A polarization / inertial navigation integrated navigation method based on a deep Kalman filtering network

Abstract

The application provides a polarization / inertial navigation combined navigation method based on a deep Kalman filtering network, belongs to the field of bionic polarization navigation, and comprises the following steps: taking intermediate characteristics in Kalman filtering, a polarization sensor and historical data of inertial navigation as inputs of the network, building a priori prediction error covariance matrix estimation network and a measurement residual covariance matrix estimation network in polarization / inertial filtering, simultaneously training the priori prediction error covariance matrix estimation network and the measurement residual covariance matrix estimation network by adopting a two-stage training strategy, predicting states and measurements, calculating optimal gain in polarization / inertial filtering, and fusing the prediction of states and new information according to the calculated optimal gain to obtain estimation of the states at the current time. The application realizes high-precision navigation of the polarization / inertial navigation combined navigation system and improves the environmental adaptability of the system.

Description

Technical Field

[0001] This invention belongs to the field of biomimetic polarization navigation, specifically relating to a polarization / inertial navigation integrated navigation method based on a deep Kalman filter network. Background Technology

[0002] Many organisms in nature, such as bees and dragonflies, can sense and fuse polarization and inertial information to determine their own direction. Inspired by this biological navigation mechanism, biomimetic polarization / inertial navigation has received widespread attention in recent years, offering advantages such as immunity to electromagnetic interference and high dynamic range. In biomimetic polarization / inertial navigation, the Kalman filter algorithm is the mainstream information fusion method, but its performance is highly dependent on the accuracy of the prior noise statistical model. Errors in the noise statistical characteristics propagate step-by-step to the navigation calculation stage, ultimately affecting the output accuracy of the heading and attitude angles. Therefore, eliminating the dependence of information fusion methods on the prior noise statistical characteristics is a core technology for improving biomimetic polarization / inertial navigation.

[0003] Chinese patent application CN201611062735.2 (A Combined Navigation Method Based on Polarization Information) establishes a polarization / inertial navigation combined model based on the orthogonality of the E-vector and the solar vector. It uses Kalman filtering to fuse polarization and inertial navigation data. The measurement noise covariance and process noise covariance are obtained through multiple trials, and the noise covariance remains constant during the filtering process. Chinese patent application CN202111305825.0 (A Bionic Combined Navigation Method Based on Adaptive Estimation of Polarization Measurement Noise Variance) establishes a quantitative relationship between external light intensity, polarization degree, and the angular measurement accuracy of the polarization sensor. It adjusts the covariance matrix corresponding to the polarization measurement noise in real time based on the external light intensity and polarization degree, and uses chi-square detection to determine polarization sensor anomalies. However, the process noise covariance is still determined 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.) proposes an extended Kalman filter polarization-integrated navigation method based on outlier detection and removal. It obtains the statistical characteristics of measurement noise by performing statistical analysis on the raw measurement data, while the process noise covariance is 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.) introduces an adaptive adjustment factor and proposes a method for adaptively adjusting the measured noise covariance and process noise covariance based on the characteristics of the filtering process. However, the performance depends on the selection of the adjustment factor and requires multiple experiments to determine.

[0004] However, in the polarization / inertial navigation information fusion process described in the aforementioned patent applications and papers, the measurement noise covariance and process noise covariance are manually initialized and remain unchanged during filtering. However, as a core parameter of the Kalman filter, the statistical characteristics of the noise covariance matrix directly determine the confidence level of the state estimation. When the noise model mismatches with the actual physical process, statistical errors are propagated step-by-step through the prediction-update iteration process, ultimately leading to a decrease in heading and attitude angle accuracy. Therefore, how to achieve a polarization / inertial navigation integrated navigation method that does not require noise statistical characteristics and improve the attitude accuracy of polarization / inertial navigation fusion is an urgent problem to be solved. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a polarization / inertial navigation integrated method based on a deep Kalman filter network. The method uses intermediate features of the polarization / inertial navigation filter and historical sensor data as inputs to the network. A priori prediction error covariance network and a measurement residual covariance network for the polarization / inertial navigation filter are constructed, establishing a temporal mapping between the intermediate filter features and the priori prediction error covariance matrix and the measurement residual covariance matrix. A two-stage training strategy is employed to simultaneously train both the priori prediction error covariance network and the measurement residual covariance network. The first stage is warm-up training to improve network training stability, while the second stage is task-oriented training to improve network navigation performance. Finally, priori predictions of the state and measurements are performed. The intermediate features and historical data from the polarization sensor and inertial navigation system are input into the priori prediction error covariance network and the measurement residual covariance network to calculate the optimal gain of the polarization / inertial navigation filter. The priori predictions of the state and the new information are then fused to obtain an estimate of the state at the current moment. This invention calculates the optimal gain based on the intermediate features of Kalman filtering, achieving optimal fusion of state and measurement, eliminating dependence on noise statistical characteristics, and improving the environmental adaptability of the biomimetic polarization navigation system.

