Method for constructing interactive multi-model Kalman filter network with unknown prior parameters

Abstract

The invention belongs to the technical field of filtering optimization, and relates to a method for constructing an interactive multi-model Kalman filtering network with unknown prior parameters, which comprises the following steps: S1, constructing a double-branch neural network which comprises a transition probability learning module and an observation covariance learning module; s2, generating training data; s3, sequentially training a transition probability learning module and an observation covariance learning module according to the training data; and S4, embedding the trained dual-branch neural network into an interactive multi-model Kalman filter, and updating the dual-branch neural network to an optimal state estimation sequence through iteration to generate an interactive multi-model Kalman filter network. Priori parameters are autonomously learned through the double-branch neural network composed of the transition probability learning module and the observation covariance learning module, so that manually preset prior parameters are replaced, and the problems of low positioning precision and poor real-time performance of robot autonomous navigation caused by the existing IMM-KF are solved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of filter optimization, and particularly discloses a network construction method of an interactive multi-model Kalman filter with unknown prior parameters. BACKGROUND

[0002] In the field of robot autonomous navigation and environment perception, the simultaneous localization and mapping (SLAM) technology has become a mainstream scheme for realizing high-frequency spatial positioning of robots by fusing lidar and inertial measurement unit (IMU) data. The lidar provides environmental feature constraints with high-precision distance measurement capability, and the IMU captures the instantaneous motion state of the robot through high-frequency sampling. The fusion of the two can compensate for the defects of a single sensor to a certain extent, such as the matching failure problem of the lidar in the non-textured area and the drift error of the IMU accumulated over time, thereby outputting a robot motion trajectory with high temporal resolution.

[0003] The fused trajectory of the lidar and the IMU has non-negligible noise interference, and the noise characteristics are directly related to the robot motion mode and the environmental interaction intensity. Taking a wheeled robot as an example, when the robot travels at a constant speed on a flat ground, the noise mainly manifests as low-amplitude zero drift of the IMU and vibration noise of the mechanical rotating lidar; when the robot makes a sharp turn, accelerates or bounces on a rugged terrain, the IMU will generate high-frequency noise due to vibration, and the point cloud matching result of the mechanical rotating lidar will also have a certain drift. Although the traditional interactive multi-model Kalman filter (IMM-KF) can adapt to different motion modes through parallel estimation of multiple sub-models, it is more effective than other single-model Kalman filters in such problems. However, the traditional IMM-KF needs to manually and accurately preset the prior parameters of the core, including the transition matrix, the state noise covariance matrix and the observation noise covariance matrix. If the prior parameters deviate too much from the real scene, the filtering error will increase sharply or even diverge, which will reduce the performance of the IMM-KF. In addition, in actual applications, the transition matrix of the prior parameters is usually reasonably assumed based on prior knowledge, and cannot be accurately obtained. When the assumption error is too large, it will seriously affect the performance of the IMM-KF. Moreover, the motion mode switching probability of the target is significantly affected by the environment. Sudden disturbances in the motion process may cause the mode switching probability to change instantaneously, and the fixed transition matrix cannot adapt to the changes in the above-mentioned scenarios. Therefore, the traditional IMM-KF and its related improved schemes still do not perform well in the scenario of unknown prior parameters, and it is difficult to meet the high requirements of robot autonomous navigation for positioning accuracy and real-time performance. Therefore, an improved IMM-KF in the scenario of unknown prior parameters is needed to improve the positioning accuracy and real-time performance of robot autonomous navigation. SUMMARY

[0004] The application aims to provide an interactive multiple model Kalman filter network construction method with unknown prior parameters, and solve the problems of low positioning accuracy and poor real-time performance of the existing IMM-KF in robot autonomous navigation.

