelerometer gravity gradient meter error compensation device capable of feedback compensation of the acceleration, angular motion, and self-gradient output measurement errors caused by the gravity gradient meter, which can suppress environments such as temperature and electromagnetic fields The influence of factors on the error transfer coefficient can also avoid overvoltage saturation and overvoltage damage of the front-end signal conditioning circuit of the gravity gradient instrument caused by the acceleration, angular velocity, and angular acceleration of the gravity gradient instrument. The invention also provides a method for compensating for the error of the gravimetric gradient accelerometer of the moving base rotary accelerometer which has the above effects and solves the above problems.
技术方案：本发明的动基座旋转加速度计重力梯度仪误差补偿装置，包括：Technical solution: The error compensation device of the gravity base of the moving base rotary accelerometer of the present invention includes:
用于产生正交幅度调制载波的参考信号产生模块；A reference signal generating module for generating a quadrature amplitude modulation carrier;
用于实时产生自梯度补偿信号的自梯度补偿信号产生模块；A self-gradient compensation signal generating module for generating a self-gradient compensation signal in real time;
用于实时产生重力梯度仪角运动误差补偿信号及检测重力梯度仪离心梯度的角运动误差补偿信号产生模块；An angular motion error compensation signal generating module for generating a gravity gradient instrument angular motion error compensation signal in real time and detecting a centrifugal gradient of the gravity gradient instrument;
用于实时微调角运动误差传递系数的角运动误差传递系数处理模块；An angular motion error transfer coefficient processing module for fine-tuning the angular motion error transfer coefficient in real time;
用于实时产生重力梯度仪线运动误差补偿信号的线运动误差补偿信号产生模块；A linear motion error compensation signal generating module for generating a linear motion error compensation signal of the gravity gradient instrument in real time;
用于实时微调线运动误差传递系数的线运动误差传递系数处理模块；Linear motion error transfer coefficient processing module for fine-tuning the linear motion error transfer coefficient in real time;
用于对安装在旋转圆盘上的加速度计的输出信号求和、求差运算的重力梯度仪加速度计信号处理模块；A gravity gradient accelerometer signal processing module for summing and subtracting output signals of accelerometers mounted on a rotating disc;
用于实时调节加速度计标度系数的加速度计标度系数调节模块；Accelerometer scaling coefficient adjustment module for adjusting the accelerometer scaling coefficient in real time;
用于对含有角运动误差，线运动误差，自梯度的重力梯度信号进行补偿的补偿运算模块；Compensation operation module for compensating the gravity gradient signal including angular motion error, linear motion error, and self-gradient;
用于从补偿后的重力梯度仪信号解调输出重力梯度信号的重力梯度信号恢复模块；A gravity gradient signal recovery module for demodulating and outputting a gravity gradient signal from a compensated gravity gradient instrument signal;
所述参考信号产生模块的输出连接到自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块的输入；所述自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块、重力梯度仪加速度计信号处理模块的输出连接到补偿运算模块的输入；所述补偿运算模块的输出连接到加速度计标度系数调节模块、角运动误差传递系数处理模块、线运动误差传递系数处理模块、重力梯度信号恢复模块的输入；所述线运动误差传递系数处理模块的输出连接到线运动误差补偿信号产生模块的输入；所述角运动误差传递系数处理模块的输出连接到角运动误差补偿信号产生模块的输入；所述加速度计标度系数调节模块的输出连接到重力梯度仪加速度计信号处理模块的输入。The output of the reference signal generation module is connected to the inputs of a self-gradient compensation signal generation module, an angular motion error compensation signal generation module, and a linear motion error compensation signal generation module; the self-gradient compensation signal generation module and angular motion error compensation signal generation The output of the module, the linear motion error compensation signal generation module, the gravity gradient accelerometer signal processing module is connected to the input of the compensation operation module; the output of the compensation operation module is connected to the accelerometer scale coefficient adjustment module, the angular motion error transfer coefficient The input of the processing module, the linear motion error transfer coefficient processing module, and the gravity gradient signal recovery module; the output of the linear motion error transfer coefficient processing module is connected to the input of the linear motion error compensation signal generation module; the angular motion error transfer coefficient processing The output of the module is connected to the input of the angular motion error compensation signal generating module; the output of the accelerometer scale coefficient adjustment module is connected to the input of the gravity gradient accelerometer signal processing module.
进一步的，本发明装置中，所述参考信号产生模块包括重力梯度仪旋转圆盘轴编码器和信号发生器；所述重力梯度仪旋转圆盘轴编码器检测重力梯度仪圆盘旋转的相位角φ t，所述信号发生器根据相位角φ t，产生正交幅度调制载波波sinφ t，sin2φ t，cosφ t，cos2φ t； Further, in the device of the present invention, the reference signal generating module includes a gravity gradient instrument rotating disc axis encoder and a signal generator; the gravity gradient instrument rotating disc axis encoder detects a phase angle of the rotation of the gravity gradient instrument disc. φ t, the signal generator according to the phase angle φ t, quadrature amplitude modulation carrier wave generating sinφ t, sin2φ t, cosφ t , cos2φ t;
进一步的，本发明装置中，所述角运动误差传递系数处理模块包括角运动误差传递系数初值设置模块和角运动误差传递系数调节模块，所述角运动误差传递系数初值设置模块用于设置角运动误差传递系数初值：
Figure PCTCN2019089302-appb-000001
所述角运动误差传递系数调节模块根据反馈的补偿后的重力梯度仪信号产生调节量，微调角运动误差传递系数；角运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节角运动误差传递系数；当工作在非调节模式时，角运动误差传递系保持不变。 Further, in the device of the present invention, the angular motion error transfer coefficient processing module includes an angular motion error transfer coefficient initial value setting module and an angular motion error transfer coefficient adjustment module, and the angular motion error transfer coefficient initial value setting module is used to set Initial value of angular motion error transfer coefficient:
Figure PCTCN2019089302-appb-000001
The angular motion error transfer coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient meter signal, and fine-tunes the angular motion error transfer coefficient. The angular motion error transfer coefficient processing module has two working modes, an adjustment mode and a non-slot mode. When working in the adjustment mode, the angular motion error transmission coefficient is adjusted in real time; when working in the non-adjustment mode, the angular motion error transmission system remains unchanged.
进一步的，本发明装置中，所述的角运动误差补偿信号产生模块包括角运动误差传递系数输入模块、角运动检测模块、参考信号输入模块、角运动补偿信号产生模块、离心梯度检测模块；Further, in the device of the present invention, the angular motion error compensation signal generation module includes an angular motion error transfer coefficient input module, an angular motion detection module, a reference signal input module, an angular motion compensation signal generation module, and a centrifugal gradient detection module;
所述角运动误差传递系数输入模块用于输入角运动误差传递系数；所述参考信号输入模块用于输入正交幅值调制载波；所述角运动检测模块包括角速率传感器和低通滤波器，用于检测重力梯度仪的角运动；所述角速率传感器安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的角速度ω x,ω y,ω z及角加速度ω ax,ω ay,ω az；所述低通滤波器则滤除角速度、角加速度信号中的高频噪声；所述角运动补偿信号产生模块根据正交幅值调制载波、角运动误差传递系数、角加速度、角速度产生角运动误差补偿信号；所述离心梯度检测模块有两种工作模式，标定模式和非标定模式，在标定模式下，离心梯度检测单元输出检测的离心梯度，在非标定模式下，离心梯度检测单元无输出。 The angular motion error transfer coefficient input module is used to input the angular motion error transfer coefficient; the reference signal input module is used to input a quadrature amplitude modulation carrier; the angular motion detection module includes an angular rate sensor and a low-pass filter, The angular rate sensor is used to detect the angular motion of the gravity gradient instrument; the angular rate sensor is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and measures the angular velocity ω x , ω y , ω z of the coordinate system And angular accelerations ω ax , ω ay , ω az ; the low-pass filter filters high-frequency noise in angular velocity and angular acceleration signals; the angular motion compensation signal generation module modulates the carrier and angular motion according to orthogonal amplitudes The error transfer coefficient, angular acceleration, and angular velocity generate angular motion error compensation signals. The centrifugal gradient detection module has two working modes, calibration mode and non-calibration mode. In the calibration mode, the centrifugal gradient detection unit outputs the detected centrifugal gradient. There is no output from the centrifugal gradient detection unit in non-calibration mode.
进一步的，本发明装置中，所述的角运动误差补偿信号产生模块具有三种工作模式，非补偿模式，正常模式，标定模式；非补偿模式下，产生的角运动误差补偿信号C A(t)为： Further, in the device of the present invention, the angular motion error compensation signal generating module has three working modes, non-compensation mode, normal mode, and calibration mode; in non-compensation mode, the generated angular motion error compensation signal C A (t )for:
C A(t)＝0； C A (t) = 0;
在正常模式下，产生的角运动误差补偿信号C A(t)为： In normal mode, the generated angular motion error compensation signal C A (t) is:
Figure PCTCN2019089302-appb-000002
Figure PCTCN2019089302-appb-000002
在标定模式下，产生的角运动误差补偿信号C A(t)为： In the calibration mode, the generated angular motion error compensation signal C A (t) is:
Figure PCTCN2019089302-appb-000003
Figure PCTCN2019089302-appb-000003
式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入角运动误差补偿信号产生模块的正交幅度调制载波；
Figure PCTCN2019089302-appb-000004
表示t时刻输入角运动误差补偿信号产生模块的角运动误差传递系数；ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)表示t时刻输入角运动误差补偿信号产生模块的角运动信号。 Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input angular motion error compensation signal generation module at time t;
Figure PCTCN2019089302-appb-000004
Represents the angular motion error transfer coefficient of the input angular motion error compensation signal generation module at time t; ω x (t), ω y (t), ω z (t), ω ax (t), ω ay (t), ω az (t) represents the angular motion signal of the input angular motion error compensation signal generation module at time t.
