Polarization / inertia / vision intelligent navigation method based on model error learning

Abstract

The invention provides a polarization / inertia / vision intelligent navigation method based on model error learning, which belongs to the field of navigation and comprises the following steps: modeling a polarization / inertia / vision integrated navigation system, and establishing a system state equation by taking an inertial navigation error and a camera pose error as system state quantities; establishing a system measurement equation based on the information of the polarization sensor and the visual sensor; a neural network learning modeling error is constructed by considering uncertainty modeling errors of a system state equation and a measurement equation caused by system parameter errors and environmental interference, and the precision of a polarization / inertia / vision integrated navigation system model is improved; the multi-state constraint Kalman filtering method of the embedded neural network is established for solving the problems that in an actual environment, sensor noise statistical characteristics are unknown and time-varying due to environmental factors. According to the invention, the navigation precision of the polarization / inertia / vision integrated navigation system in a complex environment can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of navigation, and particularly relates to a polarization / inertial / visual intelligent navigation method based on model error learning. Background Art

[0002] The navigation system can provide spatial motion information for unmanned systems and is the "motor nerve center" of unmanned systems. Research has found that organisms in nature possess excellent navigation capabilities. For example, bees have halteres and compound eyes and can perceive environmental / motion information such as polarization, inertia, and vision, enabling behaviors such as foraging and homing. They have advantages such as high autonomy, strong anti-interference ability, and non-accumulation of errors over time, providing a technical means for autonomous navigation in complex environments. Therefore, how to simulate the multi-sensor intelligent perception and fusion mechanism of organisms and propose an intelligent navigation method with high autonomy and strong anti-interference has become the core key to the navigation of unmanned systems in complex environments.

[0003] In recent years, many research institutions have carried out a large number of studies on multi-sensor fusion methods. For example, the paper "Integrated Polarized Skylight Sensor and MIMU With a Metric Map for Urban Ground Navigation" (Fan C, Hu X, He X, et al. Integrated polarized skylight sensor and MIMU with a metric map for urban ground navigation[J]. IEEE Sensors Journal, 2017, 18(4): 1714-1722) calculates navigation information based on multi-sensor information and uses Kalman filtering for information fusion to achieve loose integrated navigation of polarized / inertial / visual three kinds of information. Chinese Patent Application CN202010623718.1 (a method for estimating the pose of an unmanned aerial vehicle based on visual-inertial polarized light fusion) adds the heading constraint of a polarized light compass on the basis of visual measurement and inertial measurement. By imitating the structure and function of desert ants' perception of polarized light, it provides a stable heading constraint for the navigation sensors of the unmanned aerial vehicle and improves the pose estimation accuracy of the integrated navigation system. The paper "KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics" (Revach G, Shlezinger N, Ni X, et al. KalmanNet: Neural network aided Kalman filtering for partially known dynamics[J]. IEEE Transactions on Signal Processing, 2022, 70: 1532-1547) combines the state space model with a neural network to achieve accurate state estimation independent of noise statistical characteristics while maintaining the Kalman filtering framework. Chinese Patent Application CN202310474059.3 (a method for integrated navigation of an unmanned aerial vehicle with polarized vision imitating compound eyes in a low light intensity environment) uses the measurement information obtained by a polarization sensor and a polarization camera to achieve tight integrated navigation of polarized / inertial / visual three kinds of information based on the MSCKF filtering framework.

[0004] Although the multi-sensor fusion methods proposed in the above-mentioned papers and patent applications have achieved certain application effects, they do not consider the uncertainty modeling errors of the system model in complex environments such as vibration and optical interference, as well as the problem that the statistical characteristics of sensor noise are unknown and time-varying during the fusion process, which restricts the navigation performance of the system in complex application scenarios. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a polarization / inertial / visual intelligent navigation method based on model error learning, which models the polarization / inertial / visual integrated navigation system, takes the inertial navigation error and camera pose error as system state variables, and establishes a system state equation. Based on the information of the polarization sensor and the visual sensor, a system measurement equation is established. Considering the uncertainty modeling errors in the system state equation and the measurement equation caused by system parameter errors and environmental disturbances, a neural network is constructed to learn the modeling errors, so as to improve the accuracy of the polarization / inertial / visual integrated navigation system model. A multi-state constrained Kalman filtering method with an embedded neural network is established for the problem that the statistical characteristics of sensor noise are unknown and time-varying due to environmental factors (such as temperature, vibration, and optical interference) in the actual environment. Based on the multi-state constrained Kalman filtering framework, the present invention constructs an uncertainty modeling error learning network and a Kalman gain learning network, realizes precise system modeling and intelligent fusion independent of noise statistical characteristics, can improve the accuracy and robustness of the integrated navigation system in complex environments, and provides technical support for the autonomous navigation requirements of unmanned systems in satellite denial, interference countermeasure, and unfamiliar environments.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A polarization / inertial / visual intelligent navigation method based on model error learning, comprising the following steps:

[0008] Step 1: Model the polarization / inertial / visual integrated navigation system to obtain a polarization / inertial / visual integrated navigation system model. Select the inertial navigation state error and camera pose error as the state vectors, establish the polarization / inertial / visual integrated navigation system state equation based on the inertial navigation kinematic model, establish the polarization measurement equation according to the perpendicular relationship between the polarization vector and the solar vector, and establish the visual measurement equation according to the visual reprojection error;

[0009] Step 2: For the uncertainty modeling errors of the polarization / inertial / visual integrated navigation system state equation and measurement equation, with the attitude angle error and position error of the integrated navigation system as constraints, respectively construct a state transition matrix error learning network and a measurement matrix error learning network, and use the inertial navigation historical data and measurement historical data to learn the state transition matrix error and measurement matrix error, so as to realize the fine modeling of the polarization / inertial / visual integrated navigation system;

[0010] Step 3: To address the problem that the statistical characteristics of sensor noise are unknown and time-varying due to environmental factors, an intelligent fusion method embedded with a neural network is constructed; under the framework of multi-state constrained Kalman filtering, taking the attitude angle error and position error of the polarization / inertial / vision integrated navigation system as constraints, the Kalman gain is learned using measurement residuals, innovations, and posterior state estimation residual data.

[0011] Step 4: Based on the polarization / inertial / vision integrated navigation system model established in Steps 1 and 2 and the intelligent fusion method embedded with a neural network proposed in Step 3, intelligent fusion of multi-source sensing data of polarization / inertial / vision in complex environments is achieved.

[0012] Beneficial effects:

[0013] The present invention first proposes a polarization / inertial / vision intelligent navigation method based on model error learning. Based on the multi-state constrained Kalman filtering framework, an uncertainty modeling error learning network and a Kalman gain learning network are constructed, realizing precise system modeling and intelligent fusion independent of noise statistical characteristics, which can improve the accuracy and robustness of the integrated navigation system in complex environments and provide technical support for the autonomous navigation needs of unmanned systems in satellite denial, interference countermeasure, and unfamiliar environments. Description of the Drawings

[0014] Figure 1 is a flowchart of a polarization / inertial / vision intelligent navigation method based on model error learning of the present invention;

[0015] Figure 2 is a comparative curve graph of eastward position error;

[0016] Figure 3 is a comparative curve graph of northward position error;

[0017] Figure 4 is a comparative curve graph of heading angle error. Detailed Embodiments

[0018] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.)

[0019] As Figure 1 shown, a polarization / inertial / vision intelligent navigation method based on model error learning of the present invention includes the following steps:

[0020] Step 1: Model the polarization / inertial / visual integrated navigation system to obtain the polarization / inertial / visual integrated navigation system model. Select the inertial navigation state error and the camera pose error as the state vectors, establish the state equation of the polarization / inertial / visual integrated navigation system based on the inertial navigation kinematic model, establish the polarization measurement equation according to the perpendicular relationship between the polarization vector and the solar vector, and establish the visual measurement equation according to the visual reprojection error;

[0021] Step 2: Aiming at the uncertainty modeling errors of the state equation and measurement equation of the polarization / inertial / visual integrated navigation system, with the attitude angle error and position error of the integrated navigation system as constraints, construct a state transition matrix error learning network and a measurement matrix error learning network respectively. Use the inertial navigation historical data and measurement historical data to learn the state transition matrix error and measurement matrix error, and realize the fine modeling of the polarization / inertial / visual integrated navigation system;