[0005] The specific scheme of the application is as follows: An interactive multiple model Kalman filter network construction method with unknown prior parameters, characterized in that it comprises the following steps: S1, constructing a double-branch neural network, the double-branch neural network comprising a transition probability learning module and an observation covariance learning module; S2, generating training data; S3, training the transition probability learning module and the observation covariance learning module in sequence according to the training data; S4, embedding the trained double-branch neural network into an interactive multiple model Kalman filter, and generating an interactive multiple model Kalman filter network through iterative updating to an optimal state estimation sequence.

[0006] Preferably, the transition probability learning module comprises a fully connected layer FC.

[0007] Preferably, the observation covariance learning module comprises a plurality of lightweight subnetworks deployed in parallel and independent of each other, and each lightweight subnetwork comprises an input fully connected layer, a series connection gate recurrent unit and an output fully connected layer connected in sequence.

[0008] Preferably, the generation of the training data comprises: constructing a simulation system comprising a preset submodel, randomly disturbing the state noise covariance matrix of the submodel and the observation noise covariance matrix of the submodel in a set interval, and generating trajectory data covering all submodels and containing at least submodel switching based on a preset submodel switching sequence.

[0009] Preferably, the trajectory data comprises an active submodel at time , an active submodel at time , a real state of a target at time , a real state of the target at time , a state transition matrix of the submodel , a noisy observation , a state noise covariance matrix of the active submodel at time , observation noise covariance matrix of the sub-model at the time point , Markov transition probability matrix .

[0010] Preferably, training the transition probability learning module comprises: extracting posterior probability matrix of each sub-model at the time point The training sample is input into the transition probability learning module for training, and the normalized mixed probability matrix before normalization is output , and the normalized mixed probability matrix before normalization is labeled as real .

[0011] Preferably, training the observation covariance learning module comprises: The observation covariance learning module is divided into a Q-FC-GRU layer, a P-FC-GRU layer, and an S-FC-GRU layer; S321, extracting state forward update difference from training data The training sample is input into the observation covariance learning module for training, and the state noise covariance matrix at the corresponding time point is output , and the state noise covariance matrix at the corresponding time point is labeled as real S322, extracting state forward evolution difference from training data , and the state noise covariance matrix at the corresponding time point output by the trained Q-FC-GRU layer The training sample is input into the observation covariance learning module for training, and the transition matrix at the corresponding time point is output , and the transition matrix at the corresponding time point is labeled as real S323, extracting innovation from training data , observation difference , state forward evolution difference , state forward update difference , and the state noise covariance matrix at the corresponding time point output by the trained Q-FC-GRU layer , and the transition matrix at the corresponding time point output by the trained P-FC-GRU layer The training sample data is input into the observation covariance learning module for training, and the observation noise covariance at the corresponding time point is output , and the observation noise covariance at the corresponding time point is labeled as real

[0012] Preferably, embedding the trained dual-branch neural network into an interactive multi-model Kalman filter includes: S41, in At that moment, Posterior probability matrices of each sub-model at time step Input transition probability learning module to obtain ;according to get Predicted probability of submodel j at time step ;based on Predicted probability of submodel j at time step ,get Normalized transition confidence of submodel i to submodel j at time step ; New information Observational difference State forward evolution difference , State forward update difference Input the observation covariance learning module to obtain the observation covariance matrix. State noise covariance matrix ; S42, based on Normalized transition confidence of submodel i to submodel j at time step Obtain the initial fusion state of sub-model j Initial fusion covariance of sub-model j ; S43. Predictions for each sub-model ; S44. Based on the state noise covariance matrix Initial fusion covariance of sub-model j Predict the predicted state covariance of sub-model j ; S45, Based on the observation covariance matrix The predicted state covariance of sub-model j The Kalman gain of sub-model j is obtained. ; S46, According to the new information Perform state and covariance updates for each sub-model to obtain the predicted state of sub-model j at time k. The state covariance of submodel j at time k ; S47, Based on the observation covariance matrix Obtain the likelihood function of sub-model j ; S48, according to Predicted probability of submodel j at time step The likelihood function of sub-model j Obtain the posterior probability of sub-model j ; S49. Predicted state of sub-model j at time k posterior probability of sub-model j The filtered states of each sub-model are weighted and fused to obtain the result. Global optimal state estimation at time 1 ;according to Global optimal state estimation at time 1 The optimal state covariance is obtained. .