进一步的，本发明装置中，所述线运动误差传递系数处理模块包括线运动误差传递系数初值设置模块和线运动误差传递系数调节模块，所述线运动误差传递系数初值设置模块用以设置线运动误差传递系数初值：
Figure PCTCN2019089302-appb-000005
所述线运动 误差传递差系数调节模块根据反馈的补偿后的重力梯度仪信号产生调节量和微调线运动误差传递系数；线运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节线运动误差传递系数；当工作在非调节模式时，线运动误差传递系保持不变。 Further, in the device of the present invention, the linear motion error transfer coefficient processing module includes a linear motion error transfer coefficient initial value setting module and a linear motion error transfer coefficient adjustment module, and the linear motion error transfer coefficient initial value setting module is used to set Initial value of linear motion error transfer coefficient:
Figure PCTCN2019089302-appb-000005
The linear motion error transfer difference coefficient adjustment module generates an adjustment amount and fine-tunes the linear motion error transfer coefficient according to the feedback-compensated gravity gradient instrument signal; the linear motion error transfer coefficient processing module has two working modes, adjustment mode and non-slot Mode, when working in the adjustment mode, adjust the linear motion error transfer coefficient in real time; when working in the non-adjustment mode, the linear motion error transmission system remains unchanged.
进一步的，本发明装置中，所述线运动误差补偿信号产生模块包括线运动检测模块、线运动误差传递系数输入模块、参考信号输入模块、线运动补偿信号产生模块，所述线运动检测模块包括加速度计和低通滤波器，用于检测重力梯度仪的加速度；所述加速度计安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的加速度a x,a y,a z；所述低通滤波器则滤除加速度信号中的高频噪声；所述线运动误差传递系数输入模块用于输入线运动误差传递系数；所述参考信号产生模块用于输入正交幅值调制载波；所述线运动补偿信号产生模块根据输入的正交幅值调制载波、加速度信号、线运动误差传递系数产生线运动误差补偿信号。 Further, in the device of the present invention, the linear motion error compensation signal generating module includes a linear motion detection module, a linear motion error transfer coefficient input module, a reference signal input module, and a linear motion compensation signal generating module. The linear motion detection module includes An accelerometer and a low-pass filter are used to detect the acceleration of the gravity gradient instrument; the accelerometer is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument to measure the acceleration a x ay , az ; the low-pass filter filters high-frequency noise in the acceleration signal; the linear motion error transfer coefficient input module is used to input the linear motion error transfer coefficient; and the reference signal generation module is used to An orthogonal amplitude modulation carrier is input; the linear motion compensation signal generating module generates a linear motion error compensation signal according to the input orthogonal amplitude modulation carrier, acceleration signal, and linear motion error transfer coefficient.
进一步的，本发明装置中，所述线运动误差补偿信号产生模块具有两种工作模式：非补偿模式，补偿模式；非补偿模式下，产生的线运动补偿信号C L(t)为： Further, in the device of the present invention, the linear motion error compensation signal generating module has two working modes: non-compensation mode and compensation mode; in non-compensation mode, the linear motion compensation signal C L (t) is
C L(t)＝0； C L (t) = 0;
补偿模式下，产生的线运动补偿信号C L(t)为： In the compensation mode, the generated linear motion compensation signal C L (t) is:
Figure PCTCN2019089302-appb-000006
Figure PCTCN2019089302-appb-000006
式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入线运动误差补偿信号产生模块的正交幅度调制载波；
Figure PCTCN2019089302-appb-000007
表示t时刻输入线运动误差补偿信号产生模块的线运动误差传递系数；a x(t),a y(t),a z(t)表示t时刻输入线运动误差补偿信号产生模块的加速度信号。 Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input line motion error compensation signal generation module at time t;
Figure PCTCN2019089302-appb-000007
Represents the linear motion error transfer coefficient of the input linear motion error compensation signal generation module at time t; a x (t), a y (t), a z (t) represents the acceleration signal of the input linear motion error compensation signal generation module at time t.
进一步的，本发明装置中，所述补偿运算模块根据自梯度补偿信号产生模块输出的自梯度补偿信号、线运动误差补偿信号产生模块产生的线运动误差补偿信号、角运动误差补偿信号产生模块产生的角运动误差补偿信号，对重力梯度仪加速度计信号处理模块产生的含有自梯度误差、线运动误差、角运动误差的输出进行补偿。Further, in the device of the present invention, the compensation operation module generates the linear motion error compensation signal and the angular motion error compensation signal generation module generated from the self-gradient compensation signal output by the self-gradient compensation signal generation module, the linear motion error compensation signal generated by the linear motion error compensation signal generation module, and the angular motion error compensation signal generation module. The angular motion error compensation signal is used to compensate the output of the self-gradient error, linear motion error, and angular motion error generated by the gravity gradient accelerometer signal processing module.
本发明的动基座旋转加速度计重力梯度仪误差补偿方法，包括以下步骤：The method for compensating the error of a gravity accelerometer of a rotating base rotary accelerometer of the present invention includes the following steps:
1)根据反馈的补偿后的重力梯度仪信号及线运动误差传递系数处理模块的工作模式，计算t时刻的线运动误差传递系数：1) Calculate the linear motion error transfer coefficient at time t based on the feedback of the compensated gravity gradient instrument signal and the working mode of the linear motion error transfer coefficient processing module:
调节模式：
Figure PCTCN2019089302-appb-000008
非调节模式：
Figure PCTCN2019089302-appb-000009
Adjustment mode:
Figure PCTCN2019089302-appb-000008
Non-regulated mode:
Figure PCTCN2019089302-appb-000009
式中
Figure PCTCN2019089302-appb-000010
表示t时刻的线运动误差传递系数，
Figure PCTCN2019089302-appb-000011
表示t-1时刻的线运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 1(g c(t-1))是t时刻线运动误差传递系数的微调量，它是g c(t-1)的函数； Where
Figure PCTCN2019089302-appb-000010
Represents the linear motion error transfer coefficient at time t,
Figure PCTCN2019089302-appb-000011
Represents the coefficient of linear motion error transmission at time t-1; g c (t-1) represents the signal of the gravity gradient instrument after compensation at time t-1; F 1 (g c (t-1)) is the transmission of linear motion error at time t Coefficient of fine-tuning, which is a function of g c (t-1);
根据反馈的补偿后的重力梯度仪信号及角运动误差传递系数处理模块的工作模式，计算t时刻的角运动误差传递系数：Calculate the angular motion error transfer coefficient at time t according to the feedback of the compensated gravity gradient signal and the working mode of the angular motion error transfer coefficient processing module:
调节模式：
Figure PCTCN2019089302-appb-000012
非调节模式：
Figure PCTCN2019089302-appb-000013
Adjustment mode:
Figure PCTCN2019089302-appb-000012
Non-regulated mode:
Figure PCTCN2019089302-appb-000013
式中
Figure PCTCN2019089302-appb-000014
表示t时刻的角运动误差传递系数，
Figure PCTCN2019089302-appb-000015
表示t-1时刻的角运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 2(g c(t-1))表示t时刻角运动误差传递系数的微调量，它是g c(t-1)的函数；t＝0时刻的线运动误差传递系数
Figure PCTCN2019089302-appb-000016
角运动误差传递系数
Figure PCTCN2019089302-appb-000017
均通过标定得到； Where
Figure PCTCN2019089302-appb-000014
Represents the angular motion error transfer coefficient at time t,
Figure PCTCN2019089302-appb-000015
Represents the angular motion error transfer coefficient at time t-1; g c (t-1) represents the gravimetric gradient signal after compensation at time t-1; F 2 (g c (t-1)) represents the angular motion error transfer at time t Coefficient fine-tuning amount, which is a function of g c (t-1); linear motion error transfer coefficient at time t = 0
Figure PCTCN2019089302-appb-000016
Angular motion error transfer coefficient
Figure PCTCN2019089302-appb-000017
All obtained through calibration;
根据反馈的补偿后的重力梯度仪信号，计算t时刻的加速度计标度系数：Calculate the accelerometer scale factor at time t based on the compensated gravimetric gradient signal:
Figure PCTCN2019089302-appb-000018
Figure PCTCN2019089302-appb-000018
式中
Figure PCTCN2019089302-appb-000019
表示安装在旋转圆盘上的四只加速度计在t时刻的标度系数，
Figure PCTCN2019089302-appb-000020
表示安装在旋转圆盘上的四只加速度计在t-1时刻的标度系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 3(g c(t-1))表示t时刻加速度计标度系数的调节量，它是g c(t-1)的函数； Where
Figure PCTCN2019089302-appb-000019
Represents the scaling coefficients of four accelerometers mounted on a rotating disc at time t,
Figure PCTCN2019089302-appb-000020
Represents the scaling coefficients of the four accelerometers mounted on the rotating disc at time t-1; g c (t-1) represents the gravity gradient signal after compensation at time t-1; F 3 (g c (t- 1)) represents the adjustment amount of the accelerometer scale coefficient at time t, which is a function of g c (t-1);
