Polarization compass orientation method based on real-time discriminant analysis of interpretable course information

Abstract

The invention discloses a polarization compass orientation method based on real-time discriminant analysis of interpretable course information, which comprises the steps of course data modeling, real-time monitoring, discriminant analysis and noise suppression, modeling by adopting a sparse local Fisher discriminant analysis method, enabling different types of course data states to be more separated according to an inter-class dispersion matrix of a weight coefficient matrix, and improving the orientation accuracy. Similar and same course data states are more clustered by using an intra-class matrix; a minimum absolute contraction selection operator optimization model is introduced, so that a course data discrimination model is simpler and more interpretable; course process data are analyzed through monitoring indexes, so that evolution and instability of dynamic output data of the polarization compass can be monitored in real time, and fine description of the data process can be realized; noise of discriminant analysis is effectively suppressed while real course signals in dynamic course data output by the polarization compass are reserved to the maximum extent. The method solves the problem that the orientation precision of the polarization compass is affected due to weak machine learning generalization ability.

Description

Technical Field

[0001] The invention relates to the technical field of polarized light navigation, in particular to a polarized compass orientation method based on real-time discrimination and analysis of interpretable heading information. Background Art

[0002] Polarimetric navigation system is a fully autonomous navigation system that relies on polarized light in the sky to solve the carrier's heading information. The system does not require any external information and does not radiate energy outward. Therefore, it is widely used in military fields such as aerospace, aviation, and navigation. The polarization compass is a key component of the polarization navigation system. The measurement accuracy of the polarization compass directly determines the performance of the entire polarization navigation system. Therefore, how to improve the measurement accuracy of the polarization compass has always been the research focus in the field of polarization navigation. Since the orientation accuracy of the polarization compass is affected by external harsh environmental factors such as cloudy days, haze, dust, etc., and is also affected by the noise generated by the compass itself, the above factors limit the application of navigation and orientation based on atmospheric polarization light. Therefore, it is necessary to process the orientation error of the polarization compass.

[0003] In the existing methods of improving the orientation accuracy of polarized compasses by suppressing noise, machine learning algorithms are required to train neural networks. The training of neural networks requires the use of a large amount of data, and the sample data will also change in real time as the environment changes. However, due to the weak generalization ability of machine learning algorithms, the practical application of polarized compasses and the improvement of orientation accuracy are ultimately limited. Summary of the invention

[0004] Purpose of the invention: In order to solve the problem in the prior art that the orientation accuracy of the polarized compass orientation method is affected by the weak generalization ability of machine learning, the present invention provides a polarized compass orientation method based on real-time discrimination and analysis of interpretable heading information.

[0005] Technical solution: A polarization compass orientation method based on real-time discrimination and analysis of interpretable heading information, comprising the following steps:

[0006] Step 1: For the original heading signal output by the polarization compass, the sparse local Fisher discriminant analysis method is used to model the original heading signal; the minimum absolute shrinkage selection operator is introduced to optimize the model;

[0007] Step 2: Establish monitoring indicators, which are used to determine the state of heading data. The monitoring indicators include the determination index and stability index s l , and set limits;

[0008] Step 3: Obtain the original heading signal and standardize it; use the model in step 1 to obtain the discriminant feature z d; Calculate the monitoring index, and according to the calculated monitoring index and the limit value of step three, distinguish different heading data states, including heading data of different noise states;

[0009] Step 4: De-noise the noisy heading data;

[0010] Step 5: Recombine the denoised heading data with other heading data to obtain high-precision heading data.

[0011] Furthermore, in step 1, the modeling method includes:

[0012] (a1) Sampling the original heading signal to obtain the original data set;

[0013] (a2) Construct the inter-class dispersion weight coefficient matrix of the original data set and the intra-class weight coefficient matrix

[0014] (a3) According to and Construct the inter-class dispersion matrix M of the original data set b and the intra-class matrix M w .

[0015] Furthermore, in step 1, the model optimization method includes:

[0016] (b1) The objective function of the heading data constructed according to the model in step 1 is:

[0017]

[0018] Where v and s represent the variable and sample size, respectively; γ is the non-negative tuning parameter of the LASS operator; st represents the constraint; T represents the local adjustment parameter; V d represents the d-th discrimination direction;

[0019] (b2) Define a new inter-class scatter matrix To replace M b , using the orthogonal projection matrix P d Calculate the dth discriminant direction of the heading data:

[0020]

[0021] Where V = [v1, v2, ..., v d-1 ] and (ΩV) + represents the Moore-Penrose pseudoinverse of ΩV;

[0022] (b3) Using Lagrange multipliers through equation (4) without considering LASS penalty to solve the optimization equation (2)

[0023]

[0024] Among them, v d represents the d-th discriminant direction of the heading data; λd represents the Lagrange multiplier of the d-th discriminant direction;

[0025] (b4) Using the LASS operator, the optimization problem of formula (2) is transformed into formula (5):

[0026]

[0027] (b5) Equation (5) is converted into an iterative optimization form by the minimum-maximum method to solve non-convex functions.

[0028]

[0029] in, represents the optimal solution of the final iteration, U T represents the iterative optimization solution;

[0030] (b6) By solving equation (4), we can obtain The first eigenvector of and assigns the eigenvector to Recursively solve the optimization problem of formula (5), and its converged solution is the dth sparse discriminant heading data. Repeating the execution can generate all sparse discriminant directions, denoted as T = v1, v2, ..., v d .

[0031] Furthermore, in step 2, the discriminant index The definition and limit setting method include: The distinguishing characteristics of each representative data state are: Select the first dimension of discriminant features As the discriminant index of the representative data state; the upper limit of the discriminant index of each representative data state and lower limit The confidence levels are selected as 0.99 and 0.01 respectively.

[0032] Furthermore, in step 2, the stability index s l The method for setting the limit of includes: calculating s according to the 0.95 confidence level lim As the upper limit of stability, it is used to determine whether the corresponding noise data state is stable.

[0033] Furthermore, in step 3, the method for identifying the heading data state includes:

[0034] (c1) If the discrimination index is within the limit Within, and the stability index is lower than s lim, it is confirmed to be the real heading data state, and the heading data does not contain noise;

[0035] (c2) If the discriminant index is Within, and the stability index exceeds s lim , indicating the presence of an initial transition or random perturbation;

[0036] (c3) If the stability index is lower than s lim , and the discrimination index exceeds the limit This indicates that the complete heading data state gradually evolves from the real heading data to a mixed data process with noise;

[0037] (c4) If the discrimination index exceeds the limit And the stability index exceeds s lim , indicating that the heading data contains noise and the true signal has been converted into a mixed signal containing noise.

[0038] Furthermore, in step 4, the improved sliding singular spectrum analysis method is used to denoise the noisy heading data in the discriminant analysis data.

[0039] Compared with the prior art, the polarization compass orientation method based on real-time discrimination and analysis of interpretable heading information provided by the present invention has the following effects:

[0040] (1) Compared with the existing polarization compass error processing method, the heading data discrimination model of this method does not require a large amount of neural network training, is more concise and more interpretable;

[0041] (2) In the discriminant analysis stage, two monitoring indicators, including the discriminant index and the stability index, are established to analyze the heading process data. This not only enables real-time monitoring of the evolution and instability of the dynamic output data of the polarization compass, but also enables a detailed description of the data process.

[0042] (3) This method adopts the improved sliding singular spectrum analysis (MSSA) method, which also does not require a large amount of neural network training. While retaining the true heading signal in the dynamic heading data output by the polarization compass to the maximum extent, it can effectively suppress the noise of the OSLFDA discriminant analysis, thereby effectively improving the heading measurement accuracy of the polarization compass, especially the orientation accuracy of the polarization compass in harsh environments such as complex weather or occlusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the polarization compass orientation method based on real-time discrimination analysis of interpretable heading information;

[0044] Figure 2 This is the classification result diagram of the discrimination index z1 of the original heading angle data output by the polarization compass;

[0045] Figure 3 This is the result graph of the stability index s of the original heading angle data output by the polarization compass;

[0046] Figure 4 This is a comparison chart of various denoising methods for processing high-frequency heading angles;

[0047] Figure 5 This is a comparison chart of the effects of various denoising methods on high-frequency heading errors;

[0048] Figure 6 This is a diagram showing the effects of various denoising methods on high-frequency heading error boxes. DETAILED DESCRIPTION

[0049] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments.

[0050] A polarization compass orientation method based on real-time discriminant analysis of interpretable heading information, such as Figure 1 As shown, the following steps are included:

[0051] Step 1: For the original heading signal output by the polarization compass, the sparse local Fisher discriminant analysis (SLFDA) method is used to model the original heading signal. According to the use of the SLFDA weight coefficient matrix, the inter-class scatter matrix makes different types of heading data states more separated, and the intra-class matrix makes similar and same types of heading data states more clustered; the least absolute shrinkage selection operator (LASS) is introduced to optimize the model, and the sparse discriminant direction is determined by LASS to optimize the key variables related to the sparse local Fisher discriminant analysis (OSLFDA) and the polarization compass data output process, so that the heading data discrimination model is simpler and more interpretable.

[0052] The modeling methods include:

[0053] (a1) Sample the original heading signal to obtain the original data set

[0054] (a2) Construct the inter-class dispersion weight coefficient matrix of the original data set And the intra-class weight coefficient matrix

[0055]

[0056] Among them, the matrix C i，j =epx(||h i -h i || 2 / T i ) quantitatively describes the correlation between heading data state samples; T iis a local tuning parameter.

[0057] (a3) According to and Construct the inter-class dispersion matrix M of the original data set b and the intra-class matrix M w .

[0058]

[0059] Raw heading data By optimizing SLFDA (OSLFDA) through the least absolute shrinkage selection operator (LASS), real-time monitoring is performed on the basis of avoiding the overlap of heading information between different discrimination directions, making the data discrimination model more concise and more interpretable. The implementation steps are as follows:

[0060] (b1) The objective function of the heading data constructed according to the model in step 1 is:

[0061]

[0062] Where v and s represent the variable and sample size, respectively; γ is the non-negative tuning parameter of the LASS operator; st represents the constraint; T represents the local adjustment parameter; V d represents the d-th discrimination direction;

[0063] Within a certain range, the interpretability and discriminative performance of OSLFDA first increase and then decrease with the increase of LASS penalty factor. OSLFDA only shrinks a few meaningful coefficients to zero to voluntarily select key variables. Therefore, it is necessary to define a new inter-class dispersion matrix Replacing Mb solves the orthogonality constraint problem in (5).

[0064] (b2) Define a new inter-class scatter matrix To replace M b , using the orthogonal projection matrix P d Calculate the dth discriminant direction of the heading data:

[0065]

[0066] Where V = [v1, v2, ..., v d-1 ] and (ΩV) + represents the Moore-Penrose pseudoinverse of ΩV;

[0067] (b3) Using Lagrange multipliers through equation (7) without considering LASS penalty, we can solve the optimization equation (5).

[0068]

[0069] Among them, v d represents the dth discriminant direction of the heading data; d represents the Lagrange multiplier of the d-th discriminant direction.

[0070] (b4) The optimization problem of equation (5) is transformed into equation (8) using the LASS operator. The LASS operator enables OSLFDA to avoid the overlap of heading information between different discrimination directions, greatly improving the discrimination performance.

[0071]

[0072] (b5) Formula (9) converts Formula (8) into an iterative optimization form through the minimum-maximum method to solve non-convex functions.

[0073]

[0074] in, represents the optimal solution of the final iteration, U T represents the iterative optimization solution.

[0075] (b6) By solving equation (4), we can obtain The first eigenvector of and assigns the eigenvector to Recursively solve the optimization problem of formula (5), and its converged solution is the dth sparse discriminant heading data. Repeating the execution can generate all sparse discriminant directions, denoted as T = v1, v2, ..., v d .

[0076] In addition, since the polarized light compass is a dynamic navigation system, the current state depends largely on the past state. When sampling points are taken in the high-frequency range of useful data and the low-frequency range of noise data, the above modeling cannot fully characterize the entire data change process. Therefore, in the sampling process of step (a1), the data values ​​at the current moment and the previous moment need to be considered at the same time for better judgment. The sliding window technology is used to combine the current sampling time data with the sampling data at the previous moment to form a new data sample with a new window width.

[0077] Step 2: Establish monitoring indicators, which are used to determine the state of heading data. The monitoring indicators include the determination index and stability index s l , and set limits. By establishing two monitoring indicators, the discrimination index and the stability index, to analyze the heading process data, it is not only possible to monitor the evolution and instability of the dynamic output data of the polarization compass in real time, but also to achieve a detailed description of the data process. Figure 2-3 Shown is the original heading angle data discrimination index z1 and stability index s monitoring classification.

[0078]

[0079] Among them, v i represents the dth sparse discriminant heading number h k direction; Represents the average value of the first dimension discriminant z1 feature.

[0080] Discrimination Index The definition and limit setting methods include: Since the discriminant attribute is non-Gaussian, the kernel density estimation function (KDE) is introduced to calculate the control limit to capture the nonlinear characteristics of the heading data processing state. The discriminant characteristics of each representative data state are: Select the first dimension of discriminant features As the discriminant index of the representative data state; the upper limit of the discriminant index of each representative data state and lower limit The confidence levels are selected as 0.99 and 0.01 respectively.

[0081] Due to the instability of the alternating true heading signal and noise, the noise stability monitoring indicator oscillates sharply and an independent stability indicator limit s is set for it. lim . Stability index s l The limit value of lim The setting method includes: calculating s according to the 0.95 confidence level lim As the upper limit of stability, it is used to judge whether the corresponding noise data state is stable. Due to the gentle fluctuation, the control limits of other indicators of low-frequency heading and medium-frequency mixed signal state are set smaller.

[0082] Step 3: Get the original heading signal and convert it into standardization;

[0083]

[0084] Wherein, mean(H) and std(H) represent the mean value and standard deviation vector of all measurement signals used to model the original heading signal data H, respectively.

[0085] Use the model in step 1 to get the discriminant feature z d : By Project to the dth sparse discriminant direction v d Achieve discriminative features that best describe the diversity of real signals and mixed noise states

[0086] Calculate the monitoring indicators z1 and s:

[0087]

[0088] in, Represents the average value of the first dimension feature.

[0089] According to the calculated monitoring index and the limit value of step 3, different heading data states are identified, heading data with different noise states are obtained, and the entire identification result and transient process from real data to noise state are obtained in real time. The specific identification method is:

[0090] (c1) If the discrimination index is within the limit Within, and the stability index is lower than s lim , it is confirmed to be the real heading data state, and the heading data does not contain noise;

[0091] (c2) If the discriminant index is Within, and the stability index exceeds s lim , indicating the presence of an initial transition or random perturbation;

[0092] (c3) If the stability index is lower than s lim , and the discrimination index exceeds the limit This indicates that the complete heading data state gradually evolves from the real heading data to a mixed data process with noise;

[0093] (c4) If the discrimination index exceeds the limit And the stability index exceeds s lim , indicating that the heading data contains noise and the true signal has been converted into a mixed signal containing noise.

[0094] Step 4: De-noise the noisy heading data. In this embodiment, the improved sliding singular spectrum analysis method (MSSA) is used to de-noise the noisy heading data in (c4) of the discriminant analysis data. It is selected whether the data in the (c2) and (c3) states need to be de-noised as needed. While retaining the true heading data in the dynamic heading data output by the polarization compass to the maximum extent, the noise of the OSLFDA discriminant analysis is effectively suppressed.

[0095] Step 5: Recombine the denoised heading data with other heading data to obtain high-precision heading data.

[0096] like Figures 4 to 6 The figure shows the comparative effects of various denoising methods. MSSA is the experimental waveform of this method. The polarization compass orientation method based on real-time discrimination analysis of interpretable heading information has the best effect.

Claims

1. A polarization compass orientation method based on real-time discrimination analysis of interpretable heading information, characterized in that: The following steps are involved: Step 1: For the original heading signal output by the polarization compass, the sparse local Fisher discriminant analysis method is used to model the original heading signal; the minimum absolute shrinkage selection operator is introduced to optimize the model; Step 2: Establish monitoring indicators, which are used to determine the state of heading data. The monitoring indicators include the determination index and stability index s,, and set limits; Step 3: Obtain the original heading signal and standardize it; use the model in step 1 to obtain the discriminant feature z d ; Calculate the monitoring index, and according to the calculated monitoring index and the limit value of step three, distinguish different heading data states, including heading data of different noise states; Step 4: De-noise the noisy heading data; Step 5: Recombine the denoised heading data with other heading data to obtain high-precision heading data.

2. The polarization compass orientation method based on real-time discrimination and analysis of interpretable heading information according to claim 1 is characterized in that: In step 1, the modeling method includes: (a1) Sampling the original heading signal to obtain the original data set; (a2) Construct the inter-class dispersion weight coefficient matrix of the original data set And the intra-class weight coefficient matrix (a3) According to and Construct the inter-class dispersion matrix M of the original data set b and the intra-class matrix M. w .

3. The polarization compass orientation method based on real-time discrimination analysis of interpretable heading information according to claim 1 or 2, characterized in that: In step 1, the model optimization method includes: (b1) The objective function of the heading data constructed according to the model in step 1 is: Where v and s represent the variable and sample size, respectively; γ is the non-negative tuning parameter of the LASs operator; st represents the constraint; T represents the local adjustment parameter; V d represents the d-th discrimination direction; (b2) Define a new inter-class scatter matrix To replace M b , using the orthogonal projection matrix P d Calculate the dth discriminant direction of the heading data: Where V = [v1, v2, ..., v d-1 ] and (ΩV) + represents the Moore-Penrose pseudoinverse of ΩV; (b3) Using Lagrange multipliers through equation (4) without considering LASS penalty to solve the optimization equation (2) Among them, v d represents the dth discriminant direction of the heading data; d represents the Lagrange multiplier of the d-th discriminant direction; (b4) Using the LASS operator, the optimization problem of formula (2) is transformed into formula (5): (b5) Equation (5) is converted into an iterative optimization form by the minimum-maximum method to solve non-convex functions. in, represents the optimal solution of the final iteration, U T represents the iterative optimization solution; (b6) By solving equation (4), we can obtain The first eigenvector of and assigns the eigenvector to Recursively solve the optimization problem of formula (5), and its converged solution is the dth sparse discriminant heading data. Repeating the execution can generate all sparse discriminant directions, denoted as T = v1, v2, ..., v d .

4. The polarization compass orientation method based on real-time discrimination analysis of interpretable heading information according to claim 1 or 2, characterized in that: In step 2, the discriminant index The definition and limit setting method include: The distinguishing characteristics of each representative data state are: Select the first dimension of discriminant features As the discriminant index of the representative data state; the upper limit of the discriminant index of each representative data state and lower limit The confidence levels are 0.99 and 0.01 respectively.

5. The polarization compass orientation method based on real-time discrimination and analysis of interpretable heading information according to claim 1 or 2, characterized in that: In step 2, the method for setting the limit value of the stability index s1 includes: calculating s1 according to a 0.95 confidence level lim As the upper limit of stability, it is used to determine whether the corresponding noise data state is stable.

6. The polarization compass orientation method based on real-time discrimination analysis of interpretable heading information according to claim 1 or 2, characterized in that: In step 3, the method for identifying the heading data status includes: (c1) If the discrimination index is within the limit Within, and the stability index is lower than s lim , it is confirmed to be the real heading data state, and the heading data does not contain noise; (c2) If the discriminant index is Within, and the stability index exceeds s lim , indicating the presence of an initial transition or random perturbation; (c3) If the stability index is lower than s lim , and the discrimination index exceeds the limit This indicates that the complete heading data state gradually evolves from the real heading data to a mixed data process with noise; (c4) If the discrimination index exceeds the limit And the stability index exceeds s lim , indicating that the heading data contains noise and the true signal has been converted into a mixed signal containing noise.

7. The polarization compass orientation method based on real-time discrimination analysis of interpretable heading information according to claim 1 or 2, characterized in that: In step 4, the improved sliding singular spectrum analysis method is used to denoise the noisy heading data in the discriminant analysis data.

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