CN110221333B - Measurement error compensation method of vehicle-mounted INS/OD integrated navigation system - Google Patents

Measurement error compensation method of vehicle-mounted INS/OD integrated navigation system Download PDF

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CN110221333B
CN110221333B CN201910288827.XA CN201910288827A CN110221333B CN 110221333 B CN110221333 B CN 110221333B CN 201910288827 A CN201910288827 A CN 201910288827A CN 110221333 B CN110221333 B CN 110221333B
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odometer
error
vehicle
ins
inertial
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CN110221333A (en
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熊璐
陈辛波
韩燕群
夏新
陆逸适
高乐天
胡英杰
魏琰超
宋舜辉
刘伟
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Tongji University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
    • G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/52—Determining velocity

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  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
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Abstract

The invention relates to a measurement error compensation method of a vehicle-mounted INS/OD integrated navigation system, which solves the technical problems that: on a distributed driving electric intelligent automobile, a vehicle-mounted odometer auxiliary inertial navigation system is used for vehicle combined navigation, the system considers the odometer scale coefficient caused by the change of the vehicle running condition and the availability of odometer data and provides judgment of measurement compensation, the INS and the mounting offset angle and lever arm errors of the odometer systems on the left side and the right side are calibrated in combined navigation, the INS and the mounting offset angle and lever arm errors serve as measurement quantities in a measurement equation of the combined navigation system to be corrected, a filtering system which takes inertial navigation position, speed, attitude errors, inertial device random constant errors, left and right odometer scale coefficient errors and lever arm state quantities is constructed, feedback correction is carried out, and the improvement of combined navigation positioning accuracy based on measurement error compensation is realized.

Description

Measurement error compensation method of vehicle-mounted INS/OD integrated navigation system
Technical Field
The invention relates to the technical field of vehicle-mounted navigation and positioning, in particular to a measurement error compensation method of a vehicle-mounted INS/OD integrated navigation system.
Background
An Inertial Navigation System (INS) has the characteristics of high autonomy, anti-interference performance, high short-term precision, high data output rate, complete Navigation information, wide application range and the like, but the System error has the characteristic of periodic oscillation, and certain Navigation parameter errors have the characteristic of accumulation along with time and the time required by initial alignment is longer; in order to compensate for the error of the INS system, various combinations of the INS-based integrated navigation systems have appeared, such as: inertial navigation/odometer, inertial navigation/satellite, inertial navigation/geomagnetic, inertial navigation/Doppler and the like, wherein the odometer scheme has low cost and strong anti-interference capability. However, because the odometer is arranged at the wheel center of the wheel and the INS is arranged on the vehicle body, the installation positions of the two navigation subsystems are not coincident and have a certain installation angle, namely a measurement error. When the vehicle has a posture change, the output of the odometer has deviation, because if the relative posture movement between the vehicle body and the odometer cannot be accurately estimated, the navigation precision of a vehicle navigation system consisting of the INS/OD can be seriously influenced. Meanwhile, when the vehicle slips, sideslips and jumps, the odometer is generally regarded as a fault, and the output of the odometer is not credible.
In addition, because the radius of the tire changes due to different driving conditions of the vehicle, the output of the odometer changes along with the change of the radius, namely a scale coefficient exists between the actual vehicle speed and the output value of the odometer, and the change of the scale coefficient has great influence on the output of the odometer, so that the value needs to be estimated and corrected. There are three current approaches: the calibration coefficient of the odometer is regarded as a constant value which is not in accordance with the reality, the calibration coefficient is set to be the constant value and added with a random error term, the odometer cannot adapt to most working conditions, and a corresponding error model is built according to related variables such as acceleration, gradient and the like to compensate for the variation of the calibration coefficient, so that the variable factor of modeling is incomplete and troublesome.
