CN113375694A - Low-cost gyroscope all-zero-offset rapid estimation method under static base condition - Google Patents

Low-cost gyroscope all-zero-offset rapid estimation method under static base condition Download PDF

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CN113375694A
CN113375694A CN202110569622.6A CN202110569622A CN113375694A CN 113375694 A CN113375694 A CN 113375694A CN 202110569622 A CN202110569622 A CN 202110569622A CN 113375694 A CN113375694 A CN 113375694A
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moment
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matrix
zero
navigation system
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岑益挺
吕品
赖际舟
李志敏
孙鑫
白师宇
王炳清
许晓伟
余文斌
朱静漪
刘瑞
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a low-cost gyroscope total zero offset rapid estimation method under a static base condition
Figure DDA0003082156260000011
Triaxial accelerometer information fb(k) (ii) a Secondly, predicting the attitude, the speed and the position information of the carrier at the moment k according to the inertial sensor data at the moment k; then, estimating the zero offset of the triaxial gyroscope at the moment k through a Kalman filter; the operation is repeated in a circulating way. Aiming at the problem that the observability of the zero offset of the top in the direction of the sky is poor and the observability is slow in the traditional static base initial alignment method taking the speed error as the observed quantity when the zero offset of the top is large, the observability of the zero offset of the top in the direction of the sky can be improved by introducing the observation of the angle error, and the quick estimation of the zero offset of the top is realized; and professional equipment such as a rotary table is not needed, the method is suitable for being used in an external field, and the engineering application value is high.

Description

Low-cost gyroscope all-zero-offset rapid estimation method under static base condition
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to a low-cost gyroscope total zero offset rapid estimation method under a static base condition.
Background
Inertial navigation is a common navigation mode, and an inertial device is adopted to solve the attitude, the speed and the position of a carrier in a recursive navigation mode. The inertial navigation has the advantages of strong autonomy, no external interference and complete output information, and has wide application in aviation, aerospace and navigation. The precision of the inertial navigation system mainly depends on the precision of the gyroscope, so that the estimation and compensation of the deviation of the gyroscope is an effective method for improving the precision of the inertial navigation system.
Before the inertial device is actually used, the inertial device needs to be fully calibrated in advance. However, the calibration in advance can only compensate the influence of deterministic errors on the inertial system, and for the gyro zero offset, the successive start changes, especially for the inertial device with low cost, the constant zero offset is large, and usually, the online estimation is performed on the gyro zero offset by using the kalman filtering technology at the initial alignment stage of the inertial navigation system. The traditional static base estimation method taking the speed error as the observed quantity has poor observability on the zero offset of the zenith gyroscope, and limits the rapidity of estimation. While the method of improving observability through multi-position rotational alignment requires the addition of indexing mechanisms, which is very inconvenient for many practical applications.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems that the traditional low-cost gyro estimation cannot quickly estimate all zero offsets, the requirements of supporting facilities are high and the like, the method for quickly estimating all zero offsets of the low-cost gyro under the condition of a static base is provided.
The invention content is as follows: the invention provides a method for quickly estimating all zero offsets of a low-cost gyroscope under the condition of a static base, which specifically comprises the following steps:
(1) periodically acquiring inertial sensor data of the carrier at the moment k under the static condition of the carrier, wherein the inertial sensor data comprises three-axis gyro information
Figure BDA0003082156240000011
Triaxial accelerometer information fb(k)；
(2) Predicting the attitude, the speed and the position information of the carrier at the moment k according to the inertial sensor data at the moment k;
(3) estimating the zero offset of the triaxial gyro at the moment k through a Kalman filter;
(4) skipping to the step (1) and circularly reciprocating.
