CN110006447B - Random attitude MEMS combination attitude determination method without initial alignment - Google Patents

Random attitude MEMS combination attitude determination method without initial alignment Download PDF

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CN110006447B
CN110006447B CN201910271775.5A CN201910271775A CN110006447B CN 110006447 B CN110006447 B CN 110006447B CN 201910271775 A CN201910271775 A CN 201910271775A CN 110006447 B CN110006447 B CN 110006447B
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attitude
error
magnetometer
mems
state
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CN110006447A (en
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陈芳
张箭飞
巩英辉
谢佳
郭振西
季登高
孙晓松
武斌
陈志刚
王顺
余颖
张宁宁
韩伯雄
张敏刚
肖文
葛亚杰
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China Academy of Launch Vehicle Technology CALT
Beijing Institute of Near Space Vehicles System Engineering
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Beijing Institute of Near Space Vehicles System Engineering
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses an MEMS combined attitude determination method without initial alignment at any attitude, which comprises the following steps: 1) defining a modified Rodrigues parameter; 2) establishing a nonlinear attitude error state equation based on the corrected Rodrigues parameter; 3) establishing a nonlinear observation equation of the magnetometer; 4) carrying out linearization processing on the nonlinear attitude error state equation and the observation equation of the magnetometer to obtain a linearization state error model of the state error and a linearization observation model of the magnetometer; 5) and obtaining the optimal estimation of the modified Rodrigues parameter by using the obtained nonlinear state error equation and observation equation, combining a linearized state model and an observation model and using an extended Kalman filtering method, wherein the optimal estimation is used as a posture result for guidance control, and the combined posture determination of the MEMS and the magnetometer in any posture is realized.

Description

Random attitude MEMS combination attitude determination method without initial alignment
Technical Field
The invention belongs to the field of navigation guidance, and relates to an MEMS combined attitude determination method for any attitude without initial alignment.
Background
The MEMS inertial device is used as a main navigation device to construct a navigation system to realize attitude determination and positioning through integral calculation, so that initial alignment is required before transmission. The general common initial alignment scheme requires ground to establish a reference point, and performs optical aiming through a ground photoelectric theodolite to acquire initial attitude information of an initial navigation system. The corresponding ground equipment and manufacturing operation flow need to be matched, the alignment time is long, and the combat preparation is complex. The time consumed by initial alignment is an important factor influencing the launching preparation time, and the shortening of the launching preparation time is an important means for improving the rapid response capability of a missile weapon system and the combat efficiency.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the problem that the weapon combat efficiency is reduced by consuming time in initial alignment, an arbitrary attitude MEMS combination attitude determination technology without initial alignment is provided, the three-axis attitude determination is realized through a magnetometer, the ground launching preparation conditions are not required, meanwhile, the launching preparation time is greatly shortened, and the problem of initial alignment of an MEMS inertial measurement unit in unsupported launching is effectively solved.
The technical scheme of the invention is as follows: an MEMS combined attitude determination method without initial alignment at any attitude is characterized by comprising the following steps:
1) defining a modified Rodrigues parameter;
2) establishing a nonlinear attitude error state equation based on the corrected Rodrigues parameter;
3) establishing a nonlinear observation equation of the magnetometer;
4) carrying out linearization processing on the nonlinear attitude error state equation and the observation equation of the magnetometer to obtain a linearization state error model of the state error and a linearization observation model of the magnetometer;
5) and obtaining the optimal estimation of the modified Rodrigues parameter by using the obtained nonlinear state error equation and observation equation, combining a linearized state model and an observation model and using an extended Kalman filtering method, wherein the optimal estimation is used as a posture result for guidance control, and the combined posture determination of the MEMS and the magnetometer in any posture is realized.
The concrete form of correcting the Rodrigues parameter in the step 1) is as follows:
Figure BDA0002018639060000021
wherein
Figure BDA0002018639060000022
Is the unit vector of the rotation axis, theta is the angle of rotation, superscriptTRepresenting a transpose of a vector or matrix.