A method for improving vehicle-mounted SINS/OD combined navigation accuracy as in patent application No. 201210584022 discloses the following: according to the gradient of the road surface and the acceleration of the vehicle, the scale coefficient change of the mileage gauge and the relative angular motion between the chassis of the vehicle and the vehicle body are calculated, and the output of the mileage gauge is compensated to obtain the accurate running speed of the vehicle. And constructing measurement by using the difference between the SINS-resolved speed information and the OD-resolved speed information, estimating model parameters and navigation error parameters through Kalman filtering, and correcting SINS and OD data by using the obtained state quantity to obtain accurate navigation parameters. When the position is corrected, the position is estimated using the corrected speed without directly correcting the position using the state estimation value, considering that the observability of the position error is poor. The invention considers the influence of the road gradient and the vehicle acceleration on the vehicle-mounted SINS/OD combined navigation precision, and realizes the vehicle-mounted SINS/OD high-precision combined navigation by establishing a corresponding mathematical model. "
The scheme of the vehicle-mounted INS/OD combined navigation system has the following defects:
1. calibration and estimation of measurement consistency parameters for an inertial navigation system and a odometer mounted on a vehicle are lacked;
2. the dynamic change of the lever arm due to the change of the vehicle attitude is not sufficiently taken into account;
3. the method has the advantages that the mileage meter scale coefficient caused by the change of the running condition of the vehicle is not well estimated and adaptive;
4. there is a lack of judgments regarding actual odometer data availability and providing measurement compensation for the presence of slip, side-slip, jump, turn, and acceleration/deceleration conditions in a vehicle.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a measurement error compensation method of a vehicle-mounted INS/OD combined navigation system, on a distributed driving electric intelligent vehicle, a vehicle-mounted odometer is used for assisting an inertial navigation system to carry out vehicle combined navigation, the system considers the odometer scale coefficient caused by the change of the vehicle running condition, the availability of odometer data and judgment for providing measurement compensation, the installation offset angle and lever arm errors of the INS and odometer systems on the left side and the right side are calibrated in the combined navigation, and the system is used as the measurement quantity in a combined navigation system measurement equation to be corrected, so that the improvement of the combined navigation positioning accuracy based on the measurement error compensation is realized by constructing the inertial navigation position, speed, attitude error, random constant error of an inertial device and scale coefficient error of the left and the right odometer and a filter system using the lever arm as a state quantity and carrying out feedback correction.
The purpose of the invention can be realized by the following technical scheme:
a measurement error compensation method of a vehicle-mounted INS/OD combined navigation system comprises the following steps:
step 1: initializing an INS when the vehicle is static, and measuring and calibrating a mounting angle error, a lever arm error and a mileage gauge scale coefficient by using a measuring instrument and a vehicle body structure;
step 2: judging the availability of the odometer data: judging whether the vehicle slips, sideslips and jumps according to the running state of the vehicle, if so, not using the feedback of the odometer, and if not, carrying out combined navigation and inputting the output speed data of the left and right odometers into a combined filter;
and step 3: acquiring INS original navigation data in the running process of a vehicle;
and 4, step 4: performing device compensation, attitude calculation and navigation calculation on INS original navigation data, and inputting the obtained speed increment attitude, speed and position into a combined filter;
and 5: and after the data input of the combined filter is finished, establishing a state equation of the combined navigation system, estimating the state equation, and after each time of filtering, performing feedback correction on the INS calculation result by using the result of filtering estimation.
Preferably, the slip determination condition in step 2 is:
v OD ≤ωR
in the formula, v OD The vehicle speed under the vehicle system, omega is the wheel angular speed, and R is the wheel radius.
Preferably, the sideslip determination condition in step 2 is:
Δy≥v ODy ΔT
where Δ y is the lateral displacement increment under the carrier system, v ODy The vehicle speed is the lower side of the carrier system, and delta T is the change time.
Preferably, the jump determination condition in step 2 is:
Δa z ≥Δa th
in the formula,. DELTA.a z Is the actual change value of vertical acceleration, delta a th Is a reasonable variation value of the vertical acceleration.
Preferably, the velocity increment posture, the velocity and the position in the step 4 are calculated by adopting a two-subsample cone error compensation algorithm, and a corresponding calculation equation set is as follows:
Figure BDA0002024227150000031
Figure BDA0002024227150000032
Figure BDA0002024227150000033
Figure BDA0002024227150000034
in the formula,. DELTA.theta. m1 And Δ θ m2 Corresponding angle increment is sampled for the gyro at two equal intervals, T is sampling time,
Figure BDA0002024227150000035
for reference by the inertial frame, the carrier is moved from t m-1 Time t m The change in the rotation at a moment in time,
Figure BDA0002024227150000036
for reference to the inertial frame, the geographic system is set from t m Time t m-1 The rotation change of the moment, subscript i represents the inertial navigation system calculation value, upper subscript b represents the load system, upper subscript n represents the geography system, and (m) represents t m Time, (m-1) represents t m-1 At the moment, phi represents the corresponding posture with the subscript, I represents the identity matrix,
Figure BDA0002024227150000041
is a constant value.
Preferably, the step 5 comprises the following substeps:
step 51: establishing a system equation;
step 52: establishing a measurement equation;
step 53: establishing a kalman filtering system equation and discretizing a measurement equation;
step 54: and performing feedback correction by using a kalman filtering system equation.