Further, the process of predicting the posture of the carrier at the time k in the step (2) is as follows:
Figure BDA0003082156240000021
wherein q (k) ═ q0(k) q1(k) q2(k) q3(k)]TThe attitude quaternion at the moment k is marked with T to represent the transposition of the matrix;
q(k-1)＝[q0(k-1) q1(k-1) q2(k-1) q3(k-1)]Tis the attitude quaternion at the moment of k-1; Δ T is the discrete sampling period;
Figure BDA0003082156240000022
Figure BDA0003082156240000023
wherein the content of the first and second substances,
Figure BDA0003082156240000024
the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
Figure BDA0003082156240000025
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
Figure BDA0003082156240000026
wherein the content of the first and second substances,
Figure BDA0003082156240000027
is the component of the earth rotation angular rate on the navigation system at the time k-1, omegaieIs the rotation angular rate of the earth, and L (k-1) is the latitude at the moment k-1;
Figure BDA0003082156240000028
wherein the content of the first and second substances,
Figure BDA0003082156240000029
for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,
Figure BDA00030821562400000210
is the component of the velocity at time k-1 in the northeast direction of the navigation system, L (k-1), h (k-1) are the latitude and altitude at time k-1, RM、RNThe radius of the meridian and unitary mortise of the earth.
Further, the process of predicting the speed of the carrier at the time k in the step (2) is as follows:
Figure BDA00030821562400000211
wherein the content of the first and second substances,
Figure BDA0003082156240000031
is the velocity at the time of the k-time,
Figure BDA0003082156240000032
Figure BDA0003082156240000033
is the component of the velocity at time k in the northeast direction of the navigation system;
Figure BDA0003082156240000034
is the velocity at the time k-1,
Figure BDA0003082156240000035
Figure BDA0003082156240000036
is the component of the velocity at time k-1 in the northeast direction of the navigation system;
Figure BDA0003082156240000037
a posture transfer matrix from the machine system to the navigation system at the moment k;
gnis the component of the earth's gravitational acceleration on the navigation system.
Further, the process of predicting the position of the carrier at the time k in the step (2) is as follows:
Figure BDA0003082156240000038
Figure BDA0003082156240000039
Figure BDA00030821562400000310
wherein λ (k), l (k), h (k) are longitude, latitude and altitude at time k; λ (k-1), L (k-1) and h (k-1) are longitude, latitude and height at the moment of k-1; rM、RNThe radius of the meridian and unitary mortise of the earth.
Further, the step (3) includes the steps of:
(31) calculating a one-step prediction value of a state quantity
Figure BDA00030821562400000311
Figure BDA00030821562400000312
Wherein:
Figure BDA00030821562400000313
Figure BDA00030821562400000314
Figure BDA00030821562400000315
Figure BDA0003082156240000041
wherein, L is the latitude of the carrier,
Figure BDA0003082156240000042
being the output of a three-axis accelerometer
Figure BDA0003082156240000043
The component in the northeast direction of the navigation system, i.e.
Figure BDA0003082156240000044
For the attitude transfer matrix from machine hierarchy to navigation hierarchy, 0m×nIs a zero matrix of m x n, phik,k-1For the one-step transition matrix from time k-1 to time k of the filter,
Figure BDA0003082156240000045
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure BDA0003082156240000046
is an estimate of the filter state quantity at time k-1,
Figure BDA0003082156240000047
φE、φN、φUis east, north and sky platform error angle delta vE、δvNThe errors of the speed in the east direction and the north direction,
Figure BDA0003082156240000048
zero-offset for the three axes of the gyroscope;
(32) calculating a one-step predicted mean square error Pk|k-1
Figure BDA0003082156240000049
Wherein, Pk|k-1Predicting mean square error, P, for one step from time k-1 to time kk-1Estimating the mean square error for the state at the moment of k-1, and expressing a matrix transpose by using a superscript T;
Figure BDA00030821562400000410
Figure BDA00030821562400000411
representing and taking matrix
Figure BDA00030821562400000412
Row m, Γk-1The system noise matrix at the moment of the filter k-1;
Figure BDA00030821562400000413
