Polarization / inertial / visual intelligent navigation method based on model error learning

Abstract

The application provides a polarization / inertial / visual intelligent navigation method based on model error learning, and belongs to the navigation field, and comprises the following steps: modeling a polarization / inertial / visual integrated navigation system, taking inertial navigation errors and camera pose errors as system state variables, and establishing a system state equation; based on polarization sensor and visual sensor information, a system measurement equation is established; considering that system parameter errors and environmental interference cause modeling errors of the system state equation and the measurement equation, a neural network is used to learn the modeling errors, so that the precision of the polarization / inertial / visual integrated navigation system model is improved; and a multi-state constraint Kalman filtering method with a neural network embedded is established to solve the problem that the statistical characteristics of sensor noise are unknown and time-varying due to environmental factors in an actual environment. The application can improve the navigation precision of the polarization / inertial / visual integrated navigation system in a complex environment.

Description

TECHNICAL FIELD

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

[0002] The navigation system can provide spatial motion information for the unmanned system, and is the "motion nerve center" of the unmanned system. Research shows that the creatures in nature have excellent navigation ability. For example, bees have a balance rod and compound eyes, can perceive polarization, inertia, vision and other environmental / motion information, realize foraging, homing and other behaviors, have the advantages of high autonomy, strong anti-interference ability, error not accumulated with time, etc., and provide a technical means for autonomous navigation in complex environment. Therefore, how to simulate the intelligent perception and fusion mechanism of biological multi-sensor, and propose an intelligent navigation method with high autonomy and strong anti-interference, has become the core and key of the navigation of the unmanned system in the complex environment.

[0003] In recent years, many research institutions have carried out a large number of researches around 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 the navigation information based on multi-sensor information and uses Kalman filtering for information fusion, realizing loose combination navigation of polarization / 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 the polarization compass on the basis of visual measurement and inertial measurement, simulates the structure and function of the desert ant sensing polarized light, provides 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 the neural network, realizes accurate state estimation independent of noise statistics while maintaining the Kalman filtering framework. Chinese patent application CN202310474059.3 (A compound navigation method for unmanned aerial vehicle with compound eye polarization vision in weak light intensity environment) realizes tight combination navigation of polarization / inertial / visual three kinds of information based on the MSCKF filtering framework using the measurement information obtained by the polarization sensor and the polarization camera.

[0004] Although the multi-sensor fusion method proposed in the above papers and patent applications has achieved certain application effect, the modeling error of the system model in complex environments such as vibration and optical interference is not considered, and the problem that the statistical characteristics of the sensor noise are unknown and time-varying in the fusion process is not considered, which restricts the navigation performance of the system in complex application scenarios. SUMMARY

[0005] In order to solve the above technical problems, the present application proposes a polarization / inertial / visual intelligent navigation method based on model error learning, models the polarization / inertial / visual integrated navigation system, takes the inertial navigation error and the camera pose error as the system state quantity, and establishes the system state equation. Based on the polarization sensor and the visual sensor information, the system measurement equation is established. Considering the parameter error of the system and the environmental interference, the modeling error of the system state equation and the measurement equation is considered, the neural network learning modeling error is constructed, and the precision of the polarization / inertial / visual integrated navigation system model is improved. In view of the problem that the statistical characteristics of the sensor noise are unknown and time-varying due to environmental factors (temperature, vibration, optical interference, etc.) in the actual environment, a multi-state constraint Kalman filter method embedded with neural network is established. Based on the multi-state constraint Kalman filter framework, the uncertainty modeling error learning network and the Kalman gain learning network are constructed, the accurate modeling of the system and the intelligent fusion independent of the statistical characteristics of the noise are realized, and the precision and robustness of the integrated navigation system in complex environments are improved, which provides technical support for the autonomous navigation requirements of unmanned systems in satellite denial, interference countermeasures and unfamiliar environments.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[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 the polarization / inertial / visual integrated navigation system model, select the inertial navigation state error and the camera pose error as the state vector, 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 sun vector, and establish the visual measurement equation according to the visual re-projection error;