Preferably, the system equation in step 51 describes the formula:
Figure BDA0002024227150000042
wherein X is a state vector, phi 1 The method comprises the following steps: phi is a E 、φ N And phi U Respectively, attitude error, δ v, in east-north-sky geographic coordinate system n The method comprises the following steps: delta v E 、δv N And δ v U Velocity errors in the east-north-sky geographic coordinate system, respectively, δ p includes: δ L, δ λ, and δ h are position errors of longitude, latitude, and altitude, and ε comprises: epsilon x 、ε y And ε z Respectively the zero offset of three coordinate axes of the gyroscope,
Figure BDA0002024227150000043
the method comprises the following steps:
Figure BDA0002024227150000044
and
Figure BDA0002024227150000045
zero offset, δ k, of the three axes of the accelerometer, respectively 1 And δ k 2 Scale factor errors for odometer 1 and odometer 2 respectively,
Figure BDA0002024227150000046
the method comprises the following steps:
Figure BDA0002024227150000047
and
Figure BDA0002024227150000048
the lever arm values of the three coordinate axes of the odometer 1,
Figure BDA0002024227150000049
the method comprises the following steps:
Figure BDA00020242271500000410
and
Figure BDA00020242271500000411
lever arm values of three coordinate axes of the odometer 2 are respectively;
Figure BDA00020242271500000412
Figure BDA00020242271500000413
Figure BDA00020242271500000414
Figure BDA00020242271500000415
Figure BDA00020242271500000416
in the formula (I), the compound is shown in the specification,
Figure BDA00020242271500000417
is the angular velocity of the geographic system relative to the inertial system,
Figure BDA00020242271500000418
is the angular velocity error of the earth system relative to the inertial system,
Figure BDA00020242271500000419
the angular velocity error of the geographic system relative to the earth system,
Figure BDA00020242271500000420
is a coordinate transformation matrix of the carrier system to the geographical system,
Figure BDA00020242271500000421
is the angular velocity error of the carrier system relative to the inertial system,
Figure BDA00020242271500000422
is the output specific force, v, of the carrier system relative to the inertial navigation system accelerometer under the geographic system n Is the speed of the carrier under the geographic system,
Figure BDA00020242271500000423
is the angular velocity of the earth system relative to the inertial system,
Figure BDA00020242271500000424
is the angular velocity, δ v, of the geographic system relative to the Earth's system n Is the speed error of the carrier under the geographical region,
Figure BDA0002024227150000051
is the output specific force error, delta g, of the inertial navigation system accelerometer under the carrier system relative to the geographic system n As error of gravitational acceleration, R M Radius of the mortise, h local altitude, L local latitude and R N Is the radius of the meridian circle,phi alone represents the mathematical platform error angle in the strapdown inertial navigation system.
Preferably, the measurement equation in step 52 describes the formula:
Figure BDA0002024227150000052
Figure BDA0002024227150000053
Figure BDA0002024227150000054
Figure BDA0002024227150000055
in the formula, the superscript n represents a geography system, Z represents a measurement equation, the subscript INS represents an inertia system, the subscript OD represents an odometer,
Figure BDA0002024227150000056
and
Figure BDA0002024227150000057
coordinate transformation matrices, v, of odometer 1 and odometer 2, respectively, with respect to the carrier system OD1 And v OD2 The vehicle speeds of the vehicle under the carrier systems of the odometer 1 and the odometer 2 respectively,
Figure BDA0002024227150000058
indicating the angular velocity of the carrier system relative to the earth system,
Figure BDA0002024227150000059
and
Figure BDA00020242271500000510
lever arm value errors, k, of odometer 1 and odometer 2, respectively 1 And k 2 Scale factors for odometer 1 and odometer 2, respectively.
Preferably, the step 5 further comprises: feeding back the kalman filtered gyroscope and the acceleration zero offset to a device compensation position for correction, feeding back the attitude to an attitude updating compensation position, and feeding back the speed and position errors to the output value calculated by the INS for correction, namely: from the corrected
Figure BDA00020242271500000511
The course angle psi, the pitch angle theta and the roll angle gamma can be obtained through solution, and after the primary filtering feedback, the error state returns to 0.
Preferably, said modified
Figure BDA00020242271500000512
The heading angle psi, the pitch angle theta and the roll angle gamma can be obtained through solution, and the corresponding description formula is as follows:
Figure BDA00020242271500000513
in the formula, (numeral 1, numeral 2) represents a specific corresponding matrix element in the matrix.