Qk-1for the system noise at time k-1, diag represents the matrix diagonalization, where εgx、εgy、εgzAre respectively as
Figure BDA00030821562400000414
Model noise of (e ∈)ax、εay、εazAre respectively as
Figure BDA00030821562400000415
The model noise of (1);
(33) calculating filter gain K of Kalman filter at moment Kk：
Figure BDA00030821562400000416
Wherein the content of the first and second substances,
Figure BDA0003082156240000051
Figure BDA0003082156240000052
M5＝[secθsinγ△T 0 -secθcosγ△T]；
wherein HkIs a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,
Figure BDA0003082156240000053
Respectively transverse roll angle of the carrierPitch angle, course angle:
Figure BDA0003082156240000054
Figure BDA0003082156240000055
Figure BDA0003082156240000056
Figure BDA0003082156240000057
Figure BDA0003082156240000058
wherein q is0、q1、q2、q3Is a quaternion representing the attitude of the carrier;
Figure BDA0003082156240000059
wherein R iskFor the measurement noise at time k, diag represents the matrix diagonalization,
Figure BDA00030821562400000510
respectively, the noise of the horizontal velocity measurement,
Figure BDA00030821562400000511
for the noise of angle measurement, superscript-1 represents matrix inversion;
(34) calculating state estimation value of Kalman filter at k moment
Figure BDA00030821562400000512
Figure BDA00030821562400000513
Wherein the content of the first and second substances,
Figure BDA00030821562400000514
is an estimate of the filter state quantity at time k,
Figure BDA00030821562400000515
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure BDA0003082156240000061
is a measured value at the time k,
Figure BDA0003082156240000062
being the component of the velocity at time k in the northeast direction of the navigation system,
Figure BDA0003082156240000063
the heading at the time k is the current heading,
Figure BDA0003082156240000064
the course at the moment k-1;
(35) computing an estimated mean square error P of a Kalman filter at time kk|k：
Pk|k＝(I-KkHk)Pk|k-1
Wherein, Pk|kThe estimated mean square error at the moment k is shown, and I is an identity matrix;
(36) based on Kalman filters, through measurement ZkZero bias for three-axis gyroscope in state quantity
Figure BDA0003082156240000065
Figure BDA0003082156240000066
And (6) estimating.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: under the condition of a static base, the quick estimation of all zero offsets of the low-cost gyroscope can be realized, a turntable is not needed, and the engineering application is simple and convenient; compared with the traditional static base initial alignment method taking the speed error as the observed quantity, the method has the problem of poor observability of the zero offset of the top in the sky direction and slow estimation when the zero offset of the top is large; the invention only needs to be static for a period of time, and does not need professional equipment such as a turntable, so the invention is very suitable for being used in an external field and has high engineering application value.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram comparing the results of the gyro zero-offset estimation using the conventional gyro zero-offset estimation method using the velocity error as the observed quantity and the gyro X-axis zero-offset estimation according to the present invention;
FIG. 3 is a diagram comparing the results of the gyro Y-axis zero-offset estimation using the conventional gyro zero-offset estimation method using the velocity error as the observed quantity and the gyro Y-axis zero-offset estimation of the present invention;
FIG. 4 is a diagram comparing the zero offset estimation of gyroscope Z axis using traditional method using velocity error as observation and the zero offset estimation result of gyroscope Z axis in the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a method for quickly estimating all zero offsets of a low-cost gyroscope under the condition of a static base, which specifically comprises the following steps as shown in figure 1:
step 1, periodically collecting inertial sensor data of a carrier at the moment k under a static condition, wherein the inertial sensor data comprises a three-axis gyroscope
Figure BDA0003082156240000071
Three-axis accelerometer
Figure BDA0003082156240000072
And 2, predicting the attitude, the speed and the position information of the carrier at the moment k.