[0022] Step 3: Aiming at the problem that the statistical characteristics of sensor noise are unknown and time-varying due to environmental factors, construct an intelligent fusion method embedded with a neural network; under the framework of the multi-state constrained Kalman filter, with the attitude angle error and position error of the polarization / inertial / visual integrated navigation system as constraints, use the measurement residual, innovation, and posterior state estimation residual data to learn the Kalman gain;

[0023] Step 4: Based on the polarization / inertial / visual integrated navigation system model established in Step 1 and Step 2 and the intelligent fusion method embedded with a neural network proposed in Step 3, realize the intelligent fusion of multi-source sensing data of polarization / inertial / visual in complex environments.

[0024] Specifically, Step 1 includes:

[0025] Define the polarization / inertial / visual integrated navigation system error state quantities related to inertial navigation:

[0026] (1)

[0027] Among them, represents the system error state quantity related to inertial navigation, the subscript represents the navigation coordinate system, the superscript represents the vehicle coordinate system, the superscript represents the transpose of the matrix, represents the representation of the variable in the vehicle coordinate system in the navigation coordinate system, represents the attitude error angle of the vehicle, represents the position error of the vehicle, represents the velocity error of the vehicle, and respectively represent the bias errors of the gyroscope and accelerometer.

[0028] The camera pose error at each moment is expressed as:

[0029] (2)

[0030] where represents the camera pose error at the th moment, represents the representation of the variables in the camera coordinate system in the body coordinate system, represents the position error of the camera, represents the attitude error angle of the camera.

[0031] Augment the camera pose error at the th moment to the error state variables of the polarization / inertial / vision integrated navigation system, and obtain:

[0032] (3)

[0033] where represents the system error state variables, represents the camera pose error at the th moment.

[0034] The system state update is only related to the inertial navigation error state. Therefore, according to the strapdown inertial navigation error equation, the state equation related to the inertial navigation error state variables is established as:

[0035] (4)

[0036] where represents the first derivative of the inertial navigation error state variables, represents the state transition matrix, represents the process noise transfer matrix, represents the system noise, including the Gaussian white noise and random walk noise of the gyroscope and accelerometer.

[0037] Define the polarization vector in the body coordinate system as , the solar vector as , is the rotation matrix from the body coordinate system to the navigation coordinate system; after the bionic polarization sensor measures the polarization azimuth angle , the polarization vector in the body coordinate system is obtained:

[0038] (5)

[0039] Based on the perpendicular relationship between the polarization vector and the solar vector under the ideal Rayleigh scattering model, obtain:

[0040] (6)

[0041] According to the error between the ideal polarization vector and the actual polarization vector, we can get:

[0042] (7)

[0043] in, represents the sun vector in the navigation coordinate system, Indicates the calculation of the rotation matrix, represents the actual polarization vector, express The antisymmetric matrix of Indicates the three-axis misalignment angle, Represents the polarization vector error.

[0044] and There is a matrix relationship between them:

[0045] (8)

[0046] in, and They represent the heading angle and pitch angle of the carrier respectively. When the carrier's posture does not change much in a short period of time during the movement, the above formula can be simplified to:

[0047] (9)

[0048] The polarization measurement equation is established as follows:

[0049] (10)

[0050] in, represents the polarization measurement residual, represents the polarization measurement matrix, represents the polarization measurement noise.

[0051] According to the camera pinhole model, The visual measurement information at each moment is:

[0052] (11)

[0053] in, Indicates the camera The first observed moment The location of the feature points, and Indicates the Moment The horizontal and vertical coordinates of the feature points projected on the camera pixel plane, 、 and It represents the three-dimensional coordinates observed by the camera for the th feature point in the th frame image in the navigation coordinate system.

[0054] According to the visual measurement information observed by the camera and the visual measurement information predicted by inertial navigation, a reprojection error is constructed:

[0055] (12)

[0056] where represents the reprojection error of the th feature point at the th moment, represents the visual measurement information predicted by inertial navigation, represents the three-dimensional coordinates of the th feature point in the navigation coordinate system, and respectively represent the Jacobian matrices corresponding to and , represents the corresponding noise.