The principle of the invention is as follows:
before the vehicle runs, an inertial navigation system is initialized, a measuring instrument is used for preliminarily measuring an installation offset angle and a lever arm error of an INS system and an odometer system, and an odometer scale coefficient is used as a measurement quantity in a measurement equation of the integrated navigation system to be corrected, a filtering system which takes an inertial navigation position, a speed, an attitude error, an inertial device random constant error, an odometer scale coefficient error and an odometer lever arm as state quantities is constructed, and feedback correction is carried out. The invention is divided into four phases, the first phase is an INS initialization phase: in the stage, the navigation attitude angle and position are initialized by using the external course information in an auxiliary way; calibrating the initial values of the scale coefficients of the installation angle error, the lever arm and the odometer in the second stage; and the third stage is a data acquisition and processing stage, namely the availability judgment of the odometer, the device error compensation of the INS, the attitude calculation and the navigation calculation. And the fourth stage is a combined filtering and feedback correcting stage, namely, the estimated position error, the estimated speed error, the estimated attitude error and the estimated random constant error of the inertial device are fed back to the INS for feedback compensation, and the scale coefficient error of the odometer is fed back to the odometer.
Compared with the prior art, the invention has the following advantages:
(1) In the invention, the calibration and estimation of measurement consistency parameters of an inertial navigation system and a mileometer which are installed on a vehicle in the integrated navigation system and the dynamic change of a lever arm caused by the change of the vehicle attitude are considered, the error of the graduations coefficient of a mileage meter caused by the change of the vehicle running condition is expanded to be self-adaptive, the judgment of the actual data availability of the mileometer and the measurement compensation according to the vehicle slip, sideslip and jump is provided, and the availability and the precision of the integrated navigation system are improved.
Drawings
FIG. 1 is a lever arm schematic diagram of the relative positions of the INS inertial measurement unit center and the camera assembly center in the invention;
FIG. 2 is a block diagram of an integrated navigation system according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, shall fall within the protection scope of the present invention.
Examples
The method is divided into four stages, wherein the first stage is an INS initialization stage, and the second stage calibrates initial values of a mounting angle error, a lever arm and a odometer scale coefficient; and the third stage is a data acquisition and processing stage, and the availability judgment of the odometer, the device error compensation of the INS, the attitude calculation and the navigation calculation are carried out. The fourth stage is a combined filtering and feedback correction stage.
The specific implementation steps of the invention are shown in fig. 2:
(1) Carrying out INS initialization when the vehicle is static;
(2) Measuring and calibrating the installation angle error and the lever arm error by using a measuring instrument and a vehicle structure, and calibrating the graduation coefficients of the odometer to obtain a coordinate transformation matrix of the odometer 1 and the odometer 2 relative to a load system, the lever arm value errors of the odometer 1 and the odometer 2 and the graduation coefficients of the odometer 1 and the odometer 2 as shown in figure 1;
(3) And (3) judging the availability of the odometer data: judging whether to slip, sideslip and jump according to the running speed and the acceleration state of the vehicle; if yes, the odometer feedback is not used, if not, the combined navigation is carried out, and the data vehicle speed output by the left and right odometer systems is input into the combined filter;
determination conditions of vehicle running state:
1. slipping (longitudinal slipping): v. of OD ≤ωR
2. Side-slip (brake side-slip and front wheel slip): toe-in takes place when mismatching with wheel camber angle, and the acquiescence is that the vehicle matches suitably this moment, and no mismatching leads to sliding, adopts extra judgement: Δ y.gtoreq.v ODy Δ T, where Δ y is the lateral displacement increment in the carrier coordinate system, v ODy The lateral vehicle speed is the lateral vehicle speed under the carrier coordinate system;
3. jumping: the vehicle is abnormally vibrated vertically, and the judgment is carried out through the change of vertical acceleration: delta a z ≥Δa th 。
(4) Data are collected in the vehicle running process, and inertia measurement data are as follows: three axis gyroscope data
Figure BDA0002024227150000071
Triaxial accelerometer data
Figure BDA0002024227150000072
(5) Performing device compensation, attitude calculation and navigation calculation on the INS original navigation data in the step (4), and inputting the obtained information of velocity increment, such as attitude, velocity, position and the like, into the combined filter;
wherein, the gesture calculation selects an east-north-sky (E-N-U) geographic coordinate system (g system) as a navigation reference coordinate system of the strapdown inertial navigation system, and the geographic coordinate system is recorded as an N system again, and a gesture differential equation taking the N system as the reference system is as follows:
Figure BDA0002024227150000073
Figure BDA0002024227150000074
wherein the matrix
Figure BDA0002024227150000075
Indicating that i system (inertial coordinate system) is used as a reference and b system is from t m-1 Time t m The change in the rotation at a moment in time,