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

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

[0008] Step 1: Using intermediate prior features from polarization / inertial navigation filter fusion, along with historical data from the polarization sensor and inertial navigation system, as input, the input includes the difference between the state prior prediction at time t-1 and the state posterior estimate from the polarization / inertial navigation filter at time t-1. News at time t The difference between the posterior state estimates at time t-1 and time t-1 Measurement difference between time t and time t-1 Measurement matrix at time t And the differences in inertial angular velocity, acceleration, and polarized light intensity between time t and time t-1. The new information represents the difference between the measured value and the predicted value.

[0009] Step 2: Construct a priori prediction error covariance matrix estimation network for polarization / inertial navigation filtering. And measurement residual covariance matrix estimation network Prior prediction error covariance matrix estimation network Input for , , , Measurement residual covariance matrix estimation network Input for , , and prior prediction error covariance matrix estimation network The output establishes a time-series mapping between the input features and the prior prediction error covariance matrix of polarization / inertial navigation filtering and the measurement residual covariance matrix;

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

[0011] Step 4: Based on Kalman filtering, perform prior predictions of the state and measurements of the polarization / inertial navigation integrated system, and use these as intermediate prior features. , , , , and Input to the prior prediction error covariance matrix estimation network And measurement residual covariance matrix estimation network In the process, the optimal gain is calculated, and the prior prediction of the state and the innovation are fused to obtain the estimate of the current state, and then the heading angle is calculated.

[0012] The advantages of this invention compared to the prior art are as follows:

[0013] This invention discloses a polarization / inertial navigation integrated method based on a deep Kalman filter network. It leverages the powerful fitting ability of deep neural networks and the robustness and interpretability of the Kalman filter framework to establish a temporal mapping between intermediate prior features of the Kalman filter and the prior prediction error covariance matrix and innovation covariance matrix. This eliminates the dependence on the process noise covariance matrix and measurement noise covariance matrix. During the filtering process, the optimal gain fusion state prior prediction and innovation are calculated based on the intermediate prior features of the Kalman filter, achieving high-precision navigation for the polarization / inertial navigation integrated system and improving the system's environmental adaptability. Attached Figure Description

[0014] Figure 1 This is a flowchart of a polarization / inertial navigation integrated method based on a deep Kalman filter network according to the present invention;

[0015] Figure 2 This is a comparison chart of the heading angle results of the present invention and the traditional filtering method;

[0016] Figure 3 This is a comparison chart of the heading angle error results between the present invention and the traditional filtering method. Detailed Implementation

[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0018] Existing polarization / inertial navigation systems rely on the initial given noise covariance matrix and measurement noise covariance matrix, which remain unchanged during the filtering process, thus affecting the navigation accuracy of polarization sensors.

[0019] like Figure 1 As shown, this invention proposes a polarization / inertial navigation integrated method based on a deep Kalman filter network, comprising the following steps:

[0020] Step 1: Establish the network's input features using intermediate features from polarization / inertial navigation filters and historical data from polarization sensors and inertial navigation systems, including:

[0021] The network inputs include intermediate prior features fused by polarization / inertial navigation filtering, as well as historical data from the polarization sensor and inertial navigation system. This inputs include the difference between the state prior prediction from the previous time step (t-1) and the state posterior estimate from the polarization / inertial navigation filtering at the previous time step (t-1). News at time t The difference between the posterior state estimates at time t-1 and the previous time step. Measurement difference between time t and time t-1 Measurement matrix at time t And the differences in inertial angular velocity, acceleration, and polarized light intensity between time t and time t-1. The new information represents the difference between the measured value and the predicted value.

[0022] Step 2: Construct the polarization / inertial navigation filter prior prediction error covariance network and the measurement residual covariance network, and establish the temporal mapping between the intermediate features of the filter and the prior prediction error covariance matrix and the measurement residual covariance matrix, including:

[0023] Building a prior prediction error covariance matrix estimation network for polarization / inertial navigation filtering And measurement residual covariance matrix estimation network Prior prediction error covariance matrix estimation network Input for , , , Measurement residual covariance matrix estimation network Input for , , as well as The output establishes a time-series mapping between the input features and the prior prediction error covariance matrix of polarization / inertial navigation filtering and the measurement residual covariance matrix;

[0024] Step 3: Employ a two-stage training strategy to simultaneously train the prior prediction error covariance network and the measurement residual covariance network, i.e. and To improve the stability of training and the accuracy of navigation performance. The first stage is warm-up training, which uses 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 mission-oriented training, which uses the heading angle obtained by fusing the optimal gain predicted by the network and the reference heading angle as constraints to improve the network performance and navigation accuracy.