The specific form of establishing the nonlinear attitude error state equation based on the corrected Rodrigues parameter in the step 2) is as follows:
Figure BDA0002018639060000023
wherein σ ═ σ1 σ2 σ3]TTo correct for errors in the Rodrigues parameter,
Figure BDA0002018639060000024
as a MEMS gyroscopeThe error of the measurement is taken into account,
Figure BDA0002018639060000025
the projection of the rotation angular velocity of the MEMS inertial set body coordinate system relative to the reference coordinate system under the MEMS inertial set body system is realized,
Figure BDA0002018639060000026
for the measured value of MEMS inertial measurement unit output, the symbol | · | | represents the modulus of the vector, and f (σ) represents the time change rate of the state error of the modified Rodrigues parameter
Figure BDA0002018639060000027
As a function of σ.
The specific form of the nonlinear observation equation of the magnetometer established in the step 3) is as follows:
Figure BDA0002018639060000028
wherein the observation error of the magnetometer
Figure BDA0002018639060000029
Figure BDA00020186390600000210
Is a body quaternion obtained by calculating a geomagnetic field model and an attitude quaternion,
Figure BDA00020186390600000211
for magnetometer measurements, g (σ) represents a functional relationship in magnetometer measurement error that is related to the state error σ.
In the step 4), the nonlinear attitude error state equation and the observation equation of the magnetometer are subjected to linearization processing, and the specific form of the linearization model of the state error is obtained as follows:
Figure BDA00020186390600000212
wherein
Figure BDA0002018639060000031
Represents the partial derivative of the rate of change in state error time f (σ) with respect to the state error, and G represents the partial derivative of the rate of change in state error time with respect to the MEMS gyro measurement error.
The specific form of the partial derivative of the state error time change rate f (sigma) to the state error is as follows:
Figure BDA0002018639060000032
the specific form of the partial derivative G representing the state error time change rate to the MEMS gyro measurement error is as follows:
Figure BDA0002018639060000033
I3×3is a 3 x 3 dimensional identity matrix.
In the step 4), the nonlinear attitude error state equation and the observation equation of the magnetometer are subjected to linearization processing, and the specific form of the obtained linearized observation model of the magnetometer is as follows:
Figure BDA0002018639060000034
wherein
Figure BDA0002018639060000035
For observing the model for a magnetometer
Figure BDA0002018639060000036
For the partial derivative of the state error sigma,
Figure BDA0002018639060000037
representing the partial derivative of g (sigma) to the state error sigma in the magnetometer error model,
partial derivative of g (sigma) to state error sigma in the magnetometer error model
Figure BDA0002018639060000038
The specific formula of (A) is as follows:
Figure BDA0002018639060000039
Figure BDA0002018639060000041
Figure BDA0002018639060000042
the specific process of obtaining the optimal estimation of the modified Rodrigues parameter by using the extended Kalman filtering method in the step 5) is as follows: and carrying out recursion by using the obtained nonlinear state error equation and observation equation, combining a linearized state model and an observation model and using an extended Kalman filtering method to obtain the optimal estimation of the modified Rodrigues parameter, wherein the optimal estimation is used as an attitude result for guidance control, and the MEMS and magnetometer combined attitude determination of any attitude is realized.
Compared with the prior art, the invention has the advantages that: according to the MEMS/magnetometer combined attitude determination method provided by the project, a state equation and an observation equation are established based on the corrected Rodrigues parameters, the optimal estimation of errors is obtained by using an extended Kalman filtering method, the combined attitude determination without initial information under any attitude is realized, the problem of initial alignment of an inertial set in unsupported transmission is effectively solved, ground aiming facilities are not required to be equipped, and meanwhile, the transmission preparation time is greatly shortened.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an error in determining the attitude of the combination of the MEMS gyro magnetometer.
Detailed Description
The project provides a method for obtaining three-axis attitude information of a missile weapon system by only utilizing an inertial measurement unit and a three-axis magnetometer under the condition of no initial attitude information. Without any prior attitude information, the attitude error is no longer a small deviation, and the conventional small deviation linear equation cannot be used to establish the attitude error model. A quaternion model is usually adopted for describing the nonlinear attitude error, quaternions have four variables, only three quaternions are independent, so that the redundancy problem exists, the state error covariance matrix can generate singularity, and the problem of normalization is also caused by adopting quaternion calculation. The traditional processing method adopts a vector part of a quaternion to carry out modeling, and ignores a scalar part in the quaternion, namely the rotation angle, namely, the quaternion error is assumed to be a small angle. However, in practice, the initial attitude deviation of the inertial measurement unit is large, the model is not adaptive any more, and an attitude error model which can adapt to any initial large attitude angle deviation needs to be established.