[0013] Preferably, The formula for calculating the global optimal state estimate at time t is: , in, for Global optimal state estimation at time t. Let be the predicted state of sub-model j at time k. Let be the posterior probability of submodel j, where j = 1, 2, ..., n.

[0014] Preferably, the formula for calculating the optimal state covariance is: , in, For optimal state covariance, Let the state covariance of sub-model j at time k be . Let be the predicted state of sub-model j at time k. for Global optimal state estimation at time t. It is the transpose matrix. The posterior probability of submodel j, j=1,2,…,n.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects: This invention utilizes a dual-branch neural network composed of a transition probability learning module and an observation covariance learning module to autonomously learn prior parameters, thereby replacing manually preset prior parameters. The trained dual-branch neural network is embedded into the traditional Interactive Multi-Model Kalman Filter (IMM-KF) process. By iteratively updating to the optimal state estimation sequence, an IMM-KF network is generated. This achieves the same performance of the IMM-KF network with ideal optimal prior parameters as the IMM-KF network with unknown prior parameters, solving the performance degradation problem caused by parameter mismatch in the traditional IMM-KF. This improves the positioning accuracy and real-time performance of robot autonomous navigation and can meet the needs of unknown parameter estimation in scenarios such as mobile robots and target tracking. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method for constructing an interactive multi-model Kalman filter network with unknown prior parameters in Embodiment 1 of the present invention.

[0017] Figure 2 This is a flowchart of the training observation covariance learning module in Embodiment 1 of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Example 1 Methods for constructing interactive multi-model Kalman filter networks with unknown prior parameters, such as... Figure 1 As shown, it includes the following steps: S1. Construct a dual-branch neural network; The interactive multi-model Kalman filter network of the present invention includes Sub-model.

[0020] A dual-branch neural network includes a transition probability learning module and an observation covariance learning module.

[0021] The transition probability learning module includes a fully connected (FC) layer for learning the unnormalized mixture probability; its input data information is... Posterior probability matrices of each sub-model at time step The output data is the unnormalized mixture probability matrix. .

[0022] The expression for the posterior probability matrix of each sub-model at time step is: , in, for The posterior probability matrix of each sub-model at time step [time]. for The posterior probability of submodel 1 at time step, for The posterior probability of submodel 2 at time step. for Time-sub model The posterior probability.

[0023] The expression for the unnormalized mixture probability matrix is: , , in, The mixture probability matrix before normalization. The number of rows is The number of columns is The matrix, for The unnormalized mixture probability at time step transition from model i to model j. These are the Markov transition probabilities implicitly learned by the fully connected layer. for The posterior probability of submodel i at time i=1,2,… .

[0024] The observation covariance learning module comprises multiple parallel and independent lightweight subnetworks. Each lightweight subnetwork includes a sequentially connected input fully connected layer, a cascaded gated recurrent unit (GRU), and an output fully connected layer. The observation covariance learning module is used to perform feature coupling on the input data in stages, reducing redundant parameters and avoiding overfitting. Its input data consists of four types of difference features, namely, innovation... Observational difference State forward evolution difference , State forward update difference The output data information is the observation covariance matrix. .

[0025] The expressions for the four types of difference features are as follows: , , , , in, For observation with noise, for Observation with noise at all times Let J be the observation matrix of sub-model j. Let j be the state evolution matrix of sub-model j. Let be the initial fusion state of sub-model j at time k-1. This is the global optimal state estimate at time k-1. This is the global optimal state estimate at time k-2. Let be the predicted state of sub-model j at time k-1 based on time k-2.