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

[0026] Prior prediction of the state and measurements of the polarization / inertial navigation integrated system based on Kalman filtering is performed, and intermediate prior features ( , , , , Historical data on inertial angular velocity, acceleration, and polarized light intensity ( ) and inertial navigation angular velocity, acceleration, and polarized light intensity ( Input to the prior prediction error covariance matrix estimation network And measurement residual covariance matrix estimation network In the process, the optimal gain is calculated, and the prior prediction of the state and the innovation are fused to obtain the posterior estimate of the current state, and then the heading angle is calculated.

[0027] Specifically, step one includes:

[0028] The state vector of a polarization / inertial navigation integrated system can be represented as: ,in Indicates the three-dimensional misalignment angle. To represent the gyroscope scale factor error, the measurement vector can be represented as: Where y represents the measurement vector, This represents the solar vector, calculated from the astronomical almanac. This represents the attitude transfer matrix from the carrier system to the navigation system. This represents the polarization vector, which is calculated from the polarized light intensity. This indicates the matrix transpose.

[0029] When estimating the state at time t It can be represented as:

[0030] (1)

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

[0032] It can be represented as:

[0033] (2)

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

[0035] It can be represented as:

[0036] (3)

[0037] in, This represents the posterior estimate of the state at the previous time step t-1.

[0038] It can be represented as:

[0039] (4)

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

[0041] It can be represented as:

[0042] (5)

[0043] in, This represents the measurement matrix.

[0044] It can be represented as:

[0045] (6)

[0046] in, and These represent the angular velocities output by the gyroscope at the current and previous moments, respectively. and These represent the accelerations at the current and previous moments, respectively. and These represent the light intensity measured by the polarization sensor at the current and previous moments, respectively.

[0047] Specifically, step two includes:

[0048] use and The optimal gain is calculated using the prior prediction error covariance matrix and the measurement residual covariance matrix. ,in, for The input can be represented as , for The input can be represented as .

[0049] Specifically, step three includes:

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

[0051] (7)

[0052] in The Kalman gain calculated using Kalman filtering, This indicates the calculation of the 1-norm. The first stage of warm-up training can improve the stability of network training and enable training using sequences of arbitrary length.

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

[0054] (8)

[0055] in, The heading angle is obtained by information fusion using optimal gain. The current heading angle is provided as a reference. The second phase of mission-oriented training can improve the accuracy of the network in calculating the optimal gain, as well as the heading angle accuracy and environmental adaptability of the biomimetic polarization navigation system.

[0056] Specifically, step four includes:

[0057] The prior prediction of a state can be expressed as ,in, The state transition matrix is ​​represented as the measurement prediction is expressed as follows. .

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

[0059] Example:

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

[0061] Among them, small maneuver means with a maximum angular velocity of ±4° / s and a maximum acceleration of ±4m / s². 2 Motion, high-speed maneuverability means at a maximum angular velocity ±20° / s and a maximum acceleration ±20m / s². 2 sports.

[0062] Weak interference indicates low inertial navigation system error (the gyroscope's bias stability, gyroscope's angle random walk, accelerometer's bias stability, and accelerometer's velocity random walk are respectively...). , , , Polarization angle noise It is Gaussian white noise and satisfies Polarization noise It is Gaussian white noise and satisfies In strong interference, the interference is weak from 1 to 100 seconds; from 101 to 200 seconds, the inertial navigation noise becomes 3 times that of weak interference; from 201 to 300 seconds, the interference is weak; from 301 to 400 seconds, the inertial navigation noise becomes 2 times that of weak interference and the polarization angle noise also becomes 2 times that of weak interference; from 401 to 500 seconds, the interference is weak; from 501 to 600 seconds, the polarization angle noise becomes 3 times that of weak interference; from 601 to 700 seconds, the interference is weak; 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, the interference is weak; and from 901 to 1000 seconds, the light intensity is 0.5 times that of weak interference.

[0063] Using this invention to estimate the heading angle of a simulated trajectory, the resulting heading angle curve and heading angle error curve are shown below. Figure 2 and Figure 3 As shown.

[0064] Method one is the traditional Kalman filtering method, method two is the adaptive Kalman filtering method, and method three is the method of this invention. From Figure 2 As can be seen, the method of the present invention can accurately estimate the heading angle. Figure 3In this invention, the heading angle error is minimized and most stable in all three parts. Method 1 has a root mean square error (RMSE) of 0.08° in step 1, 0.37° in step 2, and 1.43° in step 3. Method 2 has an RMSE of 0.11° in step 1, 0.39° in step 2, and 0.91° in step 3. Method 3 has an RMSE of 0.04° in step 1, 0.09° in step 2, and 0.38° in step 3. Regardless of the magnitude of the maneuver or the strength of the interference, the method described in this invention can achieve the most accurate heading estimate.

