CN102735268A - Strapdown three-shaft magnetometer calibrating method based on posture optimization excitation - Google Patents

Abstract

The invention relates to a strapdown three-shaft magnetometer calibrating method based on posture optimization excitation. The strapdown three-shaft magnetometer calibrating method comprises the following steps of: (1) selecting a stable calibration environment of a geomagnetic field to calculate a reference vector of a local geomagnetic field; (2) establishing a measurement error equation of a strapdown magnetometer; (3) establishing a relation of an optimal target function and a navigation carrier posture according to a D-optimization experiment design criterion; (4) optimizing a target function by utilizing a grain group optimization algorithm; (5) rotating a navigation carrier according to an optimized posture obtained from the step (4), and simultaneously measuring magnetic field data of posture points through the strapdown magnetometer; and (6) calculating estimation of an error model parameter by utilizing a least square method according to the magnetic field measurement data. According to the method, the rotation arrangement of a navigation carrier can be optimized, the redundance rotation operation of the navigation carrier can be effectively reduced, the geomagnetism measurement error can be fully excited, magnetic-field measurement data can be reasonably distributed, the accuracy and the stability of the error model parameter estimation can be obviously omproved, and further the measurement accuracy of the strapdown magnetometer can be improved.

Description

A kind of strapdown triaxial magnetometer scaling method based on the pose refinement excitation

Technical field

The present invention is mainly concerned with the demarcation field of strapdown magnetometer, refers in particular to a kind of strapdown triaxial magnetometer scaling method based on the pose refinement excitation.

Background technology

" strapdown triaxial magnetometer " can obtain the carrier amplitude and the direction in magnetic field peripherally continuously, and assistant carrier is confirmed self attitude and position, and have that cost is low, volume is little, in light weight, advantage that reliability is high.It and other navigator are formed geomagnetic auxiliary navigation system, are widely used in space flight and aviation, ground and independent navigation platform under water.The gordian technique of geomagnetic auxiliary navigation system is that magnetometer can obtain high-precisionly in real time and is worth.But in practical application, the measurement of strapdown magnetometer receives the interference in sensor self and carrier equal error source inevitably.These error sources have suppressed the potential performance performance of magnetometer, have had a strong impact on the geomagnetic field measuring precision.Therefore, the demarcation problem of strapdown magnetometer has become one of key factor of restriction earth-magnetic navigation technical development.

To the demarcation problem of strapdown triaxial magnetometer, there are a lot of researchists to propose many effective methods in succession.Present one type of magnetometer scaling method commonly used and that be easy to realize is the mould scaling method, also claims " attitude is independent " method.These class methods do not need carrier that high-accuracy posture information and extra calibration facility are provided in the process of finding the solution the measuring error model parameter, and implementation procedure is simple, convenience of calculation.But existing mould scaling method lays particular emphasis on the research to measuring-signal noise reduction aspect mostly, and but the distribution of less relevance magnetic measurement data is to the influence of scaling method.In fact, the distribution of measurement data has significant effects to the parameter estimation of sensor measurement error model.If the measurement data irrational distribution, measuring error can't be by abundant excitation so, and parameter estimation precision and stability that existing mould scaling method is tried to achieve will reduce, and can make the estimated value substantial deviation actual value of parameter when serious, even algorithm are dispersed.Based on this, theoretical patrix scaling method need obtain the magnetic measurement data of the configuration space of whole navigation carrier.Yet exhausted big manifold navigation carrier can't realize that all full configuration space rotates.In addition, consider that from program complexity and aspect such as control cost the rotating operation of navigation carrier should reduce as best one can.Therefore, how research rationally utilizes the rotation layout of navigation carrier, with limited pose refinement excitation field measuring error, measurement data is distributed rationally, is the important channel of improving the magnetic survey precision.

Summary of the invention

The technical matters that the present invention will solve just is: to the technical matters that prior art exists, the present invention provides a kind of rotation layout of having optimized the navigation carrier, effectively reduced the redundant rotating operation of navigation carrier, fully encourages the magnetic survey error, rationally the distributed magnetic field measurement data, significantly improved precision that error model parameters estimates and stability and then improved the strapdown triaxial magnetometer scaling method based on the pose refinement excitation of strapdown magnetometer measuring accuracy.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

A kind of strapdown triaxial magnetometer scaling method based on the pose refinement excitation the steps include:

(1) selects the demarcation environment that the terrestrial magnetic field is stable, according to the terrestrial magnetic field reference vector of the geographic position of demarcating environment by international geomagnetic reference field Model Calculation locality;

