Polarization / inertial navigation integrated navigation method based on deep Kalman filter network

Abstract

The invention provides a polarization / inertial navigation integrated navigation method based on a deep Kalman filter network, and belongs to the field of bionic polarization navigation. Establishing a priori prediction error covariance matrix estimation network and a measurement residual covariance matrix estimation network in polarization / inertial navigation filtering, and training the priori prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network at the same time by adopting a two-stage training strategy; the state and measurement are predicted, the optimal gain in polarization / inertial navigation filtering is calculated, state prediction and innovation are fused according to the calculated optimal gain, and estimation of the state at the current moment is obtained. According to the invention, high-precision navigation of the polarization / inertial navigation integrated navigation system is realized, and the environment adaptability of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of bionic polarization navigation, and particularly relates to a polarization / inertial integrated navigation method based on a deep Kalman filter network. Background Art

[0002] Many organisms in nature, such as bees, dragonflies, etc., can sense and fuse polarization information and inertial information to determine their own directions. Inspired by this navigation mechanism of organisms, bionic polarization / inertial integrated navigation has received extensive attention in recent years, with advantages such as being immune to electromagnetic interference and high dynamics. In bionic polarization / inertial integrated navigation, the Kalman filter algorithm is the mainstream information fusion method, but its performance highly depends on the accuracy of the prior noise statistical model. Since the error of the noise statistical characteristics will be gradually transmitted to the navigation solution calculation link, ultimately affecting the output accuracy of the heading angle and attitude angle. Therefore, how to eliminate the dependence of the information fusion method on the prior statistical characteristics of noise is the core technology for improving bionic polarization / inertial integrated navigation.

[0003] Chinese Patent Application CN201611062735.2 (A Combined Navigation Method Based on Polarization Information) established a polarization / inertial integrated navigation model based on the orthogonality of the E vector and the solar vector, and used Kalman filtering to fuse polarization and inertial data. The measurement noise covariance and the process noise covariance were obtained through multiple attempts and remained unchanged during the filtering process. Chinese Patent Application CN202111305825.0 (A Bionic Integrated Navigation Method Based on Adaptive Estimation of Polarization Measurement Noise Variance) established a quantitative relationship between the external light intensity, the degree of polarization, and the angular measurement accuracy of the polarization sensor, and adjusted the covariance matrix corresponding to the polarization measurement noise in real time according to the external light intensity and the degree of polarization. The chi-square test was used to judge the abnormal situation of the polarization sensor, but the process noise covariance was still given empirically. The paper "Outlier-Robust Extended Kalman Filtering for Bioinspired Integrated Navigation System" (Z. Qiu, S. Wang, P. Hu and L. Guo, "Outlier-Robust Extended Kalman Filtering for Bioinspired Integrated Navigation System," in IEEE Transactions on Automation Science and Engineering, vol. 21, no. 4, pp. 5881-5894, Oct. 2024, doi: 10.1109 / TASE.2023.3319508.) proposed an extended Kalman filter polarization integrated navigation method based on outlier detection and removal, obtained the statistical characteristics of the measurement noise through statistical analysis of the original measurement data, and the process noise covariance was given empirically.The paper "Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation" (S. Akhlaghi, N. Zhou and Z. Huang, "Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation," 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 2017, pp. 1-5, doi: 10.1109 / PESGM.2017.8273755.) introduced an adaptive adjustment factor and proposed a method for adaptively adjusting the measurement noise covariance and the process noise covariance according to the characteristics of the filtering process. However, its performance depends on the selection of the adjustment factor and needs to be determined through multiple experiments.