[0057] The reprojection errors of all observed feature points within a certain period of time are cumulatively superimposed and simplified to obtain the visual measurement equation:

[0058] (13)

[0059] where represents the cumulative visual measurement residual, and respectively represent the cumulative visual measurement matrix and measurement noise.

[0060] Finally, after superimposing the polarization measurement and the visual measurement, the measurement equation of the polarization / inertial / visual integrated navigation system is:

[0061] (14)

[0062] where represents the total measurement residual, represents the total measurement matrix, represents the total measurement noise.

[0063] Specifically, the step 2 includes:

[0064] During the modeling process of step 1, the uncertainty modeling errors existing in the state equation and the measurement equation are not considered. The polarization / inertial / visual integrated navigation system model established in step 1 is corrected, considering the state transition matrix residual and the measurement matrix residual Obtained:

[0065] (15)

[0066] Wherein, and respectively represent the corrected state transition matrix and measurement matrix.

[0067] The state transition matrix error learning network and the measurement matrix error learning network are respectively constructed to realize the learning of and . The input of the state transition matrix error learning network is the historical gyroscope data and historical attitude data, and the output is the state transition matrix error ; the input of the measurement matrix error learning network is the historical polarization light intensity data and historical feature point position data, and the output is the measurement matrix error .

[0068] The main bodies of the state transition matrix error learning network and the measurement matrix error learning network are both GRU gated recurrent units, and the non-linear mapping and feature integration between the network input, GRU gated units and network output are realized through two fully connected layers. The network first performs preliminary feature extraction and dimension transformation through the fully connected layer, converting the original input data into a high-dimensional feature representation with time series correlation characteristics; then extracts the time series related features of the input sequence through the GRU unit, and recursively models the influence of historical data on the current state transition matrix error and measurement matrix error layer by layer. Finally, each element of the error matrix is learned element by element through the fully connected layer to realize the accurate learning of the state transition matrix error and the measurement matrix error.

[0069] Both the state transition matrix error learning network and the measurement matrix error learning network adopt supervised learning, comparing the pose ground truth provided by the high-precision reference with the pose estimated by the corrected system model, constructing an error signal to drive network training, and ensuring the accuracy of the estimation result. The loss function is as follows:

[0070] (16)

[0071] Wherein, represents the true heading angle, , respectively represent the true eastward position and true northward position, represents the heading angle estimated by the corrected system model, , respectively represent the eastward position and northward position estimated by the corrected system model, , represent the weighted coefficients of the error learning network, Denotes the Smooth L1 loss, which can be expressed as:

[0072] (17)

[0073] Wherein, Denotes the input of the Smooth L1 loss.

[0074] Utilize the error obtained by network learning to correct the state equation and the measurement equation to achieve accurate modeling:

[0075] (18)

[0076] Specifically, step 3 includes:

[0077] According to the prediction and update process of the multi-state constrained Kalman filter:

[0078] (19)

[0079] Wherein, the superscript Denotes the inverse of the matrix, Denotes the prior estimation error covariance matrix, Denotes the posterior estimation error covariance matrix, Denotes the measurement residual covariance matrix, Denotes the process noise covariance matrix, Denotes the measurement noise covariance matrix, Denotes the Kalman gain.

[0080] Environmental factors such as temperature, vibration, and optical interference will cause the statistical characteristics of sensor noise to be unknown and time-varying, and it is impossible to accurately calculate during the filtering process. Therefore, a Kalman gain learning network is constructed to achieve the learning of . The input of the Kalman gain learning network is historical residual data such as measurement residuals, innovations, and posterior state estimates, and the output is .

[0081] The main body of the Kalman gain learning network is a GRU gated recurrent unit, and the non-linear mapping and feature integration between the network input, GRU gated unit, and network output are realized through two fully connected layers. First, the network performs preliminary feature extraction and dimensional transformation through the fully connected layer to convert the original input into a feature representation suitable for time series modeling. Then, the GRU unit extracts the time series-related features of the input sequence, recursively modeling the influence of historical data on the current Kalman gain layer by layer. Subsequently, the attention mechanism weights the importance of different time steps and feature dimensions in the input sequence, dynamically focusing on the information that is most critical to the network learning result. Finally, the mapping relationship between the Kalman gain matrix elements and the hidden layer features is established through the fully connected layer to achieve accurate learning of the Kalman gain. The attention mechanism can be expressed as:

[0082] (20)

[0083] Among them, represents the input of the attention mechanism, and represent the output of the channel attention mechanism and the output of the spatial attention mechanism respectively, and represent the dimensions of the input information, represents the Sigmoid activation function, represents the Hadamard product, represents the mapping operation composed of two fully connected layers, represents the row column value of the channel, represents the convolution operation,

[0084] The Kalman gain learning network uses supervised learning, compares the pose ground truth provided by the high-precision benchmark with the pose estimated using the Kalman gain output by the network, constructs an error signal to drive network training, and ensures the accuracy of the Kalman gain learning result. The loss function is as follows:

[0085] (21)

[0086] Among them, represents the heading angle estimated using the Kalman gain output by the network, , respectively represent the eastward position and northward position estimated using the Kalman gain output by the network, , represent the weighting coefficients of the Kalman gain learning network.

[0087] Using the Kalman gain obtained by network learning and combining it with the update formula of the multi-state constrained Kalman filter framework to correct the state estimate, intelligent fusion independent of the noise statistical characteristics is achieved.

[0088] Specifically, step 4 includes: Based on the polarization / inertial / vision integrated navigation system model established in steps 1 and 2 and the intelligent fusion method with an embedded neural network proposed in step 3, intelligent fusion of multi-source sensing data of polarization / inertial / vision in complex environments is realized, improving the navigation accuracy and robustness of the polarization / inertial / vision integrated system.

[0089] Example:

[0090] In this example, taking the polarization / inertial / vision integrated navigation system as an example, considering the uncertainty modeling error of the system model in complex environments such as vibration and optical interference, and the problem that the sensor noise statistical characteristics are unknown and time-varying during the fusion process, which restricts the navigation performance of the integrated navigation system in complex application scenarios. Therefore, it is necessary to design an intelligent navigation method for polarization / inertial / vision with an embedded neural network to improve the navigation accuracy and robustness of the integrated navigation system in complex environments.

[0091] To prove the performance improvement effect of this method on the polarization / inertial / vision integrated navigation system, the KITTI ground motion dataset is selected for verification. The dataset provides inertial and vision sensor information as well as the reference ground truth of attitude and position. The bionic polarization sensor information is simulated through the longitude, latitude and time provided by the dataset, and Gaussian noise with a mean of 0 and a standard deviation of 0.1 is added. According to the designed method, system modeling is carried out for the polarization / inertial / vision integrated navigation system and a measurement equation is established; a state transition matrix error learning network and a measurement matrix error learning network are constructed to correct the system state equation and measurement equation; a Kalman gain learning network is constructed to achieve intelligent fusion independent of the noise statistical characteristics; multi-state constrained Kalman filtering is carried out based on the corrected system model and intelligent fusion method to realize the estimation of the state of the integrated navigation system. The comparison curve of the eastward position error is as Figure 2 shown, the comparison curve of the northward position error is as Figure 3 shown, and the comparison curve of the heading angle error is as Figure 4 shown. The dotted line graph without in the figure represents the estimation result based on the traditional method, and the dotted line graph with represents the estimation result based on the method of the present invention.

[0092] It can be found from the analysis results that the method of the present invention can accurately estimate the state of the integrated navigation system. Quantitative analysis of the results shows that the root mean square error (RMSE) of the eastward position of the traditional method is 7.967 m, the root mean square error of the northward position is 4.177 m, and the root mean square error of the heading angle is 1.287°; the root mean square error of the eastward position of the method of the present invention is 4.876 m, the root mean square error of the northward position is 2.271 m, and the root mean square error of the heading angle is 0.716°. Compared with the traditional method, the heading accuracy of the method of the present invention is improved by 44.37%, the eastward position accuracy is improved by 38.80%, and the northward position accuracy is improved by 45.63%.