[0009] Step 2, for the uncertainty modeling error of the polarization / inertial / visual integrated navigation system state equation and the measurement equation, taking the attitude angle error and the position error of the integrated navigation system as the constraint, respectively constructing the state transition matrix error learning network and the measurement matrix error learning network, learning the state transition matrix error and the measurement matrix error by using the historical data of the inertial navigation and the measurement, and realizing the fine modeling of the polarization / inertial / visual integrated navigation system;

[0010] Step 3, for the problem that the sensor noise statistics are unknown and time-varying due to environmental factors, a neural network embedded intelligent fusion method is constructed; under the framework of multi-state constraint Kalman filter, the attitude angle error and position error of the polarization / inertial / visual integrated navigation system are constrained, and the Kalman gain is learned by using the measurement residual, the innovation, and the posterior state estimation residual data;

[0011] Step 4, based on the polarization / inertial / visual integrated navigation system model established in steps 1 and 2 and the neural network embedded intelligent fusion method proposed in step 3, the intelligent fusion of the polarization / inertial / visual multi-source sensor data in a complex environment is realized.

[0012] Beneficial effects:

[0013] The present application first proposes a polarization / inertial / visual intelligent navigation method based on model error learning, constructs an uncertainty modeling error learning network and a Kalman gain learning network based on the framework of multi-state constraint Kalman filter, realizes accurate modeling of the system and intelligent fusion independent of noise statistics, and can improve the precision and robustness of the integrated navigation system in a complex environment, thereby providing technical support for the autonomous navigation requirements of unmanned systems in satellite denial, jamming countermeasures, and unfamiliar environments. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 A flowchart of a polarization / inertial / visual intelligent navigation method based on model error learning of the present application;

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

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

[0017] Figure 4 A comparative curve graph of heading angle error. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0019] As shown in Figure 1 A polarization / inertial / visual intelligent navigation method based on model error learning of the present application includes the following steps:

[0020] Step 1, model the polarization / inertial / visual integrated navigation system to obtain a polarization / inertial / visual integrated navigation system model, select inertial navigation state error and camera pose error as state vectors, establish an inertial navigation kinematics model based polarization / inertial / visual integrated navigation system state equation, establish a polarization measurement equation according to the vertical relationship between the polarization vector and the sun vector, and establish a visual measurement equation according to the visual re-projection error;

[0021] Step 2, model the uncertainty modeling error of the polarization / inertial / visual integrated navigation system state equation and the measurement equation, constrain the attitude angle error and the position error of the integrated navigation system, respectively construct a state transition matrix error learning network and a measurement matrix error learning network, and learn the state transition matrix error and the measurement matrix error using inertial navigation historical data and measurement historical data to achieve fine modeling of the polarization / inertial / visual integrated navigation system;

[0022] Step 3, construct an intelligent fusion method embedded with a neural network to address the problem of unknown and time-varying sensor noise statistical characteristics caused by environmental factors; under the framework of multi-state constraint Kalman filtering, constrain the attitude angle error and the position error of the polarization / inertial / visual integrated navigation system, and learn the Kalman gain using measurement residuals, innovations, and posterior state estimation residual data;

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

[0024] Specifically, the step 1 comprises:

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

[0026] (1)

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

[0028] The camera pose error at each time instant is denoted as

[0029] (2)

[0030] wherein denotes the camera pose error at the time instant, denotes the representation of the variable of the camera coordinate system under the carrier coordinate system, denotes the position error of the camera, denotes the attitude error angle of the camera.

[0031] The camera pose error at the time instant is augmented to the error state quantity of the polarization / inertial / visual integrated navigation system, to obtain

[0032] (3)

[0033] wherein denotes the system error state quantity, denotes the pose error of the camera at the time instant.

[0034] The system state update is only related to the inertial navigation error state, and therefore, according to the strapdown inertial navigation error equation, the state equation related to the inertial navigation error state quantity is established as

[0035] (4)

[0036] wherein denotes the first-order derivative of the inertial navigation error state quantity, denotes the state transition matrix, denotes the process noise transition matrix, denotes the system noise, including the Gaussian white noise and random walk noise of the gyroscopes and accelerometers.