2)检测旋转加速度计重力梯度仪旋转圆盘在t时刻的相位角φ t，计算t时刻的正交幅度调制载波sinφ t，sin2φ t，cosφ t，cos2φ t；检测旋转旋转加速度计重力梯度仪在t时刻的加速度
Figure PCTCN2019089302-appb-000021
检测旋转加速度计重力梯度仪在t时刻的角速度及角加速度ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)； 2) Detect the phase angle φ t of the rotating disc of the rotating accelerometer gravity gradient instrument at time t , calculate the quadrature amplitude modulation carrier sinφ t , sin2φ t , cosφ t , cos2φ t at time t ; detect the rotational rotational accelerometer gravity gradient instrument Acceleration at time t
Figure PCTCN2019089302-appb-000021
Detect the angular velocity and angular acceleration of the rotational accelerometer gravity gradient instrument at time tω x (t), ω y (t), ω z (t), ω ax (t), ω ay (t), ω az (t) ;
根据下式计算t时刻的3类线运动误差补偿信号C L1(t),C L2(t),C L3(t): Calculate the three types of linear motion error compensation signals C L1 (t), C L2 (t), and C L3 (t) at time t according to the following formula:
Figure PCTCN2019089302-appb-000022
Figure PCTCN2019089302-appb-000022
根据下式计算t时刻的3类角运动误差补偿信号C A1(t),C A2(t),C A3(t): Calculate the three types of angular motion error compensation signals C A1 (t), C A2 (t), and C A3 (t) at time t according to the following formula:
Figure PCTCN2019089302-appb-000023
Figure PCTCN2019089302-appb-000023
3)根据线运动误差补偿信号产生模块的工作模式，计算t时刻的总的线运动误差补偿信号C L(t)： 3) According to the working mode of the linear motion error compensation signal generating module, calculate the total linear motion error compensation signal C L (t) at time t:
非补偿模式时，C L(t)＝0； In non-compensation mode, C L (t) = 0;
补偿模式时，C L(t)＝C L1(t)+C L2(t)+C L3(t)； In the compensation mode, C L (t) = C L1 (t) + C L2 (t) + C L3 (t);
根据角运动误差补偿信号产生模块的工作模式，计算t时刻总的角运动误差补偿信号C A(t)： According to the working mode of the angular motion error compensation signal generating module, calculate the total angular motion error compensation signal C A (t) at time t:
非补偿模式时，C A(t)＝0； In non-compensation mode, C A (t) = 0;
正常模式时，C A(t)＝C A1(t)+C A2(t)+C A3(t)； In normal mode, C A (t) = C A1 (t) + C A2 (t) + C A3 (t);
标定模式时，C A(t)＝C A2(t)+C A3(t)； In calibration mode, C A (t) = C A2 (t) + C A3 (t);
根据自梯度补偿信号产生模块的工作模式，计算t时刻的自梯度补偿信号C sg(t)： According to the working mode of the self-gradient compensation signal generating module, calculate the self-gradient compensation signal C sg (t) at time t:
补偿模式时，
Figure PCTCN2019089302-appb-000024
In compensation mode,
Figure PCTCN2019089302-appb-000024
在非补偿模式时，C sg(t)＝0； In non-compensation mode, C sg (t) = 0;
式中
Figure PCTCN2019089302-appb-000025
是t时刻重力梯度仪的姿态角，P是自梯度模型的参数，
Figure PCTCN2019089302-appb-000026
是自梯度模型的inline通道的输出，它是姿态角的函数，
Figure PCTCN2019089302-appb-000027
是自梯度模型的cross通道的输出,它是姿态角的函数； Where
Figure PCTCN2019089302-appb-000025
Is the attitude angle of the gravity gradient instrument at time t, and P is a parameter of the self-gradient model,
Figure PCTCN2019089302-appb-000026
Is the output of the inline channel of the gradient model, which is a function of the attitude angle,
Figure PCTCN2019089302-appb-000027
Is the output of the cross channel from the gradient model, which is a function of the attitude angle;
4)对t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号g(t)，根据下式进行线运动误差补偿、角运动误差补偿、自梯度补偿；4) For the gravity gradiometer signal g (t) containing linear motion error, angular motion error, and self-gradient at time t, perform linear motion error compensation, angular motion error compensation, and self-gradient compensation according to the following formula;
g c(t)＝g(t)-C L(t)-C sg(t)-C A(t) g c (t) = g (t) -C L (t) -C sg (t) -C A (t)
式中g c(t)是t时刻补偿后的重力梯度仪信号，g(t)是t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号，C L(t)是t时刻的线运动误差补偿信号，C sg(t)是自梯度补偿信号，C A(t)是角运动误差补偿信号。 Where g c (t) is the gravity gradient instrument signal after compensation at time t, g (t) is the gravity gradient instrument signal including linear motion error, angular motion error, and self-gradient at time t, and C L (t) is time t For the linear motion error compensation signal, C sg (t) is a self-gradient compensation signal, and C A (t) is an angular motion error compensation signal.
在动基座重力梯度勘探时，由于重力梯度仪内部的加速度计存在安装误差、加速度计一阶、高阶标度系数不匹配、电路增益不匹配等，导致重力梯度仪的加速度，角速度，角加速度传递到重力梯度仪的输出，造成测量误差，此外重力梯度仪的线运动误差传递系数、角运动误差传递系数容易受温度、电磁场等环境因素的影响。同时重力梯度仪的加速度，角速度，角加速度会引起重力梯度仪前端信号调理电路过电压饱和，或过电压损坏，本发明能够解决以上问题。During gravity gradient exploration of the moving base, due to installation errors, accelerometer first-order, high-order scale coefficient mismatch, and circuit gain mismatch in the accelerometer inside the gravity gradient instrument, the acceleration, angular velocity, and angular acceleration of the gravity gradient instrument are caused. The output of the gravity gradient instrument causes measurement error. In addition, the linear motion error transfer coefficient and angular motion error transfer coefficient of the gravity gradient instrument are easily affected by environmental factors such as temperature and electromagnetic field. At the same time, acceleration, angular velocity, and angular acceleration of the gravity gradient instrument can cause overvoltage saturation or damage of the overvoltage of the signal conditioning circuit at the front end of the gravity gradient instrument. The present invention can solve the above problems.
有益效果：本发明与现有技术相比，具有以下优点：Beneficial effect: Compared with the prior art, the present invention has the following advantages:
本发明是首次给出旋转加速度计重力梯度仪线运动误差、角运动误差、自梯度实时补偿装置及方法。本发明提供一种能够对重力梯度仪线运动误差、角运动误差、自梯度进行实时补偿的装置和方法，它根据反馈的补偿后的重力梯度仪信号实时微调角运动误差传递系数、线运动误差传递系数、加速度计标度系数，能够抵消重力梯度仪环境因素比如温度、磁场等对重力梯度仪线运动误差传递系数、角运动误差传递系数、标度系数的影响，能够补偿重力梯度仪线运动、角运动、自梯度引起的测量误差，提高重力梯度仪的测量精度。同时，对重力梯度仪线运动误差、角运动误差、自梯度信号进行了正交幅值调制，直接补偿重力梯度仪解调前的信号，因此还能够解决由于重力梯度仪加速度、角速度等引起的前端信号调理电路过电压饱和，过电压损坏问题。The invention is the first time to provide a real-time compensation device and method for linear motion error, angular motion error, and self-gradient compensation of a rotary accelerometer gravity gradient instrument. The present invention provides a device and method capable of real-time compensation for linear motion error, angular motion error, and self-gradient of a gravity gradient instrument. It fine-tunes the angular motion error transfer coefficient and linear motion error in real time based on the feedback compensated gravity gradient instrument signal. The transfer coefficient and accelerometer scaling coefficient can offset the effects of environmental factors such as temperature and magnetic field on the gravity gradient instrument's linear motion error transfer coefficient, angular motion error transfer coefficient, and scale factor, and can compensate the gravity gradient instrument's linear motion. , Angular motion, self-gradient measurement error, improve the measurement accuracy of gravity gradient instrument. At the same time, the quadrature amplitude modulation of the linear motion error, angular motion error, and self-gradient signal of the gravity gradient instrument is directly compensated for the signal before the demodulation of the gravity gradient instrument, so it can also solve the problems caused by the acceleration and angular velocity of the gravity gradient instrument. The front-end signal conditioning circuit is over-saturated and over-voltage damaged.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1一种旋转加速度计重力梯度仪误差实时补偿装置原理图。FIG. 1 is a schematic diagram of a rotary accelerometer gravity gradient meter error real-time compensation device.
图2参考信号产生模块原理图。Figure 2 Schematic diagram of the reference signal generation module.
图3线运动误差传递系数处理模块及角运动误差传递系数处理模块原理图。FIG. 3 is a schematic diagram of a linear motion error transfer coefficient processing module and an angular motion error transfer coefficient processing module.
图4角运动误差补偿信号产生模块及线运动误差补偿信号产生模块原理图。FIG. 4 is a schematic diagram of an angular motion error compensation signal generating module and a linear motion error compensation signal generating module.
图5角速度率传感器、加速度计安装示意图。Figure 5 Schematic diagram of angular velocity rate sensor and accelerometer installation.
具体实施方式detailed description
下面结合实施例和说明书附图对本发明作进一步地说明。The present invention is further described below with reference to the embodiments and the accompanying drawings.