[0093] Although the above illustrative specific embodiments of the present invention have been described to facilitate the understanding of those skilled in the art of the present technology, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

Claims

1. A polarization / inertial / visual intelligent navigation method based on model error learning, characterized in that It includes the following steps: Step 1: Model the polarization / inertial / vision integrated navigation system to obtain a polarization / inertial / vision integrated navigation system model. Select the inertial navigation state error and camera pose error as the state vectors. Based on the inertial navigation kinematic model, establish the state equation of the polarization / inertial / vision integrated navigation system. According to the perpendicular relationship between the polarization vector and the solar vector, establish the polarization measurement equation. According to the visual reprojection error, establish the visual measurement equation; Step 2: Aiming at the uncertainty modeling errors of the state equation and measurement equation of the polarization / inertial / vision integrated navigation system, with the attitude angle error and position error of the integrated navigation system as constraints, respectively construct a state transition matrix error learning network and a measurement matrix error learning network. Use the inertial navigation historical data and measurement historical data to learn the state transition matrix error and measurement matrix error, and realize the fine modeling of the polarization / inertial / vision integrated navigation system; Step 3: Aiming at the problem that the statistical characteristics of sensor noise are unknown and time-varying due to environmental factors, construct an intelligent fusion method embedded with a neural network; under the framework of multi-state constrained Kalman filtering, with the attitude angle error and position error of the polarization / inertial / vision integrated navigation system as constraints, use the measurement residual, innovation, and posterior state estimation residual data to learn the Kalman gain; Step 4: Based on the polarization / inertial / vision integrated navigation system model established in Step 1 and Step 2 and the intelligent fusion method embedded with a neural network proposed in Step 3, realize the intelligent fusion of multi-source sensing data of polarization / inertial / vision in complex environments.

2. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 1, characterized in that The said Step 1 includes: Select the inertial navigation error as the state vector, and augment the camera pose error at to the error state quantity of the system, obtaining: （3） Among them, represents the system error state quantity, represents the system error state quantity related to inertial navigation, represents the pose error of the camera at the th moment. The superscript represents the transpose of the matrix, represents the representation of the variable in the body coordinate system in the navigation coordinate system, represents the attitude error angle of the vehicle, represents the position error of the vehicle, represents the velocity error of the vehicle, and respectively represent the zero bias errors of the gyroscope and the accelerometer, represents the position error of the camera, represents the attitude error angle of the camera. The system state update is only related to the inertial navigation error state. Therefore, according to the inertial navigation kinematic equation, establish a state equation related to the inertial navigation error state quantity: （4） Among them, represents the first derivative of the inertial navigation error state quantity, represents the state transition matrix, represents the process noise transfer matrix, represents the system noise, including the Gaussian white noise and random walk noise of the gyroscope and accelerometer.

3. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 2, wherein: Define the polarization vector in the vehicle coordinate system as , the solar vector as , is the rotation matrix from the vehicle coordinate system to the navigation coordinate system. Based on the perpendicular relationship between the polarization vector and the solar vector under the ideal Rayleigh scattering model and the error between the ideal polarization vector and the actual polarization vector, we get: （7） Among them, represents the solar vector in the navigation coordinate system, represents the calculated rotation matrix, represents the actual polarization vector, represents the skew-symmetric matrix of represents the three-axis misalignment angle, represents the polarization vector error; When the attitude of the carrier changes little in a short time during the movement, and there is a matrix relationship: , thus establishing the polarization measurement equation , where represents the polarization measurement residual, represents the solar vector in the navigation coordinate system, represents the polarization measurement matrix, represents the polarization measurement noise; Construct the reprojection error according to the camera pinhole model: （12） Among them, represents the reprojection error of the th feature point at the th moment, represents the position of the th feature point observed by the camera at the th moment, represents the position of the th feature point predicted by inertial navigation at the th moment, represents the three-dimensional coordinates of the th feature point in the navigation coordinate system, and respectively represent the Jacobian matrices corresponding to 0, represents the corresponding noise; Accumulate and simplify the reprojection errors of all observed feature points within a certain period of time to obtain the visual measurement equation , where represents the visual measurement residual after cumulative superposition, and respectively represent the visual measurement matrix and noise after cumulative superposition; After superimposing the polarization measurement and the visual measurement, the measurement equation of the polarization / inertial / vision integrated navigation system is obtained as: （14） wherein, represents the total measurement residual, represents the total measurement matrix, represents the total measurement noise.

4. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 1, characterized in that The said Step 2 includes: Modify the system model established in step 1, considering the residual of the system state transition matrix and the residual of the measurement matrix , respectively construct a state transition matrix error learning network and a measurement matrix error learning network to achieve the learning of and : （15） Among them, represents the corrected state transition matrix, represents the corrected measurement matrix. The input of the state transition matrix error learning network is the historical gyroscope data and the historical attitude data, and the output is the state transition matrix error ; The input of the measurement matrix error learning network is the historical polarized light intensity data and the historical normalized coordinate data of the feature points, and the output is the measurement matrix error .

5. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 4, characterized in that: The main bodies of the state transition matrix error learning network and the measurement matrix error learning network are both GRU gated recurrent units, and realize the non-linear mapping and feature integration between the network input, GRU gated unit, and network output through two fully connected layers; the network first performs preliminary feature extraction and dimensionality transformation through the fully connected layer, and converts the original input data into a high-dimensional feature representation with temporal correlation characteristics; Subsequently, extract the temporal correlation features of the input sequence through the GRU unit, and recursively model the influence of historical data on the current state transition matrix error and measurement matrix error layer by layer. Finally, perform element-wise learning on each element of the error matrix through the fully connected layer to realize the accurate learning of the state transition matrix error and measurement matrix error.

6. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 5, characterized in that: Both the state transition matrix error learning network and the measurement matrix error learning network adopt supervised learning. The true pose provided by the high-precision reference is compared with the pose estimated using the corrected system model to construct an error signal to drive network training and ensure the accuracy of the estimation result. The loss function is as follows: （16） Among them, represents the true value of the heading angle, , respectively represent the true values of the eastward position and the northward position, represents the heading angle estimated using the corrected system model, , respectively represent the eastward position and the northward position estimated using the corrected system model, , represent the weighting coefficients of the error learning network, represents the Smooth L1 loss; Use the errors learned by the state transition matrix error learning network and the measurement matrix error learning network to correct the system state equation and measurement equation, and realize accurate modeling.

7. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 1, characterized in that The said Step 3 includes: According to the prediction and update process of multi-state constrained Kalman filtering: （19） where the superscript denotes the inverse of a matrix, denotes the prior estimation error covariance matrix, denotes the posterior estimation error covariance matrix, denotes the measurement residual covariance matrix, denotes the process noise covariance matrix, denotes the measurement noise covariance matrix, denotes the Kalman gain; Environmental factors such as temperature, vibration, and optical interference can cause the statistical characteristics of sensor noise to be unknown and time-varying, making it impossible to accurately calculate during the filtering process , so a Kalman gain learning network is constructed to achieve the learning of ; the input of the Kalman gain learning network is historical residual data such as measurement residuals, innovations, and posterior state estimates, and the output is the Kalman gain .

8. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 7, characterized in that: The main body of the Kalman gain learning network is a GRU gated recurrent unit, and the nonlinear mapping and feature integration between the network input, the GRU gated unit, and the network output are realized through two fully connected layers; the network first performs preliminary feature extraction and dimensionality transformation through a fully connected layer to convert the original input into a feature representation suitable for time series modeling; then, the GRU unit extracts the time series related features of the input sequence and recursively models the influence of historical data on the current Kalman gain layer by layer; subsequently, the attention mechanism weights the importance of different time steps and feature dimensions in the input sequence to dynamically focus on the information that is most critical to the network learning result; finally, a mapping relationship between the elements of the Kalman gain matrix and the hidden layer features is established through a fully connected layer to achieve accurate learning of the Kalman gain.

9. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 8, characterized in that: The Kalman gain learning network uses supervised learning to compare the true pose provided by a high-precision reference with the pose estimated using the Kalman gain output by the network, constructing an error signal to drive network training and ensuring the accuracy of learning. The loss function is as follows: （21） Among them, represents the heading angle estimated by the Kalman gain output by the network, , respectively represent the eastward position and northward position estimated by the Kalman gain output by the network, , represent the weighting coefficients of the Kalman gain learning network.

10. A polarization / inertial / visual intelligent navigation method based on model error learning according to claim 9, characterized in that: Using the Kalman gain learned by the Kalman gain learning network, the state estimation is corrected by combining the update formula of the multi-state constrained Kalman filter framework to achieve intelligent fusion independent of noise statistical characteristics.

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