[0065] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0066] The above description is merely a preferred embodiment of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention. Contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A polarization / inertial navigation integrated navigation method based on a deep Kalman filter network, characterized in that, Includes the following steps: Step 1: Using intermediate prior features from polarization / inertial navigation filter fusion, along with historical data from the polarization sensor and inertial navigation system, as input, the input includes the difference between the state prior prediction at time t-1 and the state posterior estimate from the polarization / inertial navigation filter at time t-1. News at time t The difference between the posterior state estimates at time t-1 and time t-1 Measurement difference between time t and time t-1 Measurement matrix at time t And the differences in inertial angular velocity, acceleration, and polarized light intensity between time t and time t-1. The new information represents the difference between the measured value and the predicted value. Step 2: Construct a priori prediction error covariance matrix estimation network for polarization / inertial navigation filtering. And measurement residual covariance matrix estimation network Prior prediction error covariance matrix estimation network Input for , , , Measurement residual covariance matrix estimation network Input for , , and prior prediction error covariance matrix estimation network The output establishes a time-series mapping between the input features and the prior prediction error covariance matrix of polarization / inertial navigation filtering and the measurement residual covariance matrix; Step 3: Simultaneously train the prior prediction error covariance matrix estimation network using a two-stage training strategy. And measurement residual covariance matrix estimation network In the first stage, the optimal gain predicted by the network and the Kalman gain calculated in the Kalman filter are used as constraints to obtain the optimal gain. In the second stage, the heading angle obtained by fusing the optimal gain predicted by the network and the reference heading angle are used as constraints to improve the network performance and navigation accuracy. Step 4: Based on Kalman filtering, perform prior predictions of the state and measurements of the polarization / inertial navigation integrated system, and use these as intermediate prior features. , , , , and Input to the prior prediction error covariance matrix estimation network And measurement residual covariance matrix estimation network In the process, the optimal gain is calculated, and the prior prediction of the state and the innovation are fused to obtain the estimate of the current state, and then the heading angle is calculated.

2. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 1, characterized in that, Step one includes: The state vector of a polarization / inertial navigation integrated system is represented as follows: ,in, Indicates the three-dimensional misalignment angle. The measurement vector y represents the gyroscope scale factor error. ,in, This represents the solar vector, calculated from the astronomical almanac. This represents the attitude transfer matrix from the carrier system to the navigation system. This represents the polarization vector, which is calculated from the polarized light intensity. This indicates the matrix transpose.

3. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 2, characterized in that, Step one also includes: When estimating the state at time t, the difference between the prior state prediction at time t-1 and the posterior state estimation in the polarization / inertial filtering at time t-1 is... Represented as: (1) in, This represents the posterior estimate of the state at time t-1. Represents the prior prediction of the state at time t-1; News at time t Represented as: (2) in, This represents the measurement information at time t. This represents the prediction of the measurement at time t.

4. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 3, characterized in that, The difference between the posterior state estimates at time t-1 and time t-1 Represented as: (3) in, This represents the posterior estimate of the state at the previous time step t-1; Measurement difference between time t and time t-1 Represented as: (4) in, This represents the measurement at time t-1.

5. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 4, characterized in that, Measurement matrix at time t Represented as: (5) in, Represents the measurement matrix; Differences in inertial angular velocity, acceleration, and polarized light intensity between time t and time t-1 Represented as: (6) in, and These represent the angular velocities output by the gyroscope at time t and t-1, respectively. and Let represent the accelerations at time t and t-1, respectively. and These represent the light intensity measured by the polarization sensor at time t and time t-1, respectively.

6. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 5, characterized in that, Step two includes: Network estimation using prior prediction error covariance matrix And measurement residual covariance matrix estimation network Calculate the optimal gain using the calculated prior prediction error covariance matrix and the measurement residual covariance matrix: ; in, Network for estimating the covariance matrix of prior prediction errors The input is represented as , Network for estimating residual covariance matrix The input is represented as .

7. The polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 6, characterized in that, In step three, the first stage is warm-up training, and the loss function for warm-up training is... for: (7) in, For optimal gain, The Kalman gain calculated using Kalman filtering, This indicates the calculation of the 1-norm.

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

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

10. A polarization / inertial navigation integrated method based on a deep Kalman filter network according to claim 8, characterized in that, Step four also includes: Posterior estimation of the state at time t Represented as: 。

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