(2) under carrier coordinate system, be projected as input with the terrestrial magnetic field reference vector, set up the measuring error equation of strapdown magnetometer;

(3) the measuring error equation that obtains based on step (2) according to D-Optimization Experiment Design criterion, is set up the relation of optimization aim function and navigation attitude of carrier;

(4) adopt particle swarm optimization algorithm, N optimum attitude of search makes the optimization aim function obtain extreme value in the configuration space of navigation carrier;

(5) the navigation carrier rotates according to the attitude of the optimization that obtains in the step (4), and the strapdown magnetometer is measured the magnetic field data of these attitude points simultaneously;

(6) according to the magnetic-field measurement data, adopt the estimation of least square method error of calculation model parameter, according to error model parameters the strapdown triaxial magnetometer is demarcated.

As further improvement of the present invention:

The measuring error equation of the strapdown magnetometer in the said step (2) is:

$\begin{array}{cc}{R}_0^2=p_i^T\mathrm{\β}& i=\mathrm{1,2}...,M\end{array}$

Wherein, R ₀Be the mould value of terrestrial magnetic field reference vector, i is the magnetic measurement sequence, and M is the sampling sum, p _iBe by the projection of geomagnetic fieldvector in carrier coordinate system $B_i^b={\left(\begin{array}{ccc}{x}_i& y_i& z_i\end{array}\right)}^T$ The row vector that constitutes, β is an error model parameters to be asked, a ₁～a ₁₀It is parameter to be asked; Wherein expression formula is following

$p_i={\left[\begin{array}{cccccccccc}{x}_i^2& x_i{y}_i& x_i{z}_i& y_i^2& y_i{z}_i& z_i^2& x_i& y_i& z_i& 1\end{array}\right]}^T$

β＝[a ₁a ₂a ₃a ₄a ₅a ₆a ₇a ₈a ₉a ₁₀] ^T

D-Optimization Experiment Design criterion in the said step (3) comprises Bayes ian-D Optimization Experiment Design criterion.

Particle swarm optimization algorithm in the said step (4) comprises one type of optimization method based on particle swarm optimization algorithm.

The least square method of said step (6) is linear least square method or non-linear least square method.

Compared with prior art, the invention has the advantages that:

1, the present invention can demarcate the equipment error (zero inclined to one side error, calibration factor error, nonopiate error) and the carrier mushing error (Hard Magnetic sum of errors soft magnetism error) of magnetometer simultaneously.

2, the present invention utilizes the preferred attitude information of navigation carrier, fully encourages the magnetic survey error, and rationally the distribution measuring data can significantly improve precision and stability that error model parameters is estimated.

3, the present invention provides the preferred rotation layout of navigation carrier in the magnetometer calibration process according to D-Optimization Experiment Design criterion, and the attitude of indication navigation carrier is rotated, and can reduce the redundant and invalid rotating operation of navigation carrier effectively.If the configuration space of navigation carrier is restricted, the present invention still can be given in the preferred rotation layout that can allow under the configuration space constraint.

4, the present invention utilizes particle swarm optimization algorithm simultaneously to the individual preferred attitude of N (N >=10); The theorem in Euclid space of 3 * N dimension is searched for altogether; Can solve quickly and efficiently in the continuous sample space of higher-dimension; Find the solution the problem of optimizing the optimal value difficulty of criterion based on D-, thereby try to achieve the preferred attitude of navigation carrier.

Description of drawings

Fig. 1 is the schematic flow sheet of the inventive method.

Fig. 2 is the present invention's triaxial magnetometer scheme of installation in concrete application example.

Embodiment

Below will combine Figure of description and specific embodiment that the present invention is explained further details.

Strapdown triaxial magnetometer scaling method based on pose refinement excitation of the present invention at first goes out to demarcate the terrestrial magnetic field reference vector of environment with the international geomagnetic reference field Model Calculation, and with serve as to import the measuring error equation of setting up the strapdown triaxial magnetometer; Then, based on this error equation, adopt D-Optimization Experiment Design criterion to set up the relation of navigation attitude of carrier and optimization aim function; Then, adopt particle group optimizing method in the configuration space of navigation carrier, to search for pose refinement, make it to satisfy objective function and get extreme value, magnetometer is gathered magnetic field data at pose refinement point simultaneously; At last, adopt least square method to handle the magnetic-field measurement data, estimate the measuring error model parameter, realize demarcation the strapdown magnetometer.The present invention has optimized the rotation layout of navigation carrier; Effectively reduced the redundant rotating operation of navigation carrier; And fully encourage the magnetic survey error; Rationally the distributed magnetic field measurement data can significantly improve precision and stability that error model parameters is estimated, thereby has improved the measuring accuracy of strapdown magnetometer.