[0037] The polarization vector under the carrier coordinate system is defined as , and the sun vector is , is the rotation matrix from the carrier coordinate system to the navigation coordinate system; the polarization azimuth angle measured by the biomimetic polarization sensor is After that, the polarization vector under the carrier coordinate system is obtained as :

[0038] (5)

[0039] Based on the perpendicular relationship between the polarization vector and the sun vector under the ideal Rayleigh scattering model, it is obtained that

[0040] (6)

[0041] According to the error between the ideal polarization vector and the actual polarization vector, we have

[0042] (7)

[0043] where, denotes the sun vector in the navigation coordinate system, denotes the calculated rotation matrix, denotes the actual polarization vector, denotes the antisymmetric matrix of denotes the three-axis misalignment angle, denotes the polarization vector error.

[0044] There is a matrix relationship between

[0045] (8)

[0046] where, and denote the heading angle and the pitch angle of the carrier, respectively. When the attitude of the carrier changes little in a short time during the motion process, the above formula can be simplified as

[0047] (9)

[0048] Thus, the polarization measurement equation is established as

[0049] (10)

[0050] where, denotes the polarization measurement residual, denotes the polarization measurement matrix, denotes the polarization measurement noise.

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

[0052] (11)

[0053] where, denotes the position of the th feature point observed by the camera at the th moment, and denote the horizontal and vertical coordinates of the th feature point projected on the camera pixel plane at the th moment, , and ​​represents the third represents the third dimensional coordinates of the

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

[0055] (12)

[0056] wherein, represents the third represents the third re-projection error of the represents the visual measurement information predicted by the inertial navigation, represents the third dimensional coordinates of the and respectively represent the Jacobian matrices corresponding to , represents the corresponding noise.

[0057] All the observed feature point re-projection errors in a certain time are accumulated and superimposed and simplified to obtain a visual measurement equation:

[0058] (13)

[0059] wherein, represents the visual measurement residual after accumulation and superposition, and respectively represent the visual measurement matrix and the measurement noise after accumulation and superposition.

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

[0061] (14)

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

[0063] Specifically, the step 2 comprises:

[0064] The state equation and the uncertainty modeling error existing in the measurement equation are not considered in the modeling process of the step 1. The polarization / inertial / visual integrated navigation system model established in the step 1 is modified to consider the state transition matrix residual and the measurement matrix residual​ Obtain:

[0065] (15)

[0066] wherein, and respectively represent the corrected state transition matrix and the 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 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 feature point position data, and the output is the measurement matrix error .

[0068] The main body of the state transition matrix error learning network and the measurement matrix error learning network is the GRU gate recurrent unit, and the non-linear mapping and feature integration between the network input, the GRU gate unit and the network output are realized through two fully connected layers. The network first performs preliminary feature extraction and dimension transformation through the fully connected layer, converts the original input data into high-dimensional feature representation with time sequence correlation characteristics; then the time sequence correlation features of the input sequence are extracted through the GRU unit, and the influence of the historical data on the current state transition matrix error and the measurement matrix error is recursively modeled layer by layer. Finally, the elements of the error matrix are learned element by element through the fully connected layer, realizing 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, compare the pose true value provided by the high-precision reference with the pose estimated by the corrected system model, construct the error signal to drive the network training, and ensure the accuracy of the estimation result. The loss function is as follows:

[0070] (16)

[0071] wherein, represents the true value of the heading angle, , respectively represent the east position true value and the north position true value, represents the estimated heading angle by the corrected system model, , respectively represent the east position and the north position estimated by the corrected system model, , represents the weighted coefficient of the error learning network, Smooth L1 loss, which can be expressed as:

[0072] (17)

[0073] wherein, is the input of Smooth L1 loss.