[0026] S2, Generate training data; Because the interactive multi-model Kalman filter network of the present invention includes Each sub-model is pre-defined, and its kinematic properties are parametrically modeled to ensure that the kinematic properties of the sub-model match the actual kinematic properties of the target.

[0027] Training data refers to trajectory data generated by a simulation system, which includes multiple trajectories. Each trajectory contains all sub-models, random noise, and sub-model switching.

[0028] The generation of training data includes: constructing a simulation system comprising n preset sub-models, and randomly perturbing the sub-models within a set interval. State noise covariance matrix and submodels Observation noise covariance matrix Based on a preset sub-model switching sequence, it generates a model that covers all sub-models and contains at least... Trajectory data of secondary model switching.

[0029] Trajectory data includes Time-active submodel , Active submodel at time +1 , The true state of the target at any time , The true state of the target at time +1 Sub-model State transition matrix Noise-bearing observation , The state noise covariance matrix of the active sub-model at any given time , Observation noise covariance matrix of the active sub-model at any time Markov transition probability matrix .

[0030] The generation of trajectory data specifically includes: S21, Unified Definition The true state of the target at any time It supports state representation in 2D or 3D scenes, meeting the state description needs of different robot application scenarios; it also allows for the configuration of sub-models. State transition matrix ; S22. Construct an initial model for each sub-model. Randomly select the initial model ;exist Get it in real time Time-active submodel and Markov transition probability matrix ,according to Time-active submodel and Markov transition probability matrix Obtained through discrete distribution sampling Active submodel at time +1 ; S23, based on the obtained State transition matrix of the active sub-model at any time and State noise of the active sub-model at all times ,get The true state of the target at time +1 , The formula for calculating the true state of the target at time +1 is: , in, for The true state of the target at time +1 for The state transition matrix of the active sub-model at each time step. for The true state of the target at all times. for The state noise of the active sub-model at all times.

[0031] based on State noise of the active sub-model at any time get State noise covariance matrix of the active sub-model at each time step ; S24. Based on the obtained Observation matrix of the active sub-model at time and Observation noise of the active submodel at any time Obtain noisy observations The calculation formula for noisy observations is: , in, For observation with noise, for The observation matrix of the active sub-model at each moment. for The true state of the target at all times. for The observation noise of the active sub-model at all times.

[0032] based on Observation noise of the active submodel at any time get Observation noise covariance matrix of the active sub-model at any time .

[0033] According to steps S22 to S24, the state noise covariance matrix and observation noise covariance matrix of each sub-model are randomly perturbed within a set interval, which can avoid the algorithm overfitting due to a single noise scene and generate trajectory data in batches.

[0034] In addition, the trajectory data for each trajectory is validated to ensure that each trajectory covers all motion sub-models and that the number of motion sub-model switching times is at least [number missing]. Second-rate; S3. Train a dual-branch neural network based on the training data; S31, Training of the transition probability learning module; Extract from training data Posterior probability matrices of each sub-model at time step This training sample is used as a training sample for the transition probability learning module, and the module is trained to output a pre-normalized mixture probability matrix. And labeled as the true unnormalized mixture probability matrix. This is used to prioritize retaining samples for sub-model switching.

[0035] In the training of the transition probability learning module, supervised training is performed using the total loss function, which is expressed as follows: , in, For the total loss function, For cross-entropy loss with a smoothing term, To constrain the normalization of transition confidence.

[0036] S32, Training of the observation covariance learning module.

[0037] The observation covariance learning module is divided into a Q-FC-GRU layer for inferring state noise covariance, a P-FC-GRU layer for inferring Markov transition matrix, and an S-FC-GRU layer for inferring observation noise covariance. By training the Q-FC-GRU, P-FC-GRU, and S-FC-GRU layers of the observation covariance learning module in sequence, it is ensured that subsequent modules can directly call the output results of previous modules during real-world inference, thereby improving the accuracy of the observation covariance learning module.