如图1所示，本发明一种动基座旋转加速度计重力梯度仪误差补偿装置，包括：用于产生正交幅度调制载波的参考信号产生模块；用于实时产生自梯度补偿信号的自梯度补偿信号产生模块；用于实时产生重力梯度仪角运动误差补偿信号的角运动误差补偿信号产生模块，该模块还能检测重力梯度仪敏感的离心梯度；用于实时微调角运动误差传递系数的角运动误差传递系数处理模块；用于实时产生重力梯度仪线运动误差补偿信号的线运动误差补偿信号产生模块；用于实时微调线运动误差传递系数的线运动误差传递系数处理模块；用于对安装在旋转圆盘上的加速度计的输出信号求和、求差运算的重力梯度仪加速度计信号处理模块；用于实时调节加速度计标度系数的加速度计标度系数调节模块；用于对含有角运动误差，线运动误差，自梯度的重力梯度信号进行补偿的补偿运算模块；用于从补偿后的重力梯度仪信号解调输出重力梯度信号的重力梯度信号恢复模块；As shown in FIG. 1, an error compensation device of a moving base rotary accelerometer gravity gradient instrument of the present invention includes: a reference signal generating module for generating a quadrature amplitude modulation carrier; and a self-gradient for generating a self-gradient compensation signal in real time. Compensation signal generation module; an angular motion error compensation signal generation module for generating a gravity gradient instrument angular motion error compensation signal in real time, this module can also detect the sensitive centrifugal gradient of the gravity gradient instrument; used to fine-tune the angle of the angular motion error transfer coefficient in real time Motion error transfer coefficient processing module; linear motion error compensation signal generation module for generating a gravity gradient linear motion error compensation signal in real time; linear motion error transfer coefficient processing module for fine-tuning the linear motion error transfer coefficient in real time; A gravity gradient accelerometer signal processing module for summing and subtracting the output signals of accelerometers on a rotating disc; an accelerometer scaling coefficient adjusting module for adjusting the accelerometer scaling coefficients in real time; Motion error, linear motion error, gravity gradient signal from gradient Compensation calculation module for line compensation; a gravity gradient signal recovery module for demodulating and outputting a gravity gradient signal from a compensated gravity gradient instrument signal;
所述参考信号产生模块的输出连接到自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块的输入；所述自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块、重力梯度仪加速度计信号处理模 块的输出连接到补偿运算模块的输入；所述补偿运算模块的输出连接到加速度计标度系数调节模块、角运动误差传递系数处理模块、线运动误差传递系数处理模块、重力梯度信号恢复模块的输入；所述线运动误差传递系数处理模块的输出连接到线运动误差补偿信号产生模块的输入；所述角运动误差传递系数处理模块的输出连接到角运动误差补偿信号产生模块的输入；所述加速度计标度系数调节模块的输出连接到重力梯度仪加速度计信号处理模块的输入。The output of the reference signal generation module is connected to the inputs of a self-gradient compensation signal generation module, an angular motion error compensation signal generation module, and a linear motion error compensation signal generation module; the self-gradient compensation signal generation module and angular motion error compensation signal generation The output of the module, the linear motion error compensation signal generation module, the gravity gradient accelerometer signal processing module is connected to the input of the compensation operation module; the output of the compensation operation module is connected to the accelerometer scale coefficient adjustment module, the angular motion error transfer coefficient The input of the processing module, the linear motion error transfer coefficient processing module, and the gravity gradient signal recovery module; the output of the linear motion error transfer coefficient processing module is connected to the input of the linear motion error compensation signal generation module; the angular motion error transfer coefficient processing The output of the module is connected to the input of the angular motion error compensation signal generating module; the output of the accelerometer scale coefficient adjustment module is connected to the input of the gravity gradient accelerometer signal processing module.
如图2所示，所述参考信号产生模块包括重力梯度仪旋转圆盘轴编码器和信号发生器；所述重力梯度仪旋转圆盘轴编码器检测重力梯度仪圆盘旋转的相位角φ t，所述信号发生器根据相位角φ t，产生正交幅度调制载波波sinφ t，sin2φ t，cosφ t，cos2φ t； As shown in FIG. 2, the reference signal generating module includes a gravity gradient instrument rotating disc axis encoder and a signal generator; the gravity gradient instrument rotating disc axis encoder detects a phase angle φ t of the rotation of the gravity gradient instrument disc. , the signal generator phase angle φ t, quadrature amplitude modulation carrier wave generating sinφ t, sin2φ t, cosφ t , cos2φ t according to;
如图3(a)所示，所述角运动误差传递系数处理模块，由角运动误差传递系数初值设置模块，角运动误差传递系数调节模块组成；所述角运动误差传递系数初值设置模块，用于设置角运动误差传递系数初值：
Figure PCTCN2019089302-appb-000028
所述角运动误差传递差系数调节模块，根据反馈的补偿后的重力梯度仪信号产生调节量，微调角运动误差传递系数；角运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节角运动误差传递系数；当工作在非调节模式时，角运动误差传递系保持不变。 As shown in FIG. 3 (a), the angular motion error transfer coefficient processing module is composed of an angular motion error transfer coefficient initial value setting module and an angular motion error transfer coefficient adjustment module; the angular motion error transfer coefficient initial value setting module , Used to set the initial value of the angular motion error transfer coefficient:
Figure PCTCN2019089302-appb-000028
The angular motion error transmission difference coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient instrument signal to fine-tune the angular motion error transmission coefficient; the angular motion error transmission coefficient processing module has two working modes, adjustment mode and non-regular In joint mode, the angular motion error transfer coefficient is adjusted in real time when working in the adjustment mode; when working in non-adjustment mode, the angular motion error transmission system remains unchanged.
如图4(b)所示，所述的角运动误差补偿信号产生模块由角运动误差传递系数输入模块，角运动检测模块，参考信号输入模块，角运动补偿信号产生模块，离心梯度检测模块组成；所述角运动误差传递系数输入模块用于输入角运动误差传递系数；所述参考信号输入模块用于输入正交幅值调制载波；所述角运动检测模块由角速率传感器及低通滤波器组成，用于检测重力梯度仪的角运动；如图5所示，所述角速率传感器安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的角速度ω x,ω y,ω z及角加速度ω ax,ω ay,ω az；所述低通滤波器则滤除角速度、角加速度信号中的高频噪声；所述角运动误差产生模块根据正交幅值调制载波，角运动误差传递系数，角加速度，角速度，产生角运动误差补偿信号；所述离心梯度检测模块，有两种工作模式，标定模式和非标定模式，在标定模式下，离心梯度检测单元输出检测的离心梯度，在非标定模式下，离心梯度检测单元无输出；。 As shown in FIG. 4 (b), the angular motion error compensation signal generation module is composed of an angular motion error transfer coefficient input module, an angular motion detection module, a reference signal input module, an angular motion compensation signal generation module, and a centrifugal gradient detection module. The angular motion error transfer coefficient input module is used to input the angular motion error transfer coefficient; the reference signal input module is used to input the quadrature amplitude modulation carrier; the angular motion detection module is composed of an angular rate sensor and a low-pass filter; It is used to detect the angular motion of the gravity gradient instrument; as shown in FIG. 5, the angular rate sensor is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and measures the angular velocity of the coordinate system of the gravity gradient instrument. ω x , ω y , ω z and angular accelerations ω ax , ω ay , ω az ; the low-pass filter filters high-frequency noise in angular velocity and angular acceleration signals; the angular motion error generation module is based on orthogonality Amplitude modulation carrier, angular motion error transfer coefficient, angular acceleration, angular velocity, generating angular motion error compensation signals; the centrifugal gradient detection module has two working modes , Calibration mode and a non-calibration mode, the calibration mode, the centrifugal gradient centrifugation gradient detection unit outputs the detection, in a non-calibration mode, no output centrifugation gradient detection means;.
所述的角运动误差补偿信号产生模块具有三种工作模式，非补偿模式，正常模式，标 定模式；非补偿模式下，产生的角运动误差补偿信号C A(t)为： The angular motion error compensation signal generating module has three working modes, non-compensation mode, normal mode, and calibration mode. In non-compensation mode, the angular motion error compensation signal C A (t) is:
C A(t)＝0； C A (t) = 0;
在正常模式下，产生的角运动误差补偿信号C A(t)为： In normal mode, the generated angular motion error compensation signal C A (t) is:
Figure PCTCN2019089302-appb-000029
在标定模式下，产生的角运动误差补偿信号C A(t)为：
Figure PCTCN2019089302-appb-000029
In the calibration mode, the generated angular motion error compensation signal C A (t) is:
Figure PCTCN2019089302-appb-000030
Figure PCTCN2019089302-appb-000030
式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入角运动误差补偿信号产生模块的正交幅度调制载波；
Figure PCTCN2019089302-appb-000031
表示t时刻输入角运动误差补偿信号产生模块的角运动误差传递系数；ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)表示t时刻输入角运动误差补偿信号产生模块的角运动信号； Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input angular motion error compensation signal generation module at time t;
Figure PCTCN2019089302-appb-000031
Represents the angular motion error transfer coefficient of the input angular motion error compensation signal generation module at time t; ω x (t), ω y (t), ω z (t), ω ax (t), ω ay (t), ω az (t) represents the angular motion signal of the input angular motion error compensation signal generation module at time t;
如图3(b)所示，所述线运动误差传递系数处理模块，由线运动误差传递系数初值设置模块，线运动误差传递系数调节模块组成；所述线运动误差传递系数初值设置模块，设置线运动误差传递系数初值：
Figure PCTCN2019089302-appb-000032
所述线运动误差传递差系数调节模块，根据反馈的补偿后的重力梯度仪信号产生调节量，微调线运动误差传递系数；线运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节线运动误差传递系数；当工作在非调节模式时，线运动误差传递系保持不变； As shown in FIG. 3 (b), the linear motion error transfer coefficient processing module is composed of a linear motion error transfer coefficient initial value setting module and a linear motion error transfer coefficient adjustment module; the linear motion error transfer coefficient initial value setting module , Set the initial value of the linear motion error transfer coefficient:
Figure PCTCN2019089302-appb-000032
The linear motion error transmission difference coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient instrument signal to fine-tune the linear motion error transmission coefficient; the linear motion error transmission coefficient processing module has two working modes, adjustment mode and non-regular In joint mode, the linear motion error transmission coefficient is adjusted in real time when working in the adjustment mode; when working in non-adjustment mode, the linear motion error transmission system remains unchanged;
如图4(a)所示，所述线运动误差补偿信号产生模块由线运动检测模块，线运动误差传递系数输入模块，参考信号输入模块，组成；所述线运动检测模块由加速度计，低通滤波器组成，用于检测重力梯度仪的加速度；如图5所示，所述加速度计安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的加速度a x,a y,a z；所述低通滤波器则滤除加速度信号中的高频噪声；所述线运动误差传递系数输入模块，用于输入线运 动误差传递系数；所述参考信号产生模块用于输入正交幅值调制载波；所述线运动补偿信号产生模块根据输入的正交幅值调制载波，加速度信号，线运动误差传递系数产生线运动误差补偿信号。 As shown in FIG. 4 (a), the linear motion error compensation signal generating module is composed of a linear motion detection module, a linear motion error transfer coefficient input module, and a reference signal input module. The linear motion detection module is composed of an accelerometer, low A pass filter is used to detect the acceleration of the gravity gradient instrument; as shown in FIG. 5, the accelerometer is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and Acceleration a x , a y , a z ; the low-pass filter filters high-frequency noise in acceleration signals; the linear motion error transfer coefficient input module is used to input linear motion error transfer coefficients; the reference signal The generating module is configured to input a quadrature amplitude modulation carrier; the linear motion compensation signal generating module generates a linear motion error compensation signal according to the input quadrature amplitude modulation carrier, an acceleration signal, and a linear motion error transfer coefficient.