[0074] The error obtained by network learning is used to correct the state equation and the measurement equation, so as to realize accurate modeling:

[0075] (18)

[0076] Specifically, the step 3 comprises:

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

[0078] (19)

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

[0080] Environmental factors such as temperature, vibration, optical interference, etc. can cause the statistical characteristics of sensor noise to be unknown and time-varying, and the filter process cannot accurately calculate Therefore, a Kalman gain learning network is constructed to learn The input of the Kalman gain learning network is the historical residual data such as measurement residual, innovation, and posterior state estimation, and the output is .

[0081] 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 dimension transformation through the fully connected layer, converts the original input into a feature representation suitable for time series modeling; then extracts the time series correlation features of the input sequence through the GRU unit, recursively models the influence of historical data on the current Kalman gain layer by layer; then the importance of different time steps and feature dimensions in the input sequence is weighted through the attention mechanism, dynamically focusing on the information 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, realizing the accurate learning of the Kalman gain. The attention mechanism can be represented as:

[0082] (20)

[0083] wherein, represents the input of the attention mechanism, and represent the channel attention mechanism output and the spatial attention mechanism output 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 value of the first channel in the first row, the value of the first channel in the second row, the value of the second channel in the first row, the value of the second channel in the second row, represents the convolution operation, represents the max-pooling operation.

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

[0085] (21)

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

[0087] The Kalman gain learned by the network is combined with the update formula of the multi-state constraint Kalman filtering framework to correct the state estimation, and intelligent fusion is realized without dependence on noise statistical characteristics.

[0088] Specifically, the step 4 comprises: based on the polarization / inertial / visual integrated navigation system model established in steps 1 and 2 and the intelligent fusion method with embedded neural network proposed in step 3, intelligent fusion of polarization / inertial / visual multi-source sensing data in a complex environment is realized, and the navigation accuracy and robustness of the polarization / inertial / visual integrated system are improved.

[0089] Embodiment:

[0090] In this embodiment, the polarization / inertial / visual integrated navigation system is taken as an example. Considering the modeling error of the system model in a complex environment such as vibration and optical interference, and the problems that the statistical characteristics of sensor noise are unknown and time-varying in the fusion process, the navigation performance of the integrated navigation system in a complex application scenario is restricted. Therefore, it is necessary to design a polarization / inertial / visual intelligent navigation method with embedded neural network to improve the navigation accuracy and robustness of the integrated navigation system in a complex environment.

[0091] To prove the performance improvement effect of the method on the polarization / inertial / visual integrated navigation system, the KITTI ground motion dataset is selected for verification. The dataset provides inertial and visual sensor information as well as reference true values of attitude and position. The information of the bionic polarization sensor is simulated by the latitude and longitude 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, the polarization / inertial / visual integrated navigation system is modeled and the measurement equation is established; the state transition matrix error learning network and the measurement matrix error learning network are constructed to correct the system state equation and the measurement equation; the Kalman gain learning network is constructed to realize intelligent fusion without dependence on noise statistical characteristics; the multi-state constraint Kalman filtering is performed based on the corrected system model and the intelligent fusion method to realize the estimation of the state of the integrated navigation system. The eastward position error comparison curve is shown in Figure 2 , the northward position error comparison curve is shown in Figure 3 , and the heading angle error comparison curve is shown in Figure 4 . In the figure, the dotted line without represents the estimation result based on the traditional method, and the dotted line with represents the estimation result based on the method of the present application.

[0092] It can be found from the analysis result that the method can accurately estimate the state of the integrated navigation system. Quantitative analysis on the result can obtain that the root mean square error (RMSE) of the east direction position of the traditional method is 7.967 m, the root mean square error of the north direction 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 east direction position of the method is 4.876 m, the root mean square error of the north direction 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 is improved by 44.37%, the east direction position accuracy is improved by 38.80%, and the north direction position accuracy is improved by 45.63%.

[0093] Although the above describes the specific embodiments of the present application in detail, so that those skilled in the art can understand the present application, it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, as long as various changes are within the spirit and scope of the present application defined and determined by the appended claims, all the inventions utilizing the concept of the present application are included in the protection.