(2.1) predicting the posture of the carrier by adopting the following formula:
Figure BDA0003082156240000073
wherein:
q(k)＝[q0(k) q1(k) q2(k) q3(k)]T
the attitude quaternion at the moment k is marked with T to represent the transposition of the matrix;
q(k-1)＝[q0(k-1) q1(k-1) q2(k-1) q3(k-1)]T
is the attitude quaternion at the moment of k-1;
Δ T is the discrete sampling period;
Figure BDA0003082156240000074
Figure BDA0003082156240000075
wherein the content of the first and second substances,
Figure BDA0003082156240000076
the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
Figure BDA0003082156240000077
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
Figure BDA0003082156240000078
Figure BDA0003082156240000079
is the k-1 time earthComponent of angular rate of rotation on the navigation system, ωieIs the rotation angular rate of the earth, and L (k-1) is the latitude at the moment k-1;
Figure BDA00030821562400000710
Figure BDA00030821562400000711
for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,
Figure BDA00030821562400000712
is the component of the velocity at time k-1 in the northeast direction of the navigation system, L (k-1), h (k-1) are the latitude and altitude at time k-1, RM、RNThe radius of the meridian and unitary mortise of the earth.
(2.2) predicting the speed of the carrier by using the following formula:
Figure BDA0003082156240000081
wherein:
Figure BDA0003082156240000082
is the velocity at the time of the k-time,
Figure BDA0003082156240000083
is the component of the velocity at time k in the northeast direction of the navigation system;
Figure BDA0003082156240000084
is the velocity at the time k-1,
Figure BDA0003082156240000085
velocity at time k-1 in the navigation systemA component in the north-sky direction;
Figure BDA0003082156240000086
a posture transfer matrix from the machine system to the navigation system at the moment k;
gnis the component of the earth's gravitational acceleration on the navigation system.
(2.3) predicting the position of the carrier using the following formula:
Figure BDA0003082156240000087
Figure BDA0003082156240000088
Figure BDA0003082156240000089
wherein:
λ (k), L (k), h (k) are longitude, latitude and altitude at time k;
λ (k-1), L (k-1) and h (k-1) are longitude, latitude and height at the moment of k-1;
RM、RNthe radius of the meridian and unitary mortise of the earth.
And 3, estimating the zero offset of the three-axis gyroscope at the moment k through a Kalman filter.
(3.1) calculating one-step prediction value of State quantity
Figure BDA00030821562400000810
Figure BDA00030821562400000811
In the formula (I), the compound is shown in the specification,
Figure BDA0003082156240000091
Figure BDA0003082156240000092
Figure BDA0003082156240000093
Figure BDA0003082156240000094
wherein, L is the latitude of the carrier,
Figure BDA0003082156240000095
being the output of a three-axis accelerometer
Figure BDA0003082156240000096
The component in the northeast direction of the navigation system, i.e.
Figure BDA0003082156240000097
Figure BDA00030821562400000914
For the attitude transfer matrix from machine hierarchy to navigation hierarchy, 0m×nIs a zero matrix of m x n, phik,k-1For the one-step transition matrix from time k-1 to time k of the filter,
Figure BDA0003082156240000098
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure BDA0003082156240000099
is an estimate of the filter state quantity at time k-1,
Figure BDA00030821562400000910
φE、φN、φUis east, north and sky platform error angle delta vE、δvNThe errors of the speed in the east direction and the north direction,
Figure BDA00030821562400000911
the gyroscope is provided with three axes with zero offset.
(3.2) calculating a one-step prediction mean square error Pk|k-1：
Figure BDA00030821562400000912
In the formula (I), the compound is shown in the specification,
Pk|k-1predicting mean square error, P, for one step from time k-1 to time kk-1Estimating the mean square error for the state at the moment of k-1, and expressing a matrix transpose by using a superscript T;
Figure BDA00030821562400000913
Figure BDA0003082156240000101
representing and taking matrix
Figure BDA0003082156240000102
Row m, Γk-1The system noise matrix at the moment of the filter k-1;
Figure BDA0003082156240000103
Qk-1for the system noise at time k-1, diag represents the matrix diagonalization, where εgx、εgy、εgzAre respectively as
Figure BDA0003082156240000104
Model noise of (e ∈)ax、εay、εazAre respectively as
Figure BDA0003082156240000105
The model noise of (1).