Figure BDA0002024227150000076
can be controlled by the angular velocity of the gyroscope
Figure BDA0002024227150000077
Determining;
Figure BDA0002024227150000078
denotes that i is used as reference base and n is from t m Time t m-1 The change in the rotation at a moment in time,
Figure BDA0002024227150000079
can be calculated from the angular velocity
Figure BDA00020242271500000710
It is determined that,
Figure BDA00020242271500000711
and
Figure BDA00020242271500000712
respectively represent t m-1 And t m A strapdown attitude matrix of the time of day. If the gyro is in the time period t m-1 ,t m ]Inner (T = T) m -t m-1 ) Two times of equal interval sampling are carried out, and the angular increment is respectively delta theta m1 And Δ θ m2 A two-subsample cone error compensation algorithm is adopted, and comprises the following steps:
Figure BDA00020242271500000713
taking fourth order truncation and approximation:
Figure BDA0002024227150000081
Figure BDA0002024227150000082
navigation update period [ t ] m-1 ,t m ]In which the velocity and position can be considered to be
Figure BDA0002024227150000083
Very small in variation, i.e. visible
Figure BDA0002024227150000084
Is a constant value, recorded as
Figure BDA0002024227150000085
Then there are:
Figure BDA0002024227150000086
Figure BDA0002024227150000087
(6) After the data in (3) and (5) are input into the filter, establishing a state equation of the integrated navigation system, and adopting an error state vector which specifically comprises a position, a speed, an attitude, a gyro random constant drift epsilon and an accelerometer random constant zero offset
Figure BDA0002024227150000088
And (3) estimating the 23-dimensional error state vector by using the scale coefficient error of the left and right odometers and the total 23-dimensional error state quantity of the lever arm, and taking the result as measurement after the difference value of the speed, the position and the attitude of the settlement of the two systems is compensated for the measurement error. After each filtering, the position error estimated by the filtering
Figure BDA0002024227150000089
Error in velocity
Figure BDA00020242271500000810
Error in misalignment angle
Figure BDA00020242271500000811
Gyro random constant drift
Figure BDA00020242271500000812
Accelerometer random constant zero offset
Figure BDA00020242271500000813
And (4) performing feedback correction on the INS calculation result, and performing feedback correction on the odometer by the aid of the odometer scale coefficient error.
1. Filtering and resolving:
establishing a system equation
Figure BDA00020242271500000814
Wherein: x: an error state vector;
f: a system matrix;
g: a noise distribution matrix;
w: a zero mean gaussian white noise vector;
z: measuring a vector;
h: measuring the matrix;
v: measuring a noise state vector;
b at the relevant subscript positions denotes the carrier system, n denotes the geographic system, e denotes the earth system, and i denotes the inertial system.
Figure BDA0002024227150000091
Wherein X is a state vector, phi 1 The method comprises the following steps: phi is a E 、φ N And phi U Respectively, attitude error, δ v, in east-north-sky geographic coordinate system n The method comprises the following steps: delta v E 、δv N And δ v U Velocity errors in the east-north-sky geographic coordinate system, respectively, δ p includes: δ L, δ λ, and δ h are position errors of longitude, latitude, and altitude, and ε includes: epsilon x 、ε y And ε z Are respectively zero offset of three coordinate axes of the gyroscope,
Figure BDA0002024227150000092
the method comprises the following steps:
Figure BDA0002024227150000093
and
Figure BDA0002024227150000094
zero offset, δ k, of the three axes of the accelerometer, respectively 1 And δ k 2 Scale factor errors for odometer 1 and odometer 2 respectively,
Figure BDA0002024227150000095
the method comprises the following steps:
Figure BDA0002024227150000096
and
Figure BDA0002024227150000097
the lever arm values of the three coordinate axes of the odometer 1,
Figure BDA0002024227150000098
the method comprises the following steps:
Figure BDA0002024227150000099
and
Figure BDA00020242271500000910
lever arm values of three coordinate axes of the odometer 2 are respectively;
Figure BDA00020242271500000911
Figure BDA00020242271500000912
Figure BDA00020242271500000913
Figure BDA00020242271500000914
Figure BDA00020242271500000915
in the formula (I), the compound is shown in the specification,
Figure BDA00020242271500000916
is the angular velocity of the geographic system relative to the inertial system,
Figure BDA00020242271500000917
the angular velocity error of the earth system relative to the inertial system,
Figure BDA00020242271500000918
the angular velocity error of the geographic system relative to the earth system,
Figure BDA00020242271500000919
is a coordinate transformation matrix of carrier system to geographic system,
Figure BDA00020242271500000920
as angular velocity of the carrier system relative to the inertial systemThe error is a measure of the error,
Figure BDA00020242271500000921
is the output specific force, v, of the carrier system relative to the inertial navigation system accelerometer under the geographic system n Is the speed of the carrier under the geographic system,
Figure BDA00020242271500000922
is the angular velocity of the earth system relative to the inertial system,
Figure BDA00020242271500000923
is the angular velocity, δ v, of the geographic system relative to the Earth's system n Is the speed error of the carrier under the geographical region,
Figure BDA00020242271500000924
is the output specific force error, delta g, of the carrier system relative to the inertial navigation system accelerometer under the geographic system n As error of gravitational acceleration, R M Radius of the mortise, h local altitude, L local latitude and R N And for the meridian radius, phi alone represents the mathematical platform error angle in the strapdown inertial navigation system.