[0038] Training of the observation covariance learning module, such as Figure 2 As shown, it specifically includes: S321. Extract the forward update difference of the state from the training data. As a training sample for the Q-FC-GRU layer used for inference state noise covariance, this training sample is input into the observation covariance learning module for training, and the output is the state noise covariance matrix at the corresponding time step. The data is labeled as the real-state noise covariance matrix at the corresponding time.

[0039] S322. Extract the forward evolution difference of the state from the training data. And the state noise covariance matrix of the trained Q-FC-GRU layer output at the corresponding time step. As a training sample for the P-FC-GRU layer used for inferring the Markov transition matrix, this training sample is input into the observation covariance learning module for training, and outputs the transition matrix at the corresponding time step. , and label it as the actual transition matrix at the corresponding time.

[0040] S323, Extracting new information from training data Observational difference State forward evolution difference , State forward update difference And the state noise covariance matrix of the trained Q-FC-GRU layer output at the corresponding time step. The Markov transition matrix at the corresponding time step of the output of the trained P-FC-GRU layer. The S-FC-GRU layer, used as a training sample for inferring the observation noise covariance, is used to train the observation covariance learning module, which outputs the observation noise covariance at the corresponding time step. The data is then labeled as the actual observed noise covariance at the corresponding time point.

[0041] S4. Embed the trained bi-branch neural network into the interactive multi-model Kalman filter, and generate the interactive multi-model Kalman filter network by iteratively updating to the optimal state estimation sequence.

[0042] Dynamic system state estimation is achieved by embedding a trained bi-branch neural network into a traditional interactive multi-model Kalman filter process.

[0043] Embedding a trained bi-branch neural network into a traditional interactive multi-model Kalman filter specifically includes: S41, in At that moment, Posterior probability matrices of each sub-model at time step Input the transition probability learning module of the dual-branch neural network, and the transition probability learning module outputs... The unnormalized mixture probability of transitioning from model i to model j at time step ;according to The unnormalized mixture probability of transitioning from model i to model j at time step get Predicted probability of submodel j at time step ;based on Predicted probability of submodel j at time step ,get Normalized transition confidence of submodel i to submodel j at time step ; New information Observational difference State forward evolution difference , State forward update difference The observation covariance learning module takes as input and outputs the observation covariance matrix. State noise covariance matrix And record the observed covariance matrix. State noise covariance matrix .

[0044] The formula for calculating the prediction probability of submodel j at time step is: , in, for The predicted probability of submodel j at time step j for The normalized unmixed probability of transitioning from model i to model j at time k-1, where i is the sub-model index at time k-1, j is the target sub-model index at time k, and n is the number of sub-models.

[0045] The formula for calculating the normalized transition confidence of submodel i to submodel j at time step i is: , in, for Normalized transition confidence of submodel i transitioning to submodel j at time step for The predicted probability of submodel j at time step j for The unnormalized mixture probability of transitioning from model i to model j at time step.

[0046] S42, based on Normalized transition confidence of submodel i to submodel j at time step And the state of sub-model i at time k-1. and the state covariance matrix of sub-model i at time k-1 The initial fusion state of sub-model j is obtained. Initial fusion covariance of sub-model j .

[0047] The formula for calculating the initial fusion covariance is: , in, Let the initial fusion covariance of sub-model j be , for Normalized transition confidence of submodel i transitioning to submodel j at time step Let i be the state covariance matrix of sub-model i at time k-1. Let i be the state of sub-model i at time k-1. Let be the initial fusion state of sub-model j. This is the transpose of the matrix.

[0048] S43. Predict the sub-model j for each sub-model. Time based Predicted state at time .

[0049] Sub-model j in Time based The formula for calculating the predicted state at time t is: , in, For sub-model j in Time based Predicted state at any given time Let be the initial fusion state of sub-model j at time k-1. Let be the state evolution matrix of sub-model j.