(3.3) calculating the filtering of a Kalman filter at the k moment: wave gain Kk：
Figure BDA0003082156240000106
In the formula (I), the compound is shown in the specification,
Figure BDA0003082156240000107
Figure BDA0003082156240000108
M5＝[secθsinγ△T 0 -secθcosγ△T]
Hkis a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,
Figure BDA0003082156240000109
Roll angle, pitch angle, course angle of the carrier, respectively, can be calculated by the following formula:
Figure BDA00030821562400001010
Figure BDA00030821562400001011
Figure BDA00030821562400001012
Figure BDA00030821562400001013
Figure BDA00030821562400001014
q0、q1、q2、q3is a quaternion representing the attitude of the carrier;
Figure BDA0003082156240000111
Rkfor the measurement noise at time k, diag represents the matrix diagonalization, where
Figure BDA0003082156240000112
Respectively, the noise of the horizontal velocity measurement,
Figure BDA0003082156240000113
for the noise of the angle measurement, the superscript-1 represents the matrix inversion.
(3.4) calculating the state estimation value of the Kalman filter at the k moment
Figure BDA0003082156240000114
Figure BDA0003082156240000115
Wherein the content of the first and second substances,
Figure BDA0003082156240000116
is an estimate of the filter state quantity at time k,
Figure BDA0003082156240000117
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure BDA0003082156240000118
is a measured value at the time k,
Figure BDA0003082156240000119
velocity at time k in the northeast direction of the navigation systemIs calculated by using the prediction formula in the step 2,
Figure BDA00030821562400001110
the heading at the time k is the current heading,
Figure BDA00030821562400001111
the heading at time k-1.
(3.5) calculating the estimated mean square error P of the k-time Kalman filterk|k：
Pk|k＝(I-KkHk)Pk|k-1
Wherein, Pk|kI is the estimated mean square error at time k and I is the identity matrix.
(3.6) measurement of quantity Z based on Kalman FilterkZero bias for three-axis gyroscope in state quantity
Figure BDA00030821562400001112
Figure BDA00030821562400001113
And (6) estimating.
And 4, step 4: skipping to the step 1 and repeating the steps circularly.
The Kalman filtering is a process of alternating time updating and measurement correction, the time updating is to periodically collect inertial sensor data for prediction, and the measurement correction is to correct the result of the time updating prediction. The time of the cycle is consistent with the time of the actual operation.
The method is experimentally verified in a simulation mode. The simulation conditions were set as follows: the gyro constant drift is 10 degrees/h, and the random drift is 50 degrees/h; the accelerometer constant zero offset is 1mg, and the random drift is 1 mg; initial misalignment angle phiE、φN、φUIs 3 ', 30'; a static experiment of a simulation system is carried out, wherein the geographic longitude is 110 degrees, the geographic latitude is 20 degrees, the initial posture is zero, and the initial speed is zero. The sampling frequency of the gyroscope and the accelerometer is 100 Hz. The initial values of the state variables are all zero, and the initial covariance matrix P0System noise variance matrix Q andthe measurement noise variance matrix R is set as follows:
P0＝diag{(3')2,(3')2,(30')2,(0.01m/s)2,(0.01m/s)2,(10°)2,(10°)2,(10°)2}
Q＝diag{(50°)2,(50°)2,(50°)2,(1mg)2,(1mg)2,(1mg)2}
R＝diag{(0.01m/s)2,(0.01m/s)2,(0.5°)2}
FIG. 2, FIG. 3, and FIG. 4 are graphs comparing the results of zero offset estimation of X-axis, Y-axis, and Z-axis of a gyroscope respectively when the conventional method for estimating zero offset of a gyroscope using velocity error as observed quantity and the method of the present invention are used. As can be seen from the figures 2, 3 and 4, the X-axis and Y-axis zero offset of the gyroscope can be quickly and accurately estimated by the traditional method, but the zero offset of the gyroscope on the Z axis is poor in observability, and the zero offset of the Z axis is not accurately estimated in 1h, but the zero offset of the Z axis is accurately estimated by the method in about 500s, so that the estimation precision is improved, and the estimation speed is accelerated.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (5)

1. A low-cost gyro total zero offset rapid estimation method under the condition of a static base is characterized by comprising the following steps:
(1) periodically acquiring inertial sensor data of the carrier at the moment k under the static condition of the carrier, wherein the inertial sensor data comprises three-axis gyro information
Figure FDA0003082156230000011
Triaxial accelerometer information fb(k)；
(2) Predicting the attitude, the speed and the position information of the carrier at the moment k according to the inertial sensor data at the moment k;
(3) estimating the zero offset of the triaxial gyro at the moment k through a Kalman filter;
(4) skipping to the step (1) and circularly reciprocating.