The following develops the equations (attitude-velocity-position) in turn:
Figure BDA0002024227150000101
wherein
Figure BDA0002024227150000102
Figure BDA0002024227150000103
Figure BDA0002024227150000104
Figure BDA0002024227150000105
Figure BDA0002024227150000111
Wherein:
Figure BDA0002024227150000112
for gyro measurement errors, m-band different a, x, y and z subscripts are expressed as cross coupling coefficients between two axes in the gyro measurement, and s-band a, x and z subscripts are expressed as scale factor errors in the gyro measurement.
Figure BDA0002024227150000113
Wherein:
Figure BDA0002024227150000114
for accelerometer measurement errors, the m-band different g, x, y, z subscripts are expressed as cross-coupling coefficients in the accelerometer measurement, and the s-band g, x, z subscripts are expressed as scale factor errors in the accelerometer measurement.
Figure BDA0002024227150000115
Figure BDA0002024227150000121
The earth parameters given according to the WGS-84 (World Geodetic System 1984) Earth System are: semi-major axis: r e =6378137m, flattish ratio: f =1/298.257223563,
gravitational constant (including atmosphere): μ =3.986004418 × 10 14 m 3 /s 2 ，
Earth rotation angular rate: omega ie ＝7.2921151467×10- 5 rad/s
ge and g p Equator gravity and pole gravity respectively, and the earth gravity oblateness is as follows:
Figure BDA0002024227150000122
β 1 represents the ratio to the equatorial gravity:
Figure BDA0002024227150000123
β 2 represents the gradient of gravity falling with height:
Figure BDA0002024227150000124
setting the geographic information under the local coordinate system to be kept unchanged, h is approximately equal to 0,
longitude and latitude information:
Figure BDA0002024227150000129
the finishing formula is as follows:
Figure BDA0002024227150000125
Figure BDA0002024227150000126
Figure BDA0002024227150000127
F 15 ＝0 3×3
Figure BDA0002024227150000128
Figure BDA00020242271500001314
Figure BDA0002024227150000133
Figure BDA0002024227150000134
F 34 ＝0 3 × 3 ，F 35 ＝0 3 × 3 ，F 41 ＝F 42 ＝F 43 ＝F 44 ＝F 45 ＝F 51 ＝F 52 ＝F 53 ＝F 54 ＝F 55 ＝0 3 × 3
F 16 ＝F 26 ＝F 36 ＝F 46 ＝F 56 ＝0 3×8 ，F 61 ＝F 62 ＝F 63 ＝F 64 ＝F 65 ＝0 8×3 ，F 66 ＝0 8×8
2. establishing a measurement equation
Figure BDA0002024227150000135
Figure BDA0002024227150000136
Figure BDA0002024227150000137
Figure BDA0002024227150000138
In the formula, the superscript n represents a geographic system, Z represents a measurement equation, the subscript INS represents an inertial system, the subscript OD represents a odometer,
Figure BDA0002024227150000139
and
Figure BDA00020242271500001310
coordinate transformation matrix, v, of odometer 1 and odometer 2, respectively, with respect to the carrier system OD1 And v OD2 The vehicle speeds of the vehicle under the carrier systems of the odometer 1 and the odometer 2 respectively,
Figure BDA00020242271500001311
indicates the angular velocity of the carrier system relative to the earth system,
Figure BDA00020242271500001312
and
Figure BDA00020242271500001313
lever arm value errors, k, of odometer 1 and odometer 2, respectively 1 And k 2 Scale factor for odometer 1 and odometer 2 respectively.
The finishing process comprises the following steps:
Figure BDA0002024227150000141
V＝V
discretization of Kalman filtering system equation and measurement equation
Making approximate discretization equivalence:
X k ＝Φ k/k-1 X k-1 +Γ k-1 W k-1
in which a discretized time interval T is set s ＝t k -t k-1 Then the state transition matrix takes a first order truncation, having:
Figure BDA0002024227150000142
Figure BDA0002024227150000143
W k-1 is a system noise vector, V k For measuring the noise vector, both are zero-mean gaussian white noise vector sequences (obeying normal distribution), and they are not correlated with each other, i.e. they satisfy:
Figure BDA0002024227150000144
the fundamental assumption of noise requirements in a Kalman Filter State space model, generally requires Q k Is semi-positive and R k Is positive, i.e. Q k Not less than 0 and R k Is greater than 0. The complete Kalman filtering algorithm can be divided into five basic formulas as follows:
(1) State one-step prediction
Figure BDA0002024227150000145
(2) State one-step prediction mean square error
Figure BDA0002024227150000146
(3) Filter gain
Figure BDA0002024227150000147
(4) State estimation
Figure BDA0002024227150000148
(5) State estimation mean square error
P k ＝(I-K k H k )P k/k-1
4. Feedback correction
And feeding back the Kalman filtered gyroscope and acceleration zero offset to a device compensation position for correction, feeding back the attitude to an attitude updating compensation position, feeding back the speed and position errors to the output value calculated by the INS for correction, and returning the error state to 0 after feedback.