[0050] S44. Based on the state noise covariance matrix Initial fusion covariance of sub-model j Predict the predicted state covariance of sub-model j .

[0051] The formula for calculating the predicted state covariance of sub-model j is: , in, Let the predicted state covariance of sub-model j be . Let the initial fusion covariance of sub-model j be , Here is the state noise covariance matrix. Let j be the state evolution matrix of sub-model j. The state evolution matrix of sub-model j The transpose of .

[0052] S45, Based on the observation covariance matrix The predicted state covariance of sub-model j The Kalman gain of sub-model j is obtained. .

[0053] The formula for calculating the Kalman gain of sub-model j is: , in, For the Kalman gain of sub-model j, Let the predicted state covariance of sub-model j be . Let j be the observation matrix of sub-model j. The observation matrix of sub-model j The transpose of the matrix, Let J be the observation noise covariance matrix of sub-model j. To predict the covariance matrix of the observation The inverse matrix.

[0054] S46, According to the new information Perform state and covariance updates for each sub-model to obtain the predicted state of sub-model j at time k. The state covariance of submodel j at time k .

[0055] The formula for calculating the predicted state of sub-model j at time k is: , in, Let be the predicted state of sub-model j at time k. For sub-model j in Time based Predicted state at any given time For the Kalman gain of sub-model j, For new information.

[0056] The formula for calculating the state covariance of sub-model j at time k is: , in, Let the state covariance of sub-model j at time k be . Let the predicted state covariance of sub-model j be . For the Kalman gain of sub-model j, Let j be the observation matrix of sub-model j. It is an identity matrix.

[0057] S47, Based on the observation covariance matrix Obtain the likelihood function of sub-model j .

[0058] The formula for calculating the likelihood function of sub-model j is: , in, Let be the likelihood function of sub-model j. To observe the covariance matrix, For the new interest, For new information The transpose of the matrix, To observe the covariance matrix The inverse matrix, To observe the covariance matrix The square root of the determinant, where q is the dimension of the observation vector.

[0059] S48, according to Predicted probability of submodel j at time step The likelihood function of sub-model j Obtain the posterior probability of sub-model j .

[0060] The formula for calculating the posterior probability of sub-model j is: , in, Let be the posterior probability of sub-model j. Let be the likelihood function of sub-model j. for The predicted probability of time step model j, where C is the normalization coefficient.

[0061] S49. Predicted state of sub-model j at time k posterior probability of sub-model j The filtered states of each sub-model are weighted and fused to obtain the result. Global optimal state estimation at time 1 ;according to Global optimal state estimation at time 1 The optimal state covariance is obtained. .

[0062] The formula for calculating the global optimal state estimate at time t is: , in, for Global optimal state estimation at time t. Let be the predicted state of sub-model j at time k. Let be the posterior probability of submodel j, where j = 1, 2, ..., n.

[0063] The formula for calculating the optimal state covariance is: , in, For optimal state covariance, Let the state covariance of sub-model j at time k be . Let be the predicted state of sub-model j at time k. for Global optimal state estimation at time t. It is the transpose matrix. Let be the posterior probability of submodel j, where j = 1, 2, ..., n.

[0064] The formula for calculating the optimal state estimation sequence is: .

[0065] in, This is the optimal state estimation sequence. This is the global optimal state estimate at time N.

[0066] This invention utilizes a dual-branch neural network composed of a transition probability learning module and an observation covariance learning module to autonomously learn prior parameters, thereby replacing manually preset prior parameters. The trained dual-branch neural network is embedded into the traditional Interactive Multi-Model Kalman Filter (IMM-KF) process. By iteratively updating to the optimal state estimation sequence, an IMM-KF network is generated. This achieves the same performance of the IMM-KF network with ideal optimal prior parameters as the IMM-KF network with unknown prior parameters, solving the performance degradation problem caused by parameter mismatch in the traditional IMM-KF. This improves the positioning accuracy and real-time performance of robot autonomous navigation and can meet the needs of unknown parameter estimation in scenarios such as mobile robots and target tracking.