所述线运动误差补偿信号产生模块具有两种工作模式：非补偿模式，补偿模式；非补偿模式下，产生的线运动补偿信号C L(t)为： The linear motion error compensation signal generating module has two working modes: non-compensated mode and compensation mode; in non-compensated mode, the generated linear motion compensation signal C L (t) is:
C L(t)＝0； C L (t) = 0;
补偿模式下，产生的线运动补偿信号C L(t)为： In the compensation mode, the generated linear motion compensation signal C L (t) is:
Figure PCTCN2019089302-appb-000033
Figure PCTCN2019089302-appb-000033
式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入线运动误差补偿信号产生模块的正交幅度调制载波；
Figure PCTCN2019089302-appb-000034
表示t时刻输入线运动误差补偿信号产生模块的线运动误差传递系数；a x(t),a y(t),a z(t)表示t时刻输入线运动误差补偿信号产生模块的加速度信号。 Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input line motion error compensation signal generation module at time t;
Figure PCTCN2019089302-appb-000034
Represents the linear motion error transfer coefficient of the input linear motion error compensation signal generation module at time t; a x (t), a y (t), a z (t) represents the acceleration signal of the input linear motion error compensation signal generation module at time t.
所述补偿运算模块，根据自梯度补偿信号产生模块输出的自梯度补偿信号，线运动误差补偿信号产生模块产生的线运动误差补偿信号，角运动误差补偿信号产生模块产生的角运动误差补偿信号，对重力梯度仪加速度计信号处理模块产生的含有自梯度误差、线运动误差、角运动误差的输出进行补偿；According to the compensation operation module, according to the self-gradient compensation signal output from the self-gradient compensation signal generating module, the linear motion error compensation signal generated by the linear motion error compensation signal generating module, and the angular motion error compensation signal generated by the angular motion error compensation signal generating module, Compensate the output containing the self-gradient error, linear motion error, and angular motion error produced by the gravity gradient accelerometer signal processing module;
本发明的一种动基座旋转加速度计重力梯度仪误差补偿方法，包括以下步骤：A method for compensating the error of a gravity accelerometer of a rotating base rotary accelerometer according to the present invention includes the following steps:
1)根据反馈的补偿后的重力梯度仪信号及线运动误差传递系数处理模块的工作模式，计算t时刻的线运动误差传递系数：1) Calculate the linear motion error transfer coefficient at time t based on the feedback of the compensated gravity gradient instrument signal and the working mode of the linear motion error transfer coefficient processing module:
调节模式：
Figure PCTCN2019089302-appb-000035
非调节模式：
Figure PCTCN2019089302-appb-000036
Adjustment mode:
Figure PCTCN2019089302-appb-000035
Non-regulated mode:
Figure PCTCN2019089302-appb-000036
式中
Figure PCTCN2019089302-appb-000037
表示t时刻的线运动误差传递系数，
Figure PCTCN2019089302-appb-000038
表示t-1时刻的线运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 1(g c(t-1))是t时刻线运动误差传递系数的微调量，它是g c(t-1)的函数； Where
Figure PCTCN2019089302-appb-000037
Represents the linear motion error transfer coefficient at time t,
Figure PCTCN2019089302-appb-000038
Represents the coefficient of linear motion error transmission at time t-1; g c (t-1) represents the signal of the gravity gradient instrument after compensation at time t-1; F 1 (g c (t-1)) is the transmission of linear motion error at time t Coefficient of fine-tuning, which is a function of g c (t-1);
根据反馈的补偿后的重力梯度仪信号及角运动误差传递系数处理模块的工作模式，计算t时刻的角运动误差传递系数：Calculate the angular motion error transfer coefficient at time t according to the feedback of the compensated gravity gradient signal and the working mode of the angular motion error transfer coefficient processing module:
调节模式：
Figure PCTCN2019089302-appb-000039
非调节模式：
Figure PCTCN2019089302-appb-000040
Adjustment mode:
Figure PCTCN2019089302-appb-000039
Non-regulated mode:
Figure PCTCN2019089302-appb-000040
式中
Figure PCTCN2019089302-appb-000041
表示t时刻的角运动误差传递系数，
Figure PCTCN2019089302-appb-000042
表示t-1时刻的角运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 2(g c(t-1))表示t时刻角运动误差传递系数的微调量，它是g c(t-1)的函数；t＝0时刻的线运动误差传递系数
Figure PCTCN2019089302-appb-000043
角运动误差传递系数
Figure PCTCN2019089302-appb-000044
通过标定得到； Where
Figure PCTCN2019089302-appb-000041
Represents the angular motion error transfer coefficient at time t,
Figure PCTCN2019089302-appb-000042
Represents the angular motion error transfer coefficient at time t-1; g c (t-1) represents the gravimetric gradient signal after compensation at time t-1; F 2 (g c (t-1)) represents the angular motion error transfer at time t Coefficient fine-tuning amount, which is a function of g c (t-1); linear motion error transfer coefficient at time t = 0
Figure PCTCN2019089302-appb-000043
Angular motion error transfer coefficient
Figure PCTCN2019089302-appb-000044
Obtained through calibration;
根据反馈的补偿后的重力梯度仪信号，计算t时刻的加速度计标度系数：Calculate the accelerometer scale factor at time t based on the compensated gravimetric gradient signal:
Figure PCTCN2019089302-appb-000045
Figure PCTCN2019089302-appb-000045
式中
Figure PCTCN2019089302-appb-000046
表示安装在旋转圆盘上的四只加速度计在t时刻的标度系数，
Figure PCTCN2019089302-appb-000047
表示安装在旋转圆盘上的四只加速度计在t-1时刻的标度系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 3(g c(t-1))表示t时刻加速度计标度系数的调节量，它是g c(t-1)的函数； Where
Figure PCTCN2019089302-appb-000046
Represents the scaling coefficients of four accelerometers mounted on a rotating disc at time t,
Figure PCTCN2019089302-appb-000047
Represents the scaling coefficients of the four accelerometers mounted on the rotating disc at time t-1; g c (t-1) represents the gravity gradient signal after compensation at time t-1; F 3 (g c (t- 1)) represents the adjustment amount of the accelerometer scale coefficient at time t, which is a function of g c (t-1);
2)检测旋转加速度计重力梯度仪旋转圆盘在t时刻的相位角φ t，计算t时刻的正交幅度调制载波sinφ t，sin2φ t，cosφ t，cos2φ t；检测旋转旋转加速度计重力梯度仪在t时刻的加速度a x(t),a y(t),a z(t；)检测旋转加速度计重力梯度仪在t时刻的角速度及角加速度ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)； 2) Detect the phase angle φ t of the rotating disc of the rotating accelerometer gravity gradient instrument at time t , calculate the quadrature amplitude modulation carrier sinφ t , sin2φ t , cosφ t , cos2φ t at time t ; detect the rotational rotational accelerometer gravity gradient instrument The accelerations a x (t), a y (t), and a z (t;) at time t detect the angular velocity and angular acceleration ω x (t), ω y (t) of the rotary accelerometer gravity gradient meter at time t, ω z (t), ω ax (t), ω ay (t), ω az (t);
根据下式计算t时刻的3类线运动误差补偿信号C L1(t),C L2(t),C L3(t): Calculate the three types of linear motion error compensation signals C L1 (t), C L2 (t), and C L3 (t) at time t according to the following formula:
Figure PCTCN2019089302-appb-000048
Figure PCTCN2019089302-appb-000048
根据下式计算t时刻的3类角运动误差补偿信号C A1(t),C A2(t),C A3(t): Calculate the three types of angular motion error compensation signals C A1 (t), C A2 (t), and C A3 (t) at time t according to the following formula:
Figure PCTCN2019089302-appb-000049
Figure PCTCN2019089302-appb-000049
3)根据线运动误差补偿信号产生模块的工作模式，计算t时刻的总的线运动误差补偿信号C L(t)： 3) According to the working mode of the linear motion error compensation signal generating module, calculate the total linear motion error compensation signal C L (t) at time t:
非补偿模式时，C L(t)＝0； In non-compensation mode, C L (t) = 0;
补偿模式时，C L(t)＝C L1(t)+C L2(t)+C L3(t)； In the compensation mode, C L (t) = C L1 (t) + C L2 (t) + C L3 (t);
根据角运动误差补偿信号产生模块的工作模式，计算t时刻总的角运动误差补偿信号C A(t)： According to the working mode of the angular motion error compensation signal generating module, calculate the total angular motion error compensation signal C A (t) at time t:
非补偿模式时，C A(t)＝0； In non-compensation mode, C A (t) = 0;
正常模式时，C A(t)＝C A1(t)+C A2(t)+C A3(t)； In normal mode, C A (t) = C A1 (t) + C A2 (t) + C A3 (t);
标定模式时，C A(t)＝C A2(t)+C A3(t)； In calibration mode, C A (t) = C A2 (t) + C A3 (t);
根据自梯度补偿信号产生模块的工作模式，计算t时刻的自梯度补偿信号C sg(t)： According to the working mode of the self-gradient compensation signal generating module, calculate the self-gradient compensation signal C sg (t) at time t:
补偿模式时，
Figure PCTCN2019089302-appb-000050
In compensation mode,
Figure PCTCN2019089302-appb-000050
在非补偿模式时，C sg(t)＝0； In non-compensation mode, C sg (t) = 0;
式中
Figure PCTCN2019089302-appb-000051
是t时刻重力梯度仪的姿态角，P是自梯度模型的参数，
Figure PCTCN2019089302-appb-000052
是自梯度模型的inline通道的输出，它是姿态角的函数，
Figure PCTCN2019089302-appb-000053
是自梯度模型的cross通道的输出,它是姿态角的函数； Where
Figure PCTCN2019089302-appb-000051
Is the attitude angle of the gravity gradient instrument at time t, and P is a parameter of the self-gradient model,
Figure PCTCN2019089302-appb-000052
Is the output of the inline channel of the gradient model, which is a function of the attitude angle,
Figure PCTCN2019089302-appb-000053
Is the output of the cross channel from the gradient model, which is a function of the attitude angle;
4)对t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号g(t)，根据下式进行线运动误差补偿、角运动误差补偿、自梯度补偿；4) For the gravity gradiometer signal g (t) containing linear motion error, angular motion error, and self-gradient at time t, perform linear motion error compensation, angular motion error compensation, and self-gradient compensation according to the following formula;
g c(t)＝g(t)-C L(t)-C sg(t)-C A(t) g c (t) = g (t) -C L (t) -C sg (t) -C A (t)
式中g c(t)是t时刻补偿后的重力梯度仪信号，g(t)是t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号，C L(t)是t时刻的线运动误差补偿信号，C sg(t)是自梯度补偿信号，C A(t)是角运动误差补偿信号； Where g c (t) is the gravity gradient instrument signal after compensation at time t, g (t) is the gravity gradient instrument signal including linear motion error, angular motion error, and self-gradient at time t, and C L (t) is time t Linear motion error compensation signal, C sg (t) is a self-gradient compensation signal, and C A (t) is an angular motion error compensation signal;

Claims (10)

  1. 一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于，该装置包括：A moving base rotation accelerometer gravity gradient meter error compensation device is characterized in that the device includes:
    用于产生正交幅度调制载波的参考信号产生模块；A reference signal generating module for generating a quadrature amplitude modulation carrier;
    用于实时产生自梯度补偿信号的自梯度补偿信号产生模块；A self-gradient compensation signal generating module for generating a self-gradient compensation signal in real time;
    用于实时产生重力梯度仪角运动误差补偿信号及检测重力梯度仪离心梯度的角运动误差补偿信号产生模块；An angular motion error compensation signal generating module for generating a gravity gradient instrument angular motion error compensation signal in real time and detecting a centrifugal gradient of the gravity gradient instrument;
    用于实时微调角运动误差传递系数的角运动误差传递系数处理模块；An angular motion error transfer coefficient processing module for fine-tuning the angular motion error transfer coefficient in real time;
    用于实时产生重力梯度仪线运动误差补偿信号的线运动误差补偿信号产生模块；A linear motion error compensation signal generating module for generating a linear motion error compensation signal of the gravity gradient instrument in real time;
    用于实时微调线运动误差传递系数的线运动误差传递系数处理模块；Linear motion error transfer coefficient processing module for fine-tuning the linear motion error transfer coefficient in real time;
    用于对安装在旋转圆盘上的加速度计的输出信号求和、求差运算的重力梯度仪加速度计信号处理模块；A gravity gradient accelerometer signal processing module for summing and subtracting output signals of accelerometers mounted on a rotating disc;
    用于实时调节加速度计标度系数的加速度计标度系数调节模块；Accelerometer scaling coefficient adjustment module for adjusting the accelerometer scaling coefficient in real time;
    用于对含有角运动误差，线运动误差，自梯度的重力梯度信号进行补偿的补偿运算模块；Compensation operation module for compensating the gravity gradient signal including angular motion error, linear motion error, and self-gradient;
    用于从补偿后的重力梯度仪信号解调输出重力梯度信号的重力梯度信号恢复模块；A gravity gradient signal recovery module for demodulating and outputting a gravity gradient signal from a compensated gravity gradient instrument signal;
    所述参考信号产生模块的输出连接到自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块的输入；所述自梯度补偿信号产生模块、角运动误差补偿信号产生模块、线运动误差补偿信号产生模块、重力梯度仪加速度计信号处理模块的输出连接到补偿运算模块的输入；所述补偿运算模块的输出连接到加速度计标度系数调节模块、角运动误差传递系数处理模块、线运动误差传递系数处理模块、重力梯度信号恢复模块的输入；所述线运动误差传递系数处理模块的输出连接到线运动误差补偿信号产生模块的输入；所述角运动误差传递系数处理模块的输出连接到角运动误差补偿信号产生模块的输入；所述加速度计标度系数调节模块的输出连接到重力梯度仪加速度计信号处理模块的输入。The output of the reference signal generation module is connected to the inputs of a self-gradient compensation signal generation module, an angular motion error compensation signal generation module, and a linear motion error compensation signal generation module; the self-gradient compensation signal generation module and angular motion error compensation signal generation The output of the module, the linear motion error compensation signal generation module, the gravity gradient accelerometer signal processing module is connected to the input of the compensation operation module; the output of the compensation operation module is connected to the accelerometer scale coefficient adjustment module, the angular motion error transfer coefficient The input of the processing module, the linear motion error transfer coefficient processing module, and the gravity gradient signal recovery module; the output of the linear motion error transfer coefficient processing module is connected to the input of the linear motion error compensation signal generation module; the angular motion error transfer coefficient processing The output of the module is connected to the input of the angular motion error compensation signal generating module; the output of the accelerometer scale coefficient adjustment module is connected to the input of the gravity gradient accelerometer signal processing module.
  2. 如权利要求1所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述参考信号产生模块包括重力梯度仪旋转圆盘轴编码器和信号发生器；所述重力梯度仪旋转圆盘轴编码器检测重力梯度仪圆盘旋转的相位角φ t，所述信号发生器根据相位角φ t，产生正交幅度调制载波波sinφ t，sin2φ t，cosφ t，cos2φ t。 The error compensation device of a rotating base rotary accelerometer and gravity gradient instrument according to claim 1, wherein the reference signal generating module comprises a gravity gradient instrument rotating disc axis encoder and a signal generator; the gravity The gradient instrument rotary disc axis encoder detects the phase angle φ t of the gravity gradient instrument disc rotation, and the signal generator generates quadrature amplitude modulated carrier waves sinφ t , sin2φ t , cosφ t , cos2φ t according to the phase angle φ t . .
  3. 如权利要求1所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述角运动误差传递系数处理模块包括角运动误差传递系数初值设置模块和角运动误 差传递系数调节模块，所述角运动误差传递系数初值设置模块用于设置角运动误差传递系数初值：
    Figure PCTCN2019089302-appb-100001
    所述角运动误差传递系数调节模块根据反馈的补偿后的重力梯度仪信号产生调节量，微调角运动误差传递系数；角运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节角运动误差传递系数；当工作在非调节模式时，角运动误差传递系保持不变。     The error compensation device for a rotary base accelerometer and gravity gradient instrument according to claim 1, wherein the angular motion error transfer coefficient processing module includes an angular motion error transfer coefficient initial value setting module and angular motion error transfer. A coefficient adjustment module, the angular motion error transmission coefficient initial value setting module is configured to set an initial value of the angular motion error transmission coefficient:
    Figure PCTCN2019089302-appb-100001
    The angular motion error transfer coefficient adjustment module generates an adjustment amount according to the feedback-compensated gravity gradient meter signal, and fine-tunes the angular motion error transfer coefficient. The angular motion error transfer coefficient processing module has two working modes, an adjustment mode and a non-slot mode. When working in the adjustment mode, the angular motion error transmission coefficient is adjusted in real time; when working in the non-adjustment mode, the angular motion error transmission system remains unchanged.