While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A measurement error compensation method of a vehicle-mounted INS/OD combined navigation system is characterized by comprising the following steps:
step 1: initializing an INS when the vehicle is static, and measuring and calibrating a mounting angle error, a lever arm error and a mileage gauge scale coefficient by using a measuring instrument and a vehicle body structure;
and 2, step: judging the availability of the odometer data: judging whether the vehicle slips, sideslips and jumps according to the running state of the vehicle, if so, not using odometer feedback, and if not, carrying out combined navigation and inputting the output speed data of the left and right odometers into a combined filter;
and step 3: acquiring INS original navigation data in the running process of a vehicle;
and 4, step 4: performing device compensation, attitude calculation and navigation calculation on INS original navigation data, and inputting the obtained speed increment attitude, speed and position into a combined filter;
and 5: after the data input of the combined filter is finished, establishing a state equation of the combined navigation system, estimating the state equation, and after each time of filtering, performing feedback correction on an INS calculation result by using a result estimated by filtering;
the step 5 comprises the following sub-steps:
step 51: establishing a system equation;
step 52: establishing a measurement equation;
step 53: establishing a kalman filtering system equation and discretizing a measurement equation;
step 54: feedback correction is carried out by utilizing a kalman filtering system equation;
the specific process of step 51 is as follows: after the data in the step 2 and the step 4 are input into the filter, a state equation of the integrated navigation system is established, the 23-dimensional error state vector is estimated by adopting an error state vector which specifically comprises position, speed, attitude, gyro random constant drift epsilon, accelerometer random constant zero bias v, left and right odometer scale coefficient errors and 23-dimensional error state quantity of a lever arm, the speed settled by the two systems, the difference value of the position and the attitude and the result obtained after compensating the measurement error are used as measurement, and after each time of filtering, the position error estimated by filtering is utilized
Figure FDA0003954178880000011
Error in velocity
Figure FDA0003954178880000012
Error of misalignment angle
Figure FDA0003954178880000013
Gyro random constant drift
Figure FDA0003954178880000014
Accelerometer random constant zero offset
Figure FDA0003954178880000015
Performing feedback correction on the INS calculation result, and performing feedback correction on the odometer by the odometer scale coefficient error;
through filtering calculation, a system equation is established as follows:
Figure FDA0003954178880000021
wherein: x: an error state vector;
f: a system matrix;
g: a noise distribution matrix;
w: a zero mean gaussian white noise vector;
z: measuring the vector;
h: measuring a matrix;
v: measuring a noise state vector;
b at the relevant subscript position represents the carrier system, n represents the geographic system, e represents the earth system, i represents the inertial system;
Figure FDA00039541788800000223
wherein X is a state vector, phi 1 The method comprises the following steps: phi is a unit of E 、φ N And phi U Respectively, attitude error, δ v, in east-north-sky geographic coordinate system n The method comprises the following steps: delta v E 、δv N And δ v U Velocity errors in the east-north-sky geographic coordinate system, respectively, δ p includes: δ L, δ λ, and δ h are position errors of longitude, latitude, and altitude, and ε includes: epsilon x 、ε y And ε z Respectively the zero offset of three coordinate axes of the gyroscope,
Figure FDA0003954178880000022
the method comprises the following steps:
Figure FDA0003954178880000023
and
Figure FDA0003954178880000024
zero offset, δ k, of the three axes of the accelerometer, respectively 1 And δ k 2 Scale factor errors for odometer 1 and odometer 2 respectively,
Figure FDA0003954178880000025
the method comprises the following steps:
Figure FDA0003954178880000026
and
Figure FDA0003954178880000027
the lever arm values of the three coordinate axes of the odometer 1,
Figure FDA0003954178880000028
the method comprises the following steps:
Figure FDA0003954178880000029
and
Figure FDA00039541788800000210
lever arm values of three coordinate axes of the odometer 2 are respectively;
Figure FDA00039541788800000211
Figure FDA00039541788800000212
Figure FDA00039541788800000213
Figure FDA00039541788800000214
Figure FDA00039541788800000215
in the formula (I), the compound is shown in the specification,
Figure FDA00039541788800000216
is the angular velocity of the geographic system relative to the inertial system,
Figure FDA00039541788800000217
the angular velocity error of the earth system relative to the inertial system,
Figure FDA00039541788800000218
the angular velocity error of the geographic system relative to the earth system,
Figure FDA00039541788800000219
is a coordinate transformation matrix of carrier system to geographic system,
Figure FDA00039541788800000220
is the angular velocity error of the carrier system relative to the inertial system,
Figure FDA00039541788800000221
is the output specific force, v, of the carrier system relative to the inertial navigation system accelerometer under the geographic system n Is the speed of the carrier under the geographic system,
Figure FDA00039541788800000222
is the angular velocity of the earth system relative to the inertial system,
Figure FDA0003954178880000031
is the angular velocity, δ v, of the geographic system relative to the Earth's system n Is the speed error of the carrier under the geographical region,
Figure FDA0003954178880000032
is the output specific force error, delta g, of the inertial navigation system accelerometer under the carrier system relative to the geographic system n As error of gravitational acceleration, R M Radius of the mortise, h local altitude, L local latitude and R N And for the meridian radius, the single phi represents a mathematical platform error angle in the strapdown inertial navigation system.