[0067] Example 2 The performance of the aforementioned interactive multi-model Kalman filter network was tested and verified through simulation experiments.

[0068] The interactive multi-model Kalman filter network IMM-KN was used as the test group, along with three control groups. Filtering was performed simultaneously on multiple simulation test trajectories, with up to 50 simulation experiments. The three control groups were: Comparison group 1 uses the original observations directly from the sensor observations without filtering. Comparison group 2 uses the Interactive Multi-Model Kalman Filter (IMM-KFR) with precise prior parameters, where the ideal optimal transition matrix P and state noise covariance matrix are known. and observation noise covariance matrix ; Comparison group 3 uses the interactive multi-model Kalman filter (IMM-KFW) to estimate prior parameters, simulating the Markov transition matrix P, state noise covariance matrix Q, and observation noise covariance matrix R pre-set by human experience.

[0069] The benchmark for testing and verification is the root mean square error (RMSE) of the position, which includes the RMSE in the x-direction. Root mean square error of position in the y direction .

[0070] The formula for calculating the root mean square error of position in the x-direction is: , in, The root mean square error of the position in the x-direction; This is the optimal estimate of the position in the x-direction at time k; Let k be the actual position in the x-direction at time k; The time steps for the statistics are taken as the time series length corresponding to 1000s-2500s.

[0071] The formula for calculating the root mean square error of position in the y-direction is: , in, The root mean square error of the position in the y-direction; This is the optimal estimate of the position in the y-direction at time k; The actual position in the y-direction at time k; The time steps for the statistics are taken as the time series length corresponding to 1000s-2500s.

[0072] For a single simulation experiment, the RMSE of the test group and the three control groups are shown in Table 1.

[0073] Table 1. RMSE of the test group and the 3 comparison groups in a single simulation experiment.

[0074] As shown in Table 1, the IMM-KN proposed in this application, under the conditions of Markov transition matrix P, state noise covariance matrix Q, and observation noise covariance matrix R, autonomously learns the core parameters through a dual-branch neural network. Its position estimation accuracy is almost on par with that of the IMM-KFR with known precise prior parameters. Specifically, the root mean square error of the IMM-KN position in the x-direction is... Only the root mean square error of the position in the x-direction of IMM-KFR. The root mean square error of the IMM-KN position in the y-direction is 2.43% higher. Only the root mean square error of the position in the y-direction of IMM-KFR The accuracy of IMM-KFW, which relies on manually estimated prior parameters, is significantly lower due to parameter mismatch and other factors. The root mean square error of IMM-KFW in the x-direction is 0.53%. Compared to the root mean square error of IMM-KFR in the x-direction The root mean square error of the IMM-KFW position in the y-direction increased by 86.7%. Compared to the root mean square error of IMM-KFR in the y-direction It increased by 80.6%.

[0075] For multiple simulation experiments, i.e., 50 simulation experiments, the RMSE of the test group and the 3 control groups are shown in Table 2.

[0076] Table 2 shows the RMSE of the test group and the 3 control groups in the multiple simulation experiments.

[0077] As shown in Table 2, under the conditions of Markov transition matrix P, state noise covariance matrix Q, and observation noise covariance matrix R, the mean RMSE of the IMM-KN in this application is only 2.43% higher in the x-direction and 2.35% higher in the y-direction than the mean RMSE of IMM-KFR in 50 experiments. However, the mean RMSE of IMM-KFW with manually estimated prior parameters is 15.6% higher in the x-direction and 14.8% higher in the y-direction than the mean RMSE of IMM-KFR.