2. The method for fast estimating all zero offsets of low-cost gyros under the condition of a static base according to claim 1, wherein the process of predicting the attitude of the carrier at the k moment in the step (2) is as follows:
Figure FDA0003082156230000012
wherein q (k) ═ q0(k) q1(k) q2(k) q3(k)]TThe attitude quaternion at the moment k is marked with T to represent the transposition of the matrix;
q(k-1)＝[q0(k-1) q1(k-1) q2(k-1) q3(k-1)]Tis the attitude quaternion at the moment of k-1; Δ T is the discrete sampling period;
Figure FDA0003082156230000013
Figure FDA0003082156230000014
wherein the content of the first and second substances,
Figure FDA0003082156230000015
the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
Figure FDA0003082156230000016
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
Figure FDA0003082156230000017
wherein the content of the first and second substances,
Figure FDA0003082156230000018
is the component of the earth rotation angular rate on the navigation system at the time k-1, omegaieIs the rotation angular rate of the earth, and L (k-1) is the latitude at the moment k-1;
Figure FDA0003082156230000021
wherein the content of the first and second substances,
Figure FDA0003082156230000022
for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,
Figure FDA0003082156230000023
is the component of the velocity at time k-1 in the northeast direction of the navigation system, L (k-1), h (k-1) are the latitude and altitude at time k-1, RM、RNThe radius of the meridian and unitary mortise of the earth.
3. The method for fast estimating all zero offsets of low-cost gyros under the condition of a static base as claimed in claim 1, wherein the process of predicting the speed of the carrier at the time k in the step (2) is as follows:
Figure FDA0003082156230000024
wherein the content of the first and second substances,
Figure FDA0003082156230000025
is the velocity at the time of the k-time,
Figure FDA0003082156230000026
Figure FDA0003082156230000027
is the component of the velocity at time k in the northeast direction of the navigation system;
Figure FDA0003082156230000028
is the velocity at the time k-1,
Figure FDA0003082156230000029
Figure FDA00030821562300000210
is the component of the velocity at time k-1 in the northeast direction of the navigation system;
Figure FDA00030821562300000211
a posture transfer matrix from the machine system to the navigation system at the moment k;
gnis the component of the earth's gravitational acceleration on the navigation system.
4. The method for fast estimating all zero offsets of low-cost gyros under the condition of a static base according to claim 1, wherein the process of predicting the position of the carrier at the time k in the step (2) is as follows:
Figure FDA00030821562300000212
Figure FDA00030821562300000213
Figure FDA00030821562300000214
wherein λ (k), L (k), h (k) are the longitude of time kLatitude and height; λ (k-1), L (k-1) and h (k-1) are longitude, latitude and height at the moment of k-1; rM、RNThe radius of the meridian and unitary mortise of the earth.