[0004] However, in the polarization / INS information fusion process of the above-mentioned patent application and paper, the measurement noise covariance and the process noise covariance are initially assigned manually and remain unchanged during filtering. However, as the core parameters of the Kalman filter, the statistical characteristics of the noise covariance matrix directly determine the confidence level of state estimation. When the noise model mismatches the true physical process, statistical errors will be gradually transmitted through the prediction-update iteration process, ultimately resulting in a decrease in the accuracy of the heading and attitude angles. Therefore, how to implement a polarization / INS integrated navigation method without the statistical characteristics of noise and improve the attitude accuracy of polarization / INS fusion is an urgent problem to be solved. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a polarization / INS integrated navigation method based on a deep Kalman filter network, which uses the intermediate features of polarization / INS filtering and the historical data of sensors as the input of the network; constructs a prior prediction error covariance network and a measurement residual covariance network for polarization / INS filtering, and establishes a temporal mapping between the intermediate features of filtering and the prior prediction error covariance matrix and the measurement residual covariance matrix; adopts a two-stage training strategy to train the prior prediction error covariance network and the measurement residual covariance network simultaneously. The first stage is warm-up training to improve the stability of network training, and the second stage is task-oriented training to improve the navigation performance of the network; finally, prior predictions are made for the state and measurement, the intermediate features and the historical data of the polarization sensor and INS are input into the prior prediction error covariance network and the measurement residual covariance network, the optimal gain of polarization / INS filtering is calculated, and the prior prediction and innovation of the state are fused to obtain the estimation of the state at the current moment. The present invention calculates the optimal gain based on the intermediate features of the Kalman filter, realizes the optimal fusion of the state and measurement, eliminates the dependence on the statistical characteristics of noise, and improves the environmental adaptability of the bionic polarization navigation system.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A polarization / INS integrated navigation method based on a deep Kalman filter network, comprising the following steps:

[0008] Step 1: Use the intermediate prior features of polarization / INS filtering and the historical data of the polarization sensor and INS as the input, and the input includes the difference between the prior prediction of the state at time t-1 and the posterior estimation of the state in the polarization / INS filtering at time t-1 , the innovation at time t , the difference between the posterior estimations of the states at time t-1 and time t-1 , the measurement difference between time t and time t-1 , the measurement matrix at time t and the differences in the inertial angular velocity, acceleration, and polarization light intensity between time t and time t-1 ; the innovation represents the difference between the measured value and the predicted value;

[0009] Step 2: Construct a prior prediction error covariance matrix estimation network and a measurement residual covariance matrix estimation network in the polarization / INS filtering. The input of the prior prediction error covariance matrix estimation network is as , , , , and the input of the measurement residual covariance matrix estimation network is For 、 、 and the output of the prior prediction error covariance matrix estimation network To establish a temporal mapping of the input features to the prior prediction error covariance matrix and the measurement residual covariance matrix of the polarization / INS filter

[0010] Step 3: Simultaneously train the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network using a two-stage training strategy. In the first stage, use the optimal gain predicted by the network and the Kalman gain calculated in the Kalman filter as constraints to obtain the optimal gain. In the second stage, use the heading angle obtained by fusing the optimal gain predicted by the network and the reference heading angle as a constraint to improve the performance of the network and the accuracy of navigation

[0011] Step 4: Perform prior prediction on the state and measurement of the polarization / INS integrated navigation system based on the Kalman filter. Use 、 、 、 、 and as the intermediate prior features and input them into the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network to calculate the optimal gain, and fuse the prior prediction of the state and the innovation to obtain the estimation of the current state, and then calculate the heading angle

[0012] The beneficial effects of the present invention compared with the prior art are as follows:

[0013] A polarization / INS integrated navigation method based on a deep Kalman filter network of the present invention utilizes the powerful fitting ability of the deep neural network and the robustness and interpretability of the Kalman filter framework, establishes a temporal mapping of the Kalman filter intermediate prior features to the prior prediction error covariance matrix and the innovation covariance matrix, eliminates the dependence on the process noise covariance matrix and the measurement noise covariance matrix, calculates the optimal gain by fusing the state prior prediction and the innovation according to the Kalman filter intermediate prior features during the filtering process, realizes high-precision navigation of the polarization / INS integrated navigation system, and improves the environmental adaptability of the system Description of the Drawings

[0014] Figure 1 is a flowchart of a polarization / INS integrated navigation method based on a deep Kalman filter network of the present invention

[0015] Figure 2 is a comparison diagram of the heading angle results between the present invention and the traditional filtering method

[0016] Figure 3 This is a comparison chart of the heading angle error between the present invention and traditional filtering methods. Detailed implementation manners

[0017] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0018] Existing polarization / INS integrated navigation depends on the initial given of the noise covariance matrix and the measurement noise covariance matrix, and remains unchanged during the filtering process, thus affecting the navigation accuracy of the polarization sensor.