  4. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述的角运动误差补偿信号产生模块包括角运动误差传递系数输入模块、角运动检测模块、参考信号输入模块、角运动补偿信号产生模块、离心梯度检测模块；The error compensation device for a rotary base accelerometer and gravity gradient meter according to claim 1, 2 or 3, wherein the angular motion error compensation signal generating module comprises an angular motion error transfer coefficient input module, an angle Motion detection module, reference signal input module, angular motion compensation signal generation module, centrifugal gradient detection module;
    所述角运动误差传递系数输入模块用于输入角运动误差传递系数；所述参考信号输入模块用于输入正交幅值调制载波；所述角运动检测模块包括角速率传感器和低通滤波器，用于检测重力梯度仪的角运动；所述角速率传感器安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的角速度ω x,ω y,ω z及角加速度ω ax,ω ay,ω az；所述低通滤波器则滤除角速度、角加速度信号中的高频噪声；所述角运动补偿信号产生模块根据正交幅值调制载波、角运动误差传递系数、角加速度、角速度产生角运动误差补偿信号；所述离心梯度检测模块有两种工作模式，标定模式和非标定模式，在标定模式下，离心梯度检测单元输出检测的离心梯度，在非标定模式下，离心梯度检测单元无输出。 The angular motion error transfer coefficient input module is used to input the angular motion error transfer coefficient; the reference signal input module is used to input a quadrature amplitude modulation carrier; the angular motion detection module includes an angular rate sensor and a low-pass filter, The angular rate sensor is used to detect the angular motion of the gravity gradient instrument; the angular rate sensor is installed on the x-axis, y-axis, and z-axis of the coordinate system of the gravity gradient instrument, and measures the angular velocity ω x , ω y , ω z of the coordinate system And angular accelerations ω ax , ω ay , ω az ; the low-pass filter filters high-frequency noise in angular velocity and angular acceleration signals; the angular motion compensation signal generation module modulates the carrier and angular motion according to orthogonal amplitudes The error transfer coefficient, angular acceleration, and angular velocity generate angular motion error compensation signals. The centrifugal gradient detection module has two working modes, calibration mode and non-calibration mode. In the calibration mode, the centrifugal gradient detection unit outputs the detected centrifugal gradient. There is no output from the centrifugal gradient detection unit in non-calibration mode.
  5. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述的角运动误差补偿信号产生模块具有三种工作模式，非补偿模式，正常模式，标定模式；非补偿模式下，产生的角运动误差补偿信号C A(t)为： The error compensation device for a rotating base rotary accelerometer gravity gradient meter according to claim 1, 2 or 3, wherein the angular motion error compensation signal generating module has three working modes, a non-compensating mode, Normal mode, calibration mode; in non-compensated mode, the angular motion error compensation signal C A (t) is:
    C A(t)＝0； C A (t) = 0;
    在正常模式下，产生的角运动误差补偿信号C A(t)为： In normal mode, the generated angular motion error compensation signal C A (t) is:
    Figure PCTCN2019089302-appb-100002
    Figure PCTCN2019089302-appb-100002
    在标定模式下，产生的角运动误差补偿信号C A(t)为： In the calibration mode, the generated angular motion error compensation signal C A (t) is:
    Figure PCTCN2019089302-appb-100003
    Figure PCTCN2019089302-appb-100003
    式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入角运动误差补偿信号产生模块的正交幅度调制载波；
    Figure PCTCN2019089302-appb-100004
    表示t时刻输入角运动误差补偿信号产生模块的角运动误差传递系数；ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)表示t时刻输入角运动误差补偿信号产生模块的角运动信号。     Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input angular motion error compensation signal generation module at time t;
    Figure PCTCN2019089302-appb-100004
    Represents the angular motion error transfer coefficient of the input angular motion error compensation signal generation module at time t; ω x (t), ω y (t), ω z (t), ω ax (t), ω ay (t), ω az (t) represents the angular motion signal of the input angular motion error compensation signal generation module at time t.
  6. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述线运动误差传递系数处理模块包括线运动误差传递系数初值设置模块和线运动误差传递系数调节模块，所述线运动误差传递系数初值设置模块用以设置线运动误差传递系数初值：
    Figure PCTCN2019089302-appb-100005
    所述线运动误差传递差系数调节模块根据反馈的补偿后的重力梯度仪信号产生调节量和微调线运动误差传递系数；线运动误差传递系数处理模块具有两种工作模式，调节模式和非条节模式，当工作在调节模式时，实时调节线运动误差传递系数；当工作在非调节模式时，线运动误差传递系保持不变。     The error compensation device for a rotating base rotary accelerometer gravity gradient instrument according to claim 1, 2 or 3, wherein the linear motion error transfer coefficient processing module includes a linear motion error transfer coefficient initial value setting module and A linear motion error transfer coefficient adjustment module, the linear motion error transfer coefficient initial value setting module is used to set an initial value of the linear motion error transfer coefficient:
    Figure PCTCN2019089302-appb-100005
    The linear motion error transfer difference coefficient adjustment module generates an adjustment amount and fine-tunes the linear motion error transfer coefficient according to the feedback-compensated gravity gradient instrument signal; the linear motion error transfer coefficient processing module has two working modes, adjustment mode and non-slot Mode, when working in the adjustment mode, adjust the linear motion error transfer coefficient in real time; when working in the non-adjustment mode, the linear motion error transmission system remains unchanged.
  7. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述线运动误差补偿信号产生模块包括线运动检测模块、线运动误差传递系数输入模块、参考信号输入模块、线运动补偿信号产生模块，所述线运动检测模块包括加速度计和低通滤波器，用于检测重力梯度仪的加速度；所述加速度计安装在重力梯度仪测量坐标系的x轴，y轴,z轴，测量重力梯度仪测量坐标系的加速度a x,a y,a z；所述低通滤波器则滤除加速度信号中的高频噪声；所述线运动误差传递系数输入模块用于输入线运动误差传递系数；所述参考信号产生模块用于输入正交幅值调制载波；所述线运动补偿信号产生模块根据输入的正交幅值调制载波、加速度信号、线运动误差传递系数产生线运动误差补偿信号。 The error compensation device for a rotating base rotary accelerometer gravity gradient instrument according to claim 1, 2 or 3, wherein the linear motion error compensation signal generating module comprises a linear motion detection module and a linear motion error transfer coefficient An input module, a reference signal input module, and a linear motion compensation signal generating module. The linear motion detection module includes an accelerometer and a low-pass filter for detecting the acceleration of the gravity gradient instrument. The accelerometer is installed on the gravity gradient instrument to measure coordinates The x-axis, y-axis, and z-axis of the system are used to measure the acceleration ax , ay , and az of the coordinate system by the gravity gradient meter; the low-pass filter removes high-frequency noise from the acceleration signal; and the linear motion The error transfer coefficient input module is used to input a linear motion error transfer coefficient; the reference signal generating module is used to input a quadrature amplitude modulation carrier; the line motion compensation signal generating module is used to modulate a carrier and acceleration signal according to the input quadrature amplitude The linear motion error transfer coefficient generates a linear motion error compensation signal.
  8. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述线运动误差补偿信号产生模块具有两种工作模式：非补偿模式，补偿模式；非补偿模式下，产生的线运动补偿信号C L(t)为： The error compensation device for a rotating base rotary accelerometer gravity gradient instrument according to claim 1, 2 or 3, wherein the linear motion error compensation signal generating module has two working modes: non-compensating mode and compensation Mode; in non-compensated mode, the linear motion compensation signal C L (t) is:
    C L(t)＝0； C L (t) = 0;
    补偿模式下，产生的线运动补偿信号C L(t)为： In the compensation mode, the generated linear motion compensation signal C L (t) is:
    Figure PCTCN2019089302-appb-100006
    Figure PCTCN2019089302-appb-100006
    式中sin2φ t,cos2φ t,sinφ t,cosφ t为t时刻输入线运动误差补偿信号产生模块的正交幅度调制载波；
    Figure PCTCN2019089302-appb-100007
    表示t时刻输入线运动误差补偿信号产生模块的线运动误差传递系数；a x(t),a y(t),a z(t)表示t时刻输入线运动误差补偿信号产生模块的加速度信号。     Where sin2φ t , cos2φ t , sinφ t , and cosφ t are quadrature amplitude modulation carriers of the input line motion error compensation signal generation module at time t;
    Figure PCTCN2019089302-appb-100007
    Represents the linear motion error transfer coefficient of the input linear motion error compensation signal generation module at time t; a x (t), a y (t), a z (t) represents the acceleration signal of the input linear motion error compensation signal generation module at time t.
  9. 如权利要求1、2或3所述的一种动基座旋转加速度计重力梯度仪误差补偿装置，其特征在于：所述补偿运算模块根据自梯度补偿信号产生模块输出的自梯度补偿信号、线运动误差补偿信号产生模块产生的线运动误差补偿信号、角运动误差补偿信号产生模块产生的角运动误差补偿信号，对重力梯度仪加速度计信号处理模块产生的含有自梯度误差、线运动误差、角运动误差的输出进行补偿。The error compensation device for a rotating base rotary accelerometer gravity gradient instrument according to claim 1, 2 or 3, characterized in that: the compensation operation module generates a self-gradient compensation signal and line output by the self-gradient compensation signal generating module. The linear motion error compensation signal generated by the motion error compensation signal generation module and the angular motion error compensation signal generated by the angular motion error compensation signal generation module. The self-gradient error, linear motion error, angle The output of the motion error is compensated.