5. The method for fast estimating all zero offsets of low-cost gyros under static base conditions according to claim 1, wherein said step (3) comprises the following steps:
(31) calculating a one-step prediction value of a state quantity
Figure FDA0003082156230000031
Figure FDA0003082156230000032
Wherein:
Figure FDA0003082156230000033
Figure FDA0003082156230000034
Figure FDA0003082156230000035
Figure FDA0003082156230000036
wherein, L is the latitude of the carrier,
Figure FDA0003082156230000037
being the output of a three-axis accelerometer
Figure FDA0003082156230000038
The component in the northeast direction of the navigation system, i.e.
Figure FDA0003082156230000039
Figure FDA00030821562300000310
For the attitude transfer matrix from machine hierarchy to navigation hierarchy, 0m×nIs a zero matrix of m x n, phik，k-1For the one-step transition matrix from time k-1 to time k of the filter,
Figure FDA00030821562300000311
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure FDA00030821562300000312
is an estimate of the filter state quantity at time k-1,
Figure FDA00030821562300000313
φE、φN、φUis east, north and sky platform error angle delta vE、δvNThe errors of the speed in the east direction and the north direction,
Figure FDA00030821562300000314
zero-offset for the three axes of the gyroscope;
(32) calculating a one-step predicted mean square error Pk|k-1
Figure FDA00030821562300000315
Wherein, Pk|k-1Predicting mean square error, P, for one step from time k-1 to time kk-1Estimating the mean square error for the state at the moment of k-1, and expressing a matrix transpose by using a superscript T;
Figure FDA0003082156230000041
Figure FDA0003082156230000042
representing and taking matrix
Figure FDA0003082156230000043
Row m, Γk-1The system noise matrix at the moment of the filter k-1;
Qk-1＝diag{εgx 2，εgy 2，εgz 2，εax 2，εay 2，εaz 2}；
Qk-1for the system noise at time k-1, diag represents the matrix diagonalization, where εgx、εgy、εgzAre respectively as
Figure FDA0003082156230000044
Model noise of (e ∈)ax、εay、εazAre respectively as
Figure FDA0003082156230000045
The model noise of (1);
(33) calculating filter gain K of Kalman filter at moment Kk：
Figure FDA0003082156230000046
Wherein the content of the first and second substances,
Figure FDA0003082156230000047
Figure FDA0003082156230000048
M5＝[secθsinγΔT 0 -secθcosγΔT]；
wherein HkIs a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,
Figure FDA0003082156230000049
Roll angle, pitch angle, course angle of the carrier:
Figure FDA00030821562300000410
Figure FDA00030821562300000411
Figure FDA00030821562300000412
Figure FDA00030821562300000413
Figure FDA0003082156230000051
wherein q is0、q1、q2、q3Is a quaternion representing the attitude of the carrier;
Figure FDA0003082156230000052
wherein R iskFor the measurement noise at time k, diag represents the matrix diagonalization,
Figure FDA0003082156230000053
are respectively asThe noise of the horizontal velocity measurement is reduced,
Figure FDA0003082156230000054
for the noise of angle measurement, superscript-1 represents matrix inversion;
(34) calculating state estimation value of Kalman filter at k moment
Figure FDA0003082156230000055
Figure FDA0003082156230000056
Wherein the content of the first and second substances,
Figure FDA0003082156230000057
is an estimate of the filter state quantity at time k,
Figure FDA0003082156230000058
the state quantity one-step prediction value from the k-1 moment to the k moment,
Figure FDA0003082156230000059
is a measured value at the time k,
Figure FDA00030821562300000510
being the component of the velocity at time k in the northeast direction of the navigation system,
Figure FDA00030821562300000511
the heading at the time k is the current heading,
Figure FDA00030821562300000512
the course at the moment k-1;
(35) computing an estimated mean square error P of a Kalman filter at time kk|k：
Pk|k＝(I-KkHk)Pk|k-1
Wherein, Pk|kThe estimated mean square error at the moment k is shown, and I is an identity matrix;
(36) based on Kalman filters, through measurement ZkZero bias for three-axis gyroscope in state quantity
Figure FDA00030821562300000513
Figure FDA00030821562300000514
And (6) estimating.
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