CN113375694A - Low-cost gyroscope all-zero-offset rapid estimation method under static base condition - Google Patents
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Abstract
The invention discloses a low-cost gyroscope total zero offset rapid estimation method under a static base conditionTriaxial 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
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 informationTriaxial 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:
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;
wherein the content of the first and second substances,the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
wherein the content of the first and second substances,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;
wherein the content of the first and second substances,for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,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:
wherein the content of the first and second substances,is the velocity at the time of the k-time, is the component of the velocity at time k in the northeast direction of the navigation system;
is the velocity at the time k-1, is the component of the velocity at time k-1 in the northeast direction of the navigation system;
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:
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:
Wherein:
wherein, L is the latitude of the carrier,being the output of a three-axis accelerometerThe component in the northeast direction of the navigation system, i.e.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,the state quantity one-step prediction value from the k-1 moment to the k moment,is an estimate of the filter state quantity at time k-1,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,zero-offset for the three axes of the gyroscope;
(32) calculating a one-step predicted mean square error Pk|k-1
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;
Qk-1for the system noise at time k-1, diag represents the matrix diagonalization, where εgx、εgy、εgzAre respectively asModel noise of (e ∈)ax、εay、εazAre respectively asThe model noise of (1);
(33) calculating filter gain K of Kalman filter at moment Kk:
Wherein the content of the first and second substances,
M5=[secθsinγ△T 0 -secθcosγ△T];
wherein HkIs a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,Respectively transverse roll angle of the carrierPitch angle, course angle:
wherein q is0、q1、q2、q3Is a quaternion representing the attitude of the carrier;
wherein R iskFor the measurement noise at time k, diag represents the matrix diagonalization,respectively, the noise of the horizontal velocity measurement,for the noise of angle measurement, superscript-1 represents matrix inversion;
Wherein the content of the first and second substances,is an estimate of the filter state quantity at time k,the state quantity one-step prediction value from the k-1 moment to the k moment,is a measured value at the time k,being the component of the velocity at time k in the northeast direction of the navigation system,the heading at the time k is the current heading,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 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.
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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 gyroscopeThree-axis accelerometer
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:
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;
wherein the content of the first and second substances,the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
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;
for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,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:
wherein:
is the velocity at the time of the k-time,is the component of the velocity at time k in the northeast direction of the navigation system;
is the velocity at the time k-1,velocity at time k-1 in the navigation systemA component in the north-sky direction;
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:
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.
In the formula (I), the compound is shown in the specification,
wherein, L is the latitude of the carrier,being the output of a three-axis accelerometerThe component in the northeast direction of the navigation system, i.e. 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,the state quantity one-step prediction value from the k-1 moment to the k moment,is an estimate of the filter state quantity at time k-1,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,the gyroscope is provided with three axes with zero offset.
(3.2) calculating a one-step prediction mean square error Pk|k-1:
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;
Qk-1for the system noise at time k-1, diag represents the matrix diagonalization, where εgx、εgy、εgzAre respectively asModel noise of (e ∈)ax、εay、εazAre respectively asThe model noise of (1).
(3.3) calculating the filtering of a Kalman filter at the k moment: wave gain Kk:
In the formula (I), the compound is shown in the specification,
M5=[secθsinγ△T 0 -secθcosγ△T]
Hkis a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,Roll angle, pitch angle, course angle of the carrier, respectively, can be calculated by the following formula:
q0、q1、q2、q3is a quaternion representing the attitude of the carrier;
Rkfor the measurement noise at time k, diag represents the matrix diagonalization, whereRespectively, the noise of the horizontal velocity measurement,for the noise of the angle measurement, the superscript-1 represents the matrix inversion.
Wherein the content of the first and second substances,is an estimate of the filter state quantity at time k,the state quantity one-step prediction value from the k-1 moment to the k moment,is a measured value at the time k,velocity at time k in the northeast direction of the navigation systemIs calculated by using the prediction formula in the step 2,the heading at the time k is the current heading,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 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 informationTriaxial 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:
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;
wherein the content of the first and second substances,the component of the angular speed of the machine system relative to the navigation system at the moment k on the machine system;
a posture transfer matrix from the navigation system to the body system at the moment of k-1;
wherein the content of the first and second substances,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;
wherein the content of the first and second substances,for the component of the angular velocity of the navigation system relative to the earth system at time k-1 on the navigation system,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:
wherein the content of the first and second substances,is the velocity at the time of the k-time, is the component of the velocity at time k in the northeast direction of the navigation system;
is the velocity at the time k-1, is the component of the velocity at time k-1 in the northeast direction of the navigation system;
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:
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:
Wherein:
wherein, L is the latitude of the carrier,being the output of a three-axis accelerometerThe component in the northeast direction of the navigation system, i.e. 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,the state quantity one-step prediction value from the k-1 moment to the k moment,is an estimate of the filter state quantity at time k-1,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,zero-offset for the three axes of the gyroscope;
(32) calculating a one-step predicted mean square error Pk|k-1
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;
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 asModel noise of (e ∈)ax、εay、εazAre respectively asThe model noise of (1);
(33) calculating filter gain K of Kalman filter at moment Kk:
Wherein the content of the first and second substances,
M5=[secθsinγΔT 0 -secθcosγΔT];
wherein HkIs a measurement matrix at time k, I2×2Is a 2 x 2 unit matrix, gamma, theta,Roll angle, pitch angle, course angle of the carrier:
wherein q is0、q1、q2、q3Is a quaternion representing the attitude of the carrier;
wherein R iskFor the measurement noise at time k, diag represents the matrix diagonalization,are respectively asThe noise of the horizontal velocity measurement is reduced,for the noise of angle measurement, superscript-1 represents matrix inversion;
Wherein the content of the first and second substances,is an estimate of the filter state quantity at time k,the state quantity one-step prediction value from the k-1 moment to the k moment,is a measured value at the time k,being the component of the velocity at time k in the northeast direction of the navigation system,the heading at the time k is the current heading,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;
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祝燕华等: "低成本捷联惯导系统的静基座快速精对准方法", 《上海交通大学学报》, vol. 42, no. 5, pages 836 - 840 * |
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