2. The method as claimed in claim 1, wherein the slip determination condition in step 2 is:
v OD ≤ωR
in the formula, v OD The vehicle speed under the vehicle system, omega is the wheel angular speed, and R is the wheel radius.
3. The method as claimed in claim 2, wherein the sideslip determination condition in step 2 is:
Δy≥v ODy ΔT
where Δ y is the lateral displacement increment in the carrier system, v ODy The vehicle speed is the lower side of the carrier system, and delta T is the change time.
4. The method as claimed in claim 3, wherein the jump determination condition in step 2 is:
Δa z ≥Δa th
in the formula,. DELTA.a z Is the actual change value of vertical acceleration, Δ a th Is a reasonable variation value of the vertical acceleration.
5. The method as claimed in claim 1, wherein the velocity increment attitude, the velocity and the position in the step 4 are calculated by a two-subsample cone error compensation algorithm, and the corresponding calculation equation set is as follows:
Figure FDA0003954178880000033
Figure FDA0003954178880000034
Figure FDA0003954178880000035
Figure FDA0003954178880000036
in the formula,. DELTA.theta. m1 And Δ θ m2 Corresponding angle increment is sampled for the gyro at two equal intervals, T is sampling time,
Figure FDA0003954178880000037
for reference by the inertial frame, the carrier is moved from t m-1 Time to t m The change in the rotation at a moment in time,
Figure FDA0003954178880000038
for reference to the inertial frame, the geographic system is set from t m Time to t m-1 The rotation change of the moment, subscript i represents the inertial navigation system calculation value, upper subscript b represents the load system, upper subscript n represents the geography system, and (m) represents t m Time, (m-1) represents t m-1 At the moment, phi represents the corresponding posture with the subscript, I represents the identity matrix,
Figure FDA0003954178880000041
is a constant value.
6. The method as claimed in claim 1, wherein the measurement equation in step 52 is described as:
Figure FDA0003954178880000042
Figure FDA0003954178880000043
Figure FDA0003954178880000044
Figure FDA0003954178880000045
in the formula, the superscript n represents a geographic system, Z represents a measurement equation, the subscript INS represents an inertial system, the subscript OD represents a odometer,
Figure FDA0003954178880000046
and
Figure FDA0003954178880000047
coordinate transformation matrix, v, of odometer 1 and odometer 2, respectively, with respect to the carrier system OD1 And v OD2 The vehicle speeds of the vehicle under the carrier systems of the odometer 1 and the odometer 2 respectively,
Figure FDA0003954178880000048
indicates the angular velocity of the carrier system relative to the earth system,
Figure FDA0003954178880000049
and
Figure FDA00039541788800000410
lever arm value errors, k, of odometer 1 and odometer 2, respectively 1 And k 2 Scale factor for odometer 1 and odometer 2 respectively.
7. The method as claimed in claim 1, wherein the step 5 further comprises: feeding back the kalman filtered gyroscope and the acceleration zero offset to a device compensation position for correction, feeding back the attitude to an attitude updating compensation position, and feeding back the speed and position errors to the output value calculated by the INS for correction, namely: by modified
Figure FDA00039541788800000411
The heading angle psi, the pitch angle theta and the rolling angle gamma can be obtained through solution, and after the primary filtering feedback, the error state returns to 0.
8. The method as claimed in claim 7, wherein the corrected measurement error is compensated for by the vehicle INS/OD combined navigation system
Figure FDA00039541788800000412
The heading angle psi, the pitch angle theta and the roll angle gamma can be obtained through solution, and the corresponding description formula is as follows:
Figure FDA00039541788800000413
in the formula, (numeral 1, numeral 2) represents a specific corresponding matrix element in the matrix.
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