As shown in Figure 1, its concrete steps are:

(1) with the triaxial magnetometer strapdown on the navigation carrier, rolling, driftage and the pitch axis direction corresponding consistent (referring to Fig. 2) of three sensitive axes of triaxial magnetometer (x, y, z axle) and the carrier that navigates.

(2) select the demarcation environment that the terrestrial magnetic field is stable, by the local terrestrial magnetic field of international geomagnetic reference field Model Calculation reference vector be according to the geographic position of demarcating environment:

$B^n={\left[\begin{array}{c}{x}^n\\ y^n\\ z^n\end{array}\right]}^T---\left(1\right)$

Notice above-mentioned terrestrial magnetic field reference vector B ⁿBe the projection value under the navigation coordinate system, the subscript in the formula " n " expression navigation coordinate system.When the navigation carrier rotates, terrestrial magnetic field reference vector B ⁿNavigation being projected as of carrier coordinate system:

$B_i^b={\left[\begin{array}{c}{x_i}^b\\ {y_i}^b\\ {z_i}^b\end{array}\right]}^T=C_n^b\left(i\right)B^n\stackrel{\mathrm{\Δ}}{=}f(B^n,C_n^b\left(i\right))---\left(2\right)$

Wherein, the subscript in the formula " b " expression carrier coordinate system, function f is represented B ⁿWith

Between mapping relations.

Be the direction cosine matrix of system from the carrier coordinate system to the navigation coordinate, it is by roll angle r _i, crab angle y _iWith angle of pitch p _iDefinite fully, its expression formula is following.H representes the relation of direction cosine matrix and Eulerian angle.

$C_n^b\left(i\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& {\cos r}_i& {\sin r}_i\\ 0& -\sin r_i& {\cos r}_i\end{array}\right]\left[\begin{array}{ccc}{\cos p}_i& \sin p_i& 0\\ -{\sin p}_i& {\cos p}_i& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{\cos y}_i& 0& -{\sin y}_i\\ 0& 1& 0\\ {\sin y}_i& 0& {\cos y}_i\end{array}\right]$

$\stackrel{\mathrm{\Δ}}{=}h(r_i,y_i,p_i)---\left(3\right)$

(3) with terrestrial magnetic field reference vector B ⁿProjection under carrier coordinate system

Be input, the measuring error equation of setting up the strapdown magnetometer is:

$\begin{array}{cc}{R}_0^2=p_i^T\mathrm{\β}& i=\mathrm{1,2}...,M\end{array}---\left(4\right)$

Wherein, R ₀Be the mould value of terrestrial magnetic field reference vector, i is the magnetic measurement sequence, and M is the sampling sum, p _iBe by $B_i^b={\left(\begin{array}{ccc}{x}_i& y_i& z_i\end{array}\right)}^T$ The row vector that constitutes.β is an error model parameters to be asked.Their expression formula is as follows.G representes p _iWith Mapping relations, a ₁～a ₁₀It is parameter to be asked;

$p_i={\left[\begin{array}{cccccccccc}{x}_i^2& x_i{y}_i& x_i{z}_i& y_i^2& y_i{z}_i& z_i^2& x_i& y_i& z_i& 1\end{array}\right]}^T$

$\stackrel{\mathrm{\Δ}}{=}g\left(B_i^b\right)$

$=g\left(f(B^n;h(r_i,y_i,p_i))\right)$

β＝[a ₁a ₂a ₃a ₄a ₅a ₆a ₇a ₈a ₉a ₁₀] ^T

(4) based on the measuring error equation, according to D-Optimization Experiment Design criterion, the foundation of choosing N pose refinement angle is to make following objective function minimum:

$\hat{P}=\arg \min J\left(P\right)=\det \left[{\left(P^{T}P\right)}^{-1}\right]---\left(5\right)$

Wherein, the P in the formula is the model matrix that the attitude angle by N the navigation carrier of optimizing constitutes:

$P={\left[\begin{array}{c}{p}_1\\ p_2\\ .\\ .\\ .\\ p_N\end{array}\right]}_{N\×10}={\left[\begin{array}{c}g\left(f(B^n;h(r_1,y_1,p_1))\right)\\ g\left(f(B^n;h(r_2,y_2,p_2))\right)\\ .\\ .\\ .\\ g\left(f(B^n;h(r_N,y_N,p_N))\right)\end{array}\right]}_{N\×10}---\left(6\right)$

This D-Optimization Experiment Design criterion comprises Bayesian-D Optimization Experiment Design criterion.