[0078] Therefore, the interactive multi-model Kalman filter network IMM-KN of the present invention achieves performance close to that of IMM-KFR with known precise prior parameters when the prior parameters are unknown and no manual intervention is required.

[0079] Example 3 To further verify the performance of the interactive multi-model Kalman filter network IMM-KN of this invention, experiments were conducted on real datasets in specific scenarios.

[0080] The publicly available RML-7 vehicle trajectory dataset was used, focusing on a 220m long, one-way four-lane urban road scenario. It covers typical vehicle maneuvering patterns in urban traffic, and the data was generated using computer vision target tracking technology. To eliminate system errors during data acquisition, the original trajectory data was calibrated. Road signs of known size were used as a reference, and the original position data was scaled and offset to ensure consistency between the position data and actual road coordinates. Finally, vehicle trajectories without missing data or abnormal jumps were selected, and 50 complete vehicle driving trajectories were chosen as validation experimental samples. Each trajectory lasted 20-30 seconds, encompassing typical vehicle maneuvers, with some trajectories exhibiting brief data gaps and observation jumps.

[0081] The observed trajectory is superimposed with Gaussian distributed noise on the preprocessed real trajectory, which is used as the input for all filtering methods. The noise mean fluctuates within a small range, and the variance is set below 5m.

[0082] The test group IMM-KN, control group 1 Origin, and control group 2 IMM-KFW were all subjected to filtering on the aforementioned 50 vehicle driving trajectories. The comparison standard for testing and verification was the root mean square error of position (RMSE), which included the root mean square error of position in the x-direction. Root mean square error of position in the y direction .

[0083] For 50 experiments (i.e., multiple experiments), the RMSE of the test group and the two control groups are shown in Table 3.

[0084] Table 3. RMSE of the multiple experimental test group and the two control groups

[0085] As shown in Table 3, the IMM-KN of this application has the lowest mean RMSE in 50 experiments under the conditions of Markov transition matrix P, state noise covariance matrix Q, and observation noise covariance matrix R. The performance of IMM-KN is better than that of Origin and IMM-KFW.

[0086] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing an interactive multi-model Kalman filter network with unknown prior parameters, characterized in that, Includes the following steps: S1. Construct a dual-branch neural network, which includes a transition probability learning module and an observation covariance learning module; S2, Generate training data; S3. Train the transition probability learning module and the observation covariance learning module sequentially based on the training data; S4. Embed the trained bi-branch neural network into the interactive multi-model Kalman filter, and generate the interactive multi-model Kalman filter network by iteratively updating to the optimal state estimation sequence.

2. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that: The transition probability learning module includes a fully connected (FC) layer.

3. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that: The observation covariance learning module includes multiple parallel and independent lightweight sub-networks, each of which includes an input fully connected layer, a cascaded gated recurrent unit, and an output fully connected layer connected in sequence.

4. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that, The generated training data includes: Build including A simulation system with a preset sub-model, where the sub-model is randomly perturbed within a set interval. State noise covariance matrix and submodels Observation noise covariance matrix Based on a preset sub-model switching sequence, it generates a model that covers all sub-models and contains at least... Trajectory data of secondary model switching.

5. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 4, characterized in that: The trajectory data includes Time-active submodel , Active submodel at time +1 , The true state of the target at any time , The true state of the target at time +1 Sub-model State transition matrix Noise-bearing observation , The state noise covariance matrix of the active sub-model at any given time , Observation noise covariance matrix of the active sub-model at any time Markov transition probability matrix .

6. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that, The training transition probability learning module includes: Extract from training data Posterior probability matrices of each sub-model at time step This training sample is used as a training sample for the transition probability learning module, and the module is trained to output a pre-normalized mixture probability matrix. And labeled as the true unnormalized mixture probability matrix. .

7. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that, The training observation covariance learning module includes: The observation covariance learning module is divided into Q-FC-GRU layer, P-FC-GRU layer and S-FC-GRU layer. S321. Extract the forward update difference of the