Claims

1. A polarization / inertial / visual intelligent navigation method based on model error learning, characterized in that, Includes the following steps: 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 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 based on the perpendicular relationship between the polarization vector and the solar vector. Establish the visual measurement equation based on the visual reprojection error. Step 2: To model the uncertainty errors in the state equations and measurement equations of the polarization / inertial / vision integrated navigation system, and using the attitude angle error and position error of the integrated navigation system as constraints, a state transition matrix error learning network and a measurement matrix error learning network are constructed respectively. The state transition matrix error and measurement matrix error are learned using historical inertial navigation data and historical measurement data to achieve fine modeling of the polarization / inertial / vision integrated navigation system. Step 3: To address the problem of unknown and time-varying statistical characteristics of sensor noise caused by environmental factors, an intelligent fusion method with embedded neural networks is constructed. Under the multi-state constrained Kalman filter framework, the attitude angle error and position error of the polarization / inertial / vision integrated navigation system are used as constraints, and the Kalman gain is learned using measurement residual, innovation, and posterior state estimation residual data. Step 4: Based on the polarization / inertial / vision integrated navigation system model established in Steps 1 and 2, and the intelligent fusion method with embedded neural network proposed in Step 3, intelligent fusion of polarization / inertial / vision multi-source sensor data is realized in complex environments.

2. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 1, characterized in that, Step 1 includes: Choose the inertial navigation error as the state vector, and... The camera pose error at time 1 is augmented to the system's error state variables, resulting in: （3） in, Represents the system error state quantity. This represents the system error state quantities related to inertial navigation. Indicates the first The pose error of the camera at each moment, superscript To represent the transpose of a matrix, The representation of variables in the vehicle coordinate system in the navigation coordinate system. The representation of variables in the camera coordinate system in the carrier coordinate system. Indicates the attitude error angle of the carrier. This indicates the positional error of the carrier. Indicates the speed error of the carrier. and These represent the zero bias errors of the gyroscope and accelerometer, respectively. This indicates the camera's positional error. Indicates the camera's attitude error angle; The system state update is only related to the inertial navigation error state. Therefore, based on the inertial navigation kinematic equations, a state equation related to the inertial navigation error state quantity is established: （4） in, The first derivative of the state quantity of inertial navigation error. Represents the state transition matrix. Represents the process noise transfer matrix. This represents system noise, including Gaussian white noise and random walk noise from gyroscopes and accelerometers.

3. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 2, characterized in that: Define the polarization vector in the carrier coordinate system as The solar vector is , Given the rotation matrix from the carrier 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 obtain: （7） in, This represents the solar vector in the navigation coordinate system. This indicates the calculation of the rotation matrix. Represents the actual polarization vector. express antisymmetric matrix, Indicates the misalignment angle of the three axes. Indicates polarization vector error; When the posture of the carrier does not change much in a short period of time during the movement, and There is a matrix relationship between them: Therefore, the polarization measurement equation is established. ,in, Indicates the residual of polarization measurement. This represents the solar vector in the navigation coordinate system. Represents the polarization measurement matrix. Indicates polarization measurement noise; Construct the reprojection error based on the camera pinhole model: （12） in, Indicates the first Time of the first Reprojection error of each feature point Indicates the camera's number The first time observed The position of each feature point Indicates the first The first time predicted by inertial navigation The position of each feature point Indicates the first The three-dimensional coordinates of each feature point in the navigation coordinate system and Respectively represent and , The corresponding Jacobian matrix, Indicates the corresponding noise; The reprojection errors of all observed feature points within a certain time period are accumulated, superimposed, and simplified to obtain the visual measurement equation. ,in, This represents the visual measurement residual after cumulative stacking. and These represent the visual measurement matrix after cumulative superposition and the noise, respectively; By superimposing polarization measurements and visual measurements, the measurement equations for the polarization / inertial / visual integrated navigation system are obtained as follows: （14） in, This represents the total measurement residual. Represents the overall measurement matrix. This represents the total measurement noise.

4. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 1, characterized in that, Step 2 includes: The system model established in step 1 is revised, taking into account the residuals of the system state transition matrix. and measurement matrix residuals A state transition matrix error learning network and a measurement matrix error learning network are constructed respectively to achieve the following: and Learning: （15） in, This represents the corrected state transition matrix. H represents the corrected measurement matrix; F represents the total measurement matrix; and F represents the state transition matrix. The input to the state transition matrix error learning network is historical gyroscope data and historical attitude data, and the output is the state transition matrix error. The measurement matrix error learning network takes historical polarization intensity data and normalized coordinate data of historical feature points as input, and outputs the measurement matrix error. .

5. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 4, characterized in that: The main components of both the state transition matrix error learning network and the measurement matrix error learning network are GRU gated recurrent units, and nonlinear mapping and feature integration between network input, GRU gated units and network output are achieved through two fully connected layers. The network first performs preliminary feature extraction and dimensionality transformation through fully connected layers, converting the original input data into a high-dimensional feature representation with temporal correlation characteristics. Subsequently, the temporal correlation features of the input sequence are extracted through GRU units, and the influence of historical data on the current state transition matrix error and measurement matrix error is recursively modeled layer by layer. Finally, the error matrix is ​​learned element by element through a fully connected layer to achieve accurate learning of the state transition matrix error and measurement matrix error.

6. The 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. They compare the true pose value provided by the high-precision benchmark with the pose estimated by the corrected system model to construct error signals to drive network training and ensure the accuracy of the estimation results. loss function As shown below: （16） in, This represents the true value of the heading angle. , These represent the true values ​​for the eastward and northward positions, respectively. This represents the heading angle estimated using the modified system model. , These represent the eastward and northward positions estimated using the modified system model, respectively. , These represent the weighting coefficients of the error learning network. Indicates Smooth L1 loss; The errors learned by the state transition matrix error learning network and the measurement matrix error learning network are used to correct the system state equation and measurement equation, thereby achieving accurate modeling.

7. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 4, characterized in that, Step 3 includes: Based on the prediction and update process of multi-state constrained Kalman filtering: （19） Among them, superscript Represents the inverse of a matrix. This represents the prior estimation error covariance matrix. Denotes the posterior estimation error covariance matrix. Represents the measurement residual covariance matrix. Represents the process noise covariance matrix. Represents the measurement noise covariance matrix. Indicates Kalman gain; Environmental factors such as temperature, vibration, and optical interference can cause the sensor's noise statistics to be unknown and time-varying, making accurate calculation impossible during the filtering process. Therefore, a Kalman gain learning network is constructed to achieve [the desired effect]. The learning of Kalman gain networks involves taking measurement residuals, innovations, and posterior state estimates as inputs, and outputting the Kalman gain. .

8. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 7, characterized in that: The core of the Kalman gain learning network is the GRU gated recurrent unit, which is used to achieve nonlinear 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 layers, converting the original input into a feature representation suitable for temporal modeling. Then, the GRU units extract the temporal-related features of the input sequence, recursively modeling the influence of historical data on the current Kalman gain layer by layer. Subsequently, an attention mechanism is used to weight the importance of different time steps and feature dimensions in the input sequence, dynamically focusing on the information most critical to the network learning result. Finally, the fully connected layers establish the mapping relationship between the Kalman gain matrix elements and the hidden layer features, achieving accurate learning of the Kalman gain.

9. The polarization / inertial / visual intelligent navigation method based on model error learning according to claim 8, characterized in that: The Kalman gain learning network employs supervised learning, comparing the true pose value provided by a high-precision benchmark with the pose estimated using the Kalman gain output by the network. This constructs an error signal to drive network training, ensuring the accuracy of the learning process. The loss function... As shown below: （21） in, This represents the heading angle estimated using the Kalman gain output from the network. , These represent the eastward and northward positions estimated using the Kalman gain from the network output, respectively. , This represents 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: By utilizing the Kalman gain learned through a Kalman gain learning network and combining it with the update formula of a multi-state constrained Kalman filter framework to correct the state estimate, intelligent fusion independent of noise statistical characteristics is achieved.

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