(5) adopt particle swarm optimization algorithm, N optimum attitude of search makes majorized function J (P) obtain minimum value in the configuration space of navigation carrier.The configuration space of navigation carrier is: r _Min, y _Min, p _MinRepresent minimum value respectively, r _Max, y _Max, p _MaxRepresent maximal value respectively.

$\left\{\begin{array}{c}r\∈\left[\begin{array}{cc}{r}_{\min }& r_{\max }\end{array}\right]\\ y\∈\left[\begin{array}{cc}{y}_{\min }& y_{\max }\end{array}\right]\\ p\∈\left[\begin{array}{cc}{p}_{\min }& p_{\max }\end{array}\right]\end{array}\right.---\left(7\right)$

Being defined as of particle:

X＝[r ₁,y ₁,p ₁r ₂,y ₂,p ₂…r _N,y _N,p _N] ^T(8)

This particle swarm optimization algorithm comprises one type of optimization method based on particle swarm optimization algorithm.

(6) the navigation carrier rotates according to top pose refinement of trying to achieve, and the magnetic field data of these attitude points of strapdown magnetometer measurement simultaneously is:

(7) according to magnetic-field measurement data

by formula (6) can the computation model matrix be

then; Adopt least square method, can obtain the estimation of error model parameters:

$\widehat{\mathrm{\β}}={\left({\tilde{P}}^T\tilde{P}\right)}^{-1}{\left[\begin{array}{c}{R}_0^2\\ R_0^2\\ .\\ .\\ .\\ R_0^2\end{array}\right]}_{N\×1}---\left(9\right)$

This least square method is linear least square method or non-linear least square method.

Below only be preferred implementation of the present invention, protection scope of the present invention also not only is confined to the foregoing description, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art some improvement and retouching not breaking away under the principle of the invention prerequisite should be regarded as protection scope of the present invention.

Claims (5)

1. strapdown triaxial magnetometer scaling method based on pose refinement excitation is characterized in that step is:

(1) selects the demarcation environment that the terrestrial magnetic field is stable, according to the terrestrial magnetic field reference vector of the geographic position of demarcating environment by international geomagnetic reference field Model Calculation locality;

(2) under carrier coordinate system, be projected as input with the terrestrial magnetic field reference vector, set up the measuring error equation of strapdown magnetometer;

(3) the measuring error equation that obtains based on step (2) according to D-Optimization Experiment Design criterion, is set up the relation of optimization aim function and navigation attitude of carrier;

(4) adopt particle swarm optimization algorithm, N optimum attitude of search makes the optimization aim function obtain extreme value in the configuration space of navigation carrier;

(5) the navigation carrier rotates according to the attitude of the optimization that obtains in the step (4), and the strapdown magnetometer is measured the magnetic field data of these attitude points simultaneously;

(6) according to the magnetic-field measurement data, adopt the estimation of least square method error of calculation model parameter, according to error model parameters the strapdown triaxial magnetometer is demarcated.

2. according to the said strapdown triaxial magnetometer scaling method of claim 1, it is characterized in that the measuring error equation of the strapdown magnetometer in the said step (2) is based on the pose refinement excitation:

Wherein, R ₀Be the mould value of terrestrial magnetic field reference vector, i is the magnetic measurement sequence, and M is the sampling sum, p _iBe by the projection of geomagnetic fieldvector in carrier coordinate system The row vector that constitutes, β is an error model parameters to be asked, a ₁～a ₁₀It is parameter to be asked; Wherein expression formula is following

。

β＝[a ₁a ₂a ₃a ₄a ₅a ₆a ₇a ₈a ₉a ₁₀] ^T

3. according to the said strapdown triaxial magnetometer scaling method of claim 1, it is characterized in that the D-Optimization Experiment Design criterion in the said step (3) comprises Bayes ian-D Optimization Experiment Design criterion based on the pose refinement excitation.

4. according to the said strapdown triaxial magnetometer scaling method of claim 1, it is characterized in that the particle swarm optimization algorithm in the said step (4) comprises one type of optimization method based on particle swarm optimization algorithm based on the pose refinement excitation.

5. according to the said strapdown triaxial magnetometer scaling method of claim 1, it is characterized in that the least square method of said step (6) is linear least square method or non-linear least square method based on the pose refinement excitation.

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