In the project, the corrected Rodrigues parameters are introduced into attitude determination, four parameters of the quaternion are converted into three parameters to describe the error of the attitude angle, the vector form and the amplitude of the quaternion are reserved, the singularity problem existing in attitude angle description is avoided, and the triaxial attitude determination can be completed under the condition that no initial attitude information exists.
1. And defining a corrected Rodrigues parameter, converting four quaternions into three quaternions to describe the attitude, ensuring the independence of the three parameters, and simultaneously avoiding the singular problem and the normalization problem of an error covariance matrix in the traditional quaternion.
Modified Rodrigues parameter:
Figure BDA0002018639060000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002018639060000052
is a quaternion;
Figure BDA0002018639060000053
is the unit vector of the rotation axis, theta is the angle of rotation. The rotation angle is described by tan (theta 4), and the modified Rodrigues parameter can be adapted to the range from minus pi to pi, namely, the quaternion suitable for any rotation angleAnd (4) counting.
Quaternion deviation
Figure BDA0002018639060000054
Wherein q iscFor a quaternion observation, the corresponding corrected Rodrigues error can be expressed as:
Figure BDA0002018639060000055
in the formula, qvRepresenting a quaternion error vector portion; similarly, the quaternion error can be obtained from equation (2) as follows:
Figure BDA0002018639060000061
Figure BDA0002018639060000062
2. establishing an attitude error state equation based on the corrected Rodrigues parameter:
the equation of differentiation of equation (2) yields the following attitude error equation:
Figure BDA0002018639060000063
the error equation for quaternions is as follows:
Figure BDA0002018639060000064
wherein the gyro measurement error
Figure BDA0002018639060000065
Figure BDA0002018639060000066
The rotation angular velocity of the coordinate system of the inertial unit body relative to the reference coordinate system is in the inertial unit basisThe projection under the system is that,
Figure BDA0002018639060000067
is the measurement value output by the inertial set.
Substituting the formulas (5) and (3) into the formula (4):
Figure BDA0002018639060000068
3. establishing an observation model of the magnetometer:
and (3) establishing an observation model of the magnetometer by subtracting the magnetic field intensity vector:
Figure BDA0002018639060000069
in the formula (I), the compound is shown in the specification,
Figure BDA00020186390600000610
is a body quaternion obtained by calculating a geomagnetic field model and an attitude quaternion,
Figure BDA00020186390600000611
is a magnetometer measurement;
the formula (3) may be substituted for the formula (7):
Figure BDA0002018639060000071
4. carrying out linear processing on the nonlinear attitude error state model and the observation model of the magnetometer:
and (6) linearizing to obtain a linearized model of the state error:
Figure BDA0002018639060000072
wherein:
Figure BDA0002018639060000073
Figure BDA0002018639060000074
and (3) linearizing the formula (8) to obtain a magnetometer linearized observation model:
Figure BDA0002018639060000075
wherein
Figure BDA0002018639060000076
Wherein the content of the first and second substances,
Figure BDA0002018639060000077
the calculation formula is as follows:
Figure BDA0002018639060000078
Figure BDA0002018639060000079
Figure BDA0002018639060000081
Figure BDA0002018639060000082
5. kalman filter estimation of error model
And estimating the MEMS inertial measurement unit and magnetometer combined system under any initial attitude by adopting a nonlinear kalman filtering method according to the established state equation and the observation model to realize combined attitude determination.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
And (3) verifying the MEMS inertial measurement unit/magnetometer combined attitude determination technology under any initial attitude deviation by adopting a nonlinear Kalman filtering mode according to the established state model and the observation model, wherein a simulation result is shown in figure 2, and the result shows that the combined attitude determination model is correct and the scheme is feasible.