[0019] As Figure 1 shown, the present invention proposes a polarization / INS integrated navigation method based on a deep Kalman filter network, including the following steps:

[0020] Step 1: Use the intermediate features of polarization / INS filtering and the historical data of the polarization sensor and INS to establish the input features of the network, including:

[0021] Use the intermediate prior features of polarization / INS filtering fusion and the historical data of the polarization sensor and INS as the input of the network, including the difference between the state prior prediction at the previous moment (time t-1) and the state posterior estimation in the polarization / INS filtering at the previous moment (time t-1) the innovation at time t the difference between the state posterior estimation at time t-1 and the previous moment of time t-1 the measurement difference between time t and time t-1 the measurement matrix at time t and the differences in the inertial angular velocity, acceleration, and polarization light intensity between time t and time t-1 ; the innovation represents the difference between the measurement value and the predicted value;

[0022] Step 2: Build a prior prediction error covariance network and a measurement residual covariance network for polarization / INS filtering, and establish a time-series mapping between the filtering intermediate features and the prior prediction error covariance matrix and the measurement residual covariance matrix, including:

[0023] Build an estimation network for the prior prediction error covariance matrix in polarization / INS filtering and an estimation network for the measurement residual covariance matrix , the input of the prior prediction error covariance matrix estimation network of For 、 、 、 , the input of the measurement residual covariance matrix estimation network is For 、 、 and output, establish a temporal mapping of the input features with the polarization / inertial navigation filtering prior prediction error covariance matrix and the measurement residual covariance matrix;

[0024] Step 3. Simultaneously train the prior prediction error covariance network and the measurement residual covariance network using a two-stage training strategy, that is and to improve the stability of training and the accuracy of navigation performance. The first stage is warm-up training, using the optimal gain predicted by the network and the Kalman gain calculated in the Kalman filter as constraints, so that the network can predict a stable but less accurate optimal gain. The second stage is task-oriented training, using the heading angle obtained by fusing the optimal gain predicted by the network and the reference heading angle as a constraint to improve the performance of the network and the accuracy of navigation;

[0025] Step 4. Input the polarization / inertial navigation filtering intermediate features and the historical data of the polarization sensor and the inertial navigation into the network, calculate the optimal gain of the polarization / inertial navigation filtering, and fuse the prior prediction and innovation of the state to obtain an estimated value of the current heading angle, including:

[0026] Based on the Kalman filter, perform prior prediction on the state and measurement of the polarization / inertial integrated navigation system, and input the intermediate prior features ( 、 、 、 、 ), the historical data of the inertial angular velocity, acceleration, and polarization light intensity ( ) into the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network to calculate the optimal gain, and fuse the prior prediction and innovation of the state to obtain the posterior estimation of the current state, and then calculate the heading angle.

[0027] Specifically, the said Step 1 includes:

[0028] The state vector of the polarization / inertial integrated navigation system can be expressed as , where represents the three-dimensional misalignment angle, represents the gyro scale factor error, and the measurement vector can be expressed as , where y represents the measurement vector, represents the solar vector, which is calculated from the astronomical almanac, represents the attitude transfer matrix from the vehicle coordinate system to the navigation coordinate system, represents the polarization vector, which is calculated from the polarization light intensity. represents the matrix transpose.

[0029] When estimating the state at time t, it can be expressed as:

[0030] (1)

[0031] where, represents the posterior estimate of the state at time t - 1, represents the prior prediction of the state at time t - 1.

[0032] It can be expressed as:

[0033] (2)

[0034] where, represents the measurement information at time t, represents the prediction of the measurement at time t.

[0035] It can be expressed as:

[0036] (3)

[0037] where, represents the posterior estimate of the state at the previous moment of t - 1.

[0038] It can be expressed as:

[0039] (4)

[0040] where, represents the measurement information at time t - 1.

[0041] It can be expressed as:

[0042] (5)

[0043] where, represents the measurement matrix.

[0044] It can be expressed as:

[0045] (6)

[0046] Among them, and respectively represent the angular velocities output by the gyroscope at the current and previous moments, and respectively represent the accelerations at the current and previous moments, and respectively represent the light intensities measured by the polarization sensor at the current and previous moments.