  10. 一种动基座旋转加速度计重力梯度仪误差补偿方法，其特征在于，该方法包括以下步骤：A method for compensating the error of a rotating base rotary accelerometer gravity gradient instrument, which is characterized in that the method includes the following steps:
    1)根据反馈的补偿后的重力梯度仪信号及线运动误差传递系数处理模块的工作模式，计算t时刻的线运动误差传递系数：1) Calculate the linear motion error transfer coefficient at time t based on the feedback of the compensated gravity gradient instrument signal and the working mode of the linear motion error transfer coefficient processing module:
    调节模式：
    Figure PCTCN2019089302-appb-100008
    非调节模式：
    Figure PCTCN2019089302-appb-100009
    Adjustment mode:
    Figure PCTCN2019089302-appb-100008
    Non-regulated mode:
    Figure PCTCN2019089302-appb-100009
    式中
    Figure PCTCN2019089302-appb-100010
    表示t时刻的线运动误差传递系数，
    Figure PCTCN2019089302-appb-100011
    表示t-1时刻的线运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 1(g c(t-1))是t时刻线运动误差传递系数的微调量， 它是g c(t-1)的函数；     Where
    Figure PCTCN2019089302-appb-100010
    Represents the linear motion error transfer coefficient at time t,
    Figure PCTCN2019089302-appb-100011
    Represents the coefficient of linear motion error transmission at time t-1; g c (t-1) represents the signal of the gravity gradient instrument after compensation at time t-1; F 1 (g c (t-1)) is the transmission of linear motion error at time t Coefficient of fine-tuning, which is a function of g c (t-1);
    根据反馈的补偿后的重力梯度仪信号及角运动误差传递系数处理模块的工作模式，计算t时刻的角运动误差传递系数：Calculate the angular motion error transfer coefficient at time t according to the feedback of the compensated gravity gradient signal and the working mode of the angular motion error transfer coefficient processing module:
    调节模式：
    Figure PCTCN2019089302-appb-100012
    非调节模式：
    Figure PCTCN2019089302-appb-100013
    Adjustment mode:
    Figure PCTCN2019089302-appb-100012
    Non-regulated mode:
    Figure PCTCN2019089302-appb-100013
    式中
    Figure PCTCN2019089302-appb-100014
    表示t时刻的角运动误差传递系数，
    Figure PCTCN2019089302-appb-100015
    表示t-1时刻的角运动误差传递系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 2(g c(t-1))表示t时刻角运动误差传递系数的微调量，它是g c(t-1)的函数；t＝0时刻的线运动误差传递系数
    Figure PCTCN2019089302-appb-100016
    角运动误差传递系数
    Figure PCTCN2019089302-appb-100017
    均通过标定得到；     Where
    Figure PCTCN2019089302-appb-100014
    Represents the angular motion error transfer coefficient at time t,
    Figure PCTCN2019089302-appb-100015
    Represents the angular motion error transfer coefficient at time t-1; g c (t-1) represents the gravimetric gradient signal after compensation at time t-1; F 2 (g c (t-1)) represents the angular motion error transfer at time t Coefficient fine-tuning amount, which is a function of g c (t-1); linear motion error transfer coefficient at time t = 0
    Figure PCTCN2019089302-appb-100016
    Angular motion error transfer coefficient
    Figure PCTCN2019089302-appb-100017
    All obtained through calibration;
    根据反馈的补偿后的重力梯度仪信号，计算t时刻的加速度计标度系数：Calculate the accelerometer scale factor at time t based on the compensated gravimetric gradient signal:
    Figure PCTCN2019089302-appb-100018
    Figure PCTCN2019089302-appb-100018
    式中
    Figure PCTCN2019089302-appb-100019
    表示安装在旋转圆盘上的四只加速度计在t时刻的标度系数，
    Figure PCTCN2019089302-appb-100020
    表示安装在旋转圆盘上的四只加速度计在t-1时刻的标度系数；g c(t-1)表示t-1时刻补偿后的重力梯度仪信号；F 3(g c(t-1))表示t时刻加速度计标度系数的调节量，它是g c(t-1)的函数；     Where
    Figure PCTCN2019089302-appb-100019
    Represents the scaling coefficients of four accelerometers mounted on a rotating disc at time t,
    Figure PCTCN2019089302-appb-100020
    Represents the scaling coefficients of the four accelerometers mounted on the rotating disc at time t-1; g c (t-1) represents the gravity gradient signal after compensation at time t-1; F 3 (g c (t- 1)) represents the adjustment amount of the accelerometer scale coefficient at time t, which is a function of g c (t-1);
    2)检测旋转加速度计重力梯度仪旋转圆盘在t时刻的相位角φ t，计算t时刻的正交幅度调制载波sinφ t，sin2φ t，cosφ t，cos2φ t；检测旋转旋转加速度计重力梯度仪在t时刻的加速度
    Figure PCTCN2019089302-appb-100021
    检测旋转加速度计重力梯度仪在t时刻的角速度及角加速度 ω x(t),ω y(t),ω z(t),ω ax(t),ω ay(t),ω az(t)；     2) Detect the phase angle φ t of the rotating disc of the rotating accelerometer gravity gradient instrument at time t , calculate the quadrature amplitude modulation carrier sinφ t , sin2φ t , cosφ t , cos2φ t at time t ; detect the rotational rotational accelerometer gravity gradient instrument Acceleration at time t
    Figure PCTCN2019089302-appb-100021
    Detect the angular velocity and angular acceleration of the rotational accelerometer gravity gradient instrument at time tω x (t), ω y (t), ω z (t), ω ax (t), ω ay (t), ω az (t) ;
    根据下式计算t时刻的3类线运动误差补偿信号C L1(t),C L2(t),C L3(t): Calculate the three types of linear motion error compensation signals C L1 (t), C L2 (t), and C L3 (t) at time t according to the following formula:
    Figure PCTCN2019089302-appb-100022
    Figure PCTCN2019089302-appb-100022
    根据下式计算t时刻的3类角运动误差补偿信号C A1(t),C A2(t),C A3(t): Calculate the three types of angular motion error compensation signals C A1 (t), C A2 (t), and C A3 (t) at time t according to the following formula:
    Figure PCTCN2019089302-appb-100023
    Figure PCTCN2019089302-appb-100023
    3)根据线运动误差补偿信号产生模块的工作模式，计算t时刻的总的线运动误差补偿信号C L(t)： 3) According to the working mode of the linear motion error compensation signal generating module, calculate the total linear motion error compensation signal C L (t) at time t:
    非补偿模式时，C L(t)＝0； In non-compensation mode, C L (t) = 0;
    补偿模式时，C L(t)＝C L1(t)+C L2(t)+C L3(t)； In the compensation mode, C L (t) = C L1 (t) + C L2 (t) + C L3 (t);
    根据角运动误差补偿信号产生模块的工作模式，计算t时刻总的角运动误差补偿信号C A(t)： According to the working mode of the angular motion error compensation signal generating module, calculate the total angular motion error compensation signal C A (t) at time t:
    非补偿模式时，C A(t)＝0； In non-compensation mode, C A (t) = 0;
    正常模式时，C A(t)＝C A1(t)+C A2(t)+C A3(t)； In normal mode, C A (t) = C A1 (t) + C A2 (t) + C A3 (t);
    标定模式时，C A(t)＝C A2(t)+C A3(t)； In calibration mode, C A (t) = C A2 (t) + C A3 (t);
    根据自梯度补偿信号产生模块的工作模式，计算t时刻的自梯度补偿信号C sg(t)： According to the working mode of the self-gradient compensation signal generating module, calculate the self-gradient compensation signal C sg (t) at time t:
    补偿模式时，
    Figure PCTCN2019089302-appb-100024
    In compensation mode,
    Figure PCTCN2019089302-appb-100024
    在非补偿模式时，C sg(t)＝0； In non-compensation mode, C sg (t) = 0;
    式中
    Figure PCTCN2019089302-appb-100025
    是t时刻重力梯度仪的姿态角，P是自梯度模型的参数，
    Figure PCTCN2019089302-appb-100026
    是自 梯度模型的inline通道的输出，它是姿态角的函数，
    Figure PCTCN2019089302-appb-100027
    是自梯度模型的cross通道的输出,它是姿态角的函数；     Where
    Figure PCTCN2019089302-appb-100025
    Is the attitude angle of the gravity gradient instrument at time t, and P is a parameter of the self-gradient model,
    Figure PCTCN2019089302-appb-100026
    Is the output of the inline channel of the gradient model, which is a function of the attitude angle,
    Figure PCTCN2019089302-appb-100027
    Is the output of the cross channel from the gradient model, which is a function of the attitude angle;
    4)对t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号g(t)，根据下式进行线运动误差补偿、角运动误差补偿、自梯度补偿；4) For the gravity gradiometer signal g (t) containing linear motion error, angular motion error, and self-gradient at time t, perform linear motion error compensation, angular motion error compensation, and self-gradient compensation according to the following formula;
    g c(t)＝g(t)-C L(t)-C sg(t)-C A(t) g c (t) = g (t) -C L (t) -C sg (t) -C A (t)
    式中g c(t)是t时刻补偿后的重力梯度仪信号，g(t)是t时刻含有线运动误差、角运动误差、自梯度的重力梯度仪信号，C L(t)是t时刻的线运动误差补偿信号，C sg(t)是自梯度补偿信号，C A(t)是角运动误差补偿信号； Where g c (t) is the gravity gradient instrument signal after compensation at time t, g (t) is the gravity gradient instrument signal including linear motion error, angular motion error, and self-gradient at time t, and C L (t) is time t Linear motion error compensation signal, C sg (t) is a self-gradient compensation signal, and C A (t) is an angular motion error compensation signal;
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