Claims (7)

1. An MEMS combined attitude determination method without initial alignment at any attitude is characterized by comprising the following steps:
1) defining a modified Rodrigues parameter;
2) establishing a nonlinear attitude error state equation based on the corrected Rodrigues parameter;
3) establishing a nonlinear observation equation of the magnetometer;
4) carrying out linearization processing on the nonlinear attitude error state equation and the nonlinear observation equation of the magnetometer to obtain a linearization model of the state error and a linearization observation model of the magnetometer;
5) obtaining the optimal estimation of a modified Rodrigues parameter by using the obtained nonlinear attitude error state error equation and the nonlinear observation equation of the magnetometer and combining a state error linearized state model and a magnetometer linearized observation model, and using an extended Kalman filtering method as an attitude result for guidance control, so as to realize the combined attitude determination of the MEMS and the magnetometer in any attitude;
the concrete form of correcting the Rodrigues parameter in the step 1) is as follows:
Figure FDA0002610348510000011
wherein
Figure FDA0002610348510000012
Is the unit vector of the rotation axis, theta is the angle of rotation, superscriptTRepresents a transpose of a vector or matrix;
the specific form of establishing the nonlinear attitude error state equation based on the corrected Rodrigues parameter in the step 2) is as follows:
Figure FDA0002610348510000013
wherein σ ═ σ1 σ2 σ3]TTo correct for errors in the Rodrigues parameter,
Figure FDA0002610348510000014
in order to measure the error of the MEMS gyroscope,
Figure FDA0002610348510000015
the projection of the rotation angular velocity of the MEMS inertial set body coordinate system relative to the reference coordinate system under the MEMS inertial set body system is realized,
Figure FDA0002610348510000016
for the measured value of MEMS inertial measurement unit output, the symbol | · | | represents the modulus of the vector, and f (σ) represents the time change rate of the state error of the modified Rodrigues parameter
Figure FDA0002610348510000017
A functional relationship with σ;
the specific form of the nonlinear observation equation of the magnetometer established in the step 3) is as follows:
Figure FDA0002610348510000021
wherein the observation error of the magnetometer
Figure FDA0002610348510000022
Figure FDA0002610348510000023
Is a body quaternion obtained by calculating a geomagnetic field model and an attitude quaternion,
Figure FDA0002610348510000024
for magnetometer measurements, g (σ) represents a functional relationship in magnetometer measurement error that is related to σ.
2. The method of any-attitude MEMS combination attitude determination without initial alignment of claim 1, wherein: in the step 4), the nonlinear attitude error state equation and the nonlinear observation equation of the magnetometer are subjected to linearization processing, and the specific form of the obtained linearization model of the state error is as follows:
Figure FDA0002610348510000025
wherein
Figure FDA0002610348510000026
The partial derivative of f (σ) to the state error is expressed, and G represents the partial derivative of the time rate of change of the state error to the MEMS gyro measurement error.
3. The method of any-attitude MEMS combination attitude determination without initial alignment of claim 2, wherein: the specific form of the partial derivative of f (sigma) to the state error is:
Figure FDA0002610348510000027
I3×3is a 3 x 3 dimensional identity matrix.
4. The method of any-pose MEMS combination pose determination without initial alignment of claim 3, wherein: the specific form of the partial derivative G representing the time rate of change of the state error to the MEMS gyro measurement error is as follows:
Figure FDA0002610348510000028
5. the method of any-attitude MEMS combination attitude determination without initial alignment of claim 4, wherein: in the step 4), the nonlinear attitude error state equation and the observation equation of the magnetometer are subjected to linearization processing, and the specific form of the obtained linearized observation model of the magnetometer is as follows:
Figure FDA0002610348510000031
wherein
Figure FDA0002610348510000032
Represents the partial derivative of g (sigma) to sigma in the magnetometer linearized observed model.
6. The method of any-pose MEMS combination pose determination without initial alignment of claim 5, wherein: partial derivative of g (sigma) to sigma in the magnetometer error model
Figure FDA0002610348510000033
The specific formula of (A) is as follows:
Figure FDA0002610348510000034
Figure FDA0002610348510000035
Figure FDA0002610348510000036
7. an arbitrary-pose MEMS combination pose determination method without initial alignment, as claimed in any of claims 1-6, wherein: the specific process of obtaining the optimal estimation of the modified Rodrigues parameter by using the extended Kalman filtering method in the step 5) is as follows: and carrying out recursion by using the obtained nonlinear attitude error state error equation and the nonlinear observation equation of the magnetometer and combining the linearized state model of the state error and the linearized observation model of the magnetometer and using an extended Kalman filtering method to obtain the optimal estimation of the corrected Rodrigues parameter, wherein the optimal estimation is used as an attitude result for guidance control, and the combined attitude determination of the MEMS and the magnetometer in any attitude is realized.
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