[0047] Specifically, step two includes:

[0048] Using and to calculate the optimal gain from the prior prediction error covariance matrix and the measurement residual covariance matrix calculated, where is 's input, which can be expressed as , is 's input, which can be expressed as .

[0049] Specifically, step three includes:

[0050] The loss function of the first-stage warm-up training is:

[0051] (7)

[0052] where is the Kalman gain calculated using the Kalman filter, represents calculating the 1-norm. The first-stage warm-up training can improve the stability of network training and enable training with sequences of any length.

[0053] The loss function of the second-stage task-oriented training is:

[0054] (8)

[0055] where is the heading angle obtained by fusing information using the optimal gain, is the current heading angle provided by the reference. The second-stage task-oriented training can improve the accuracy of the optimal gain calculated by the network, as well as the heading angle accuracy and environmental adaptability of the bionic polarization navigation system.

[0056] Specifically, step four includes:

[0057] The prior prediction of the state can be expressed as , where represents the state transition matrix, and the prediction of the measurement is expressed as .

[0058] Then the posterior estimate of the state at time t is expressed as: .

[0059] Example:

[0060] The simulation trajectory consists of three parts: the first step is small maneuver with weak interference, the second step is small maneuver with strong interference, and the third step is large maneuver with strong interference. Each part contains 1000 seconds of data.

[0061] Among them, small maneuver means moving at a maximum angular velocity of ±4° / s and a maximum acceleration of ±4m / s 2 and large maneuver means moving at a maximum angular velocity of ±20° / s and a maximum acceleration of ±20m / s 2 .

[0062] Weak interference means that the error of the inertial navigation is relatively low (the bias stability of the gyroscope, the angular random walk of the gyroscope, the bias stability of the accelerometer, and the velocity random walk of the accelerometer are , , , ), the polarization angle noise is Gaussian white noise and satisfies , the polarization light noise is Gaussian white noise and satisfies . In strong interference, from 1 to 100 seconds is weak interference, from 101 to 200 seconds the noise of the inertial navigation becomes 3 times that of weak interference, from 201 to 300 seconds is weak interference, from 301 to 400 seconds the inertial navigation noise becomes 2 times that of weak interference and the polarization angle noise becomes 2 times that of weak interference, from 401 to 500 seconds is weak interference, from 501 to 600 seconds the polarization angle noise becomes 3 times that of weak interference, from 601 to 700 seconds is weak interference, from 701 to 800 seconds the polarization angle noise is 2 times that of weak interference and the light intensity is 0.8 times that of weak interference, from 801 to 900 seconds is weak interference, from 901 to 1000 seconds the light intensity is 0.5 times that of weak interference.

[0063] Using the method of the present invention to estimate the heading angle of the simulation trajectory, the obtained heading angle curve and heading angle error curve are respectively as Figure 2 and Figure 3 shown.

[0064] Method 1 is the traditional Kalman filtering method, method 2 is the adaptive Kalman filtering method, and method 3 is the method of the present invention. As can be seen from Figure 2 , the method of the present invention can accurately estimate the heading angle. At Figure 3Among them, the method of the present invention has the smallest and most stable heading angle errors in all three parts. For Method 1, the root mean square error (RMSE) of the heading angle in Step 1 is 0.08°, in Step 2 is 0.37°, and in Step 3 is 1.43°. For Method 2, the root mean square error (RMSE) of the heading angle in Step 1 is 0.11°, in Step 2 is 0.39°, and in Step 3 is 0.91°. For Method 3, the root mean square error (RMSE) of the heading angle in Step 1 is 0.04°, in Step 2 is 0.09°, and in Step 3 is 0.38°. Regardless of the magnitude of the maneuver or the strength of the interference, the method described in the present invention can achieve the most accurate heading estimation.

[0065] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0066] The above are only the preferred implementation schemes of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention. The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A polarization / INS integrated navigation method based on a deep Kalman filter network, characterized in that It includes the following steps: Step 1: Use the intermediate prior features fused by polarization / INS filtering, along with the historical data of the polarization sensor and INS, as the input. The input includes the difference between the state prior prediction at time t-1 and the state posterior estimation in the polarization / INS filtering at time t-1 , the innovation at time t , the difference between the state posterior estimations at time t-1 and time t-1 , the measurement difference between time t and time t-1 , the measurement matrix at time t and the differences in the INS angular velocity, acceleration, and polarization light intensity between time t and time t-1 ; The innovation represents the difference between the measured value and the predicted value; Step 2: Build the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network in the polarization / inertial navigation filter. The input of the prior prediction error covariance matrix estimation network is , , , , , . The input of the measurement residual covariance matrix estimation network is , , , and the output of the prior prediction error covariance matrix estimation network . Establish the temporal mapping between the input features and the prior prediction error covariance matrix and the measurement residual covariance matrix of the polarization / inertial navigation filter. Step 3: Simultaneously train the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network , in the first stage, use the optimal gain predicted by the network and the Kalman gain calculated in the Kalman filter as constraints to obtain the optimal gain. In the second stage, use the heading angle obtained by fusing the optimal gain predicted by the network and the reference heading angle as constraints to improve the performance of the network and the accuracy of navigation; Step 4: Perform prior prediction on the states and measurements of the polarization / inertial integrated navigation system, and input , , , , and into the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network to calculate the optimal gain, fuse the prior prediction and innovation of the state to obtain the estimation of the current state, and then calculate the heading angle.

2. The polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 1, wherein Step 1 includes: The state vector of the polarization / inertial integrated navigation system is expressed as , where represents the three-dimensional misalignment angle, represents the gyro scale factor error, and the measurement vector y is expressed as , where represents the solar vector, which is calculated from the astronomical almanac, represents the attitude transfer matrix from the body frame to the navigation frame, represents the polarization vector, which is calculated from the polarization light intensity; represents the matrix transpose.

3. A polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 2, wherein Step 1 also includes: When estimating the state at time t, the difference between the prior prediction of the state at time t-1 and the posterior estimation of the state in the polarization / inertial navigation filter at time t-1 is expressed as: (1) Among them, represents the posterior estimate of the state at time t - 1, represents the prior prediction of the state at time t - 1; Innovation at time t It is expressed as: (2) Among them, represents the measurement information at time t, represents the prediction of the measurement at time t.

4. A polarization / INS integrated navigation method based on a deep Kalman filter network according to claim 3, characterized in that Difference between the posterior state estimate at time t-1 and that at time t-1 Expressed as: (3) Among them, represents the posterior estimate of the state at the previous moment of t-1; Measurement difference between time t and time t-1 Expressed as: (4) Among them, represents the measurement at time t-1.

5. A polarization / INS integrated navigation method based on a deep Kalman filter network according to claim 4, characterized in that Measurement matrix at time t It is expressed as: (5) Among them, represents the measurement matrix; Differences in inertial navigation angular velocity, acceleration, and polarized light intensity between time t and time t-1 Expressed as: (6) Among them, and respectively represent the angular velocities output by the gyroscope at time t and at time t - 1, and respectively represent the accelerations at time t and at time t - 1, and respectively represent the light intensities measured by the polarization sensor at time t and at time t - 1.

6. The polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 5, characterized in that Step 2 includes; Use the prior prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network Calculate the optimal gain from the calculated prior prediction error covariance matrix and measurement residual covariance matrix: ; Among them, is the input of the prior prediction error covariance matrix estimation network and is denoted as . is the input of the measurement residual covariance matrix estimation network and is denoted as .

7. A polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 6, wherein In the third step, the first stage is warm-up training, and the loss function of the warm-up training is as follows: (7) Among them, is the optimal gain, is the Kalman gain calculated using the Kalman filter, represents the calculation of the 1-norm.

8. A polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 7, characterized in that In the third step, the second stage is task-oriented training, and the loss function of the task-oriented training is as follows: (8) Among them, is the heading angle obtained by performing information fusion using the optimal gain calculated by the network, is the current heading angle provided by the reference.

9. A polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 8, characterized in that, Step 4 includes: The prior prediction of the state is represented as ; Among them, represents the state transition matrix, and the prediction of the measurement is expressed as .

10. A polarization / inertial integrated navigation method based on a deep Kalman filter network according to claim 8, characterized in that Step 4 also includes: The posterior estimate of the state at time t It is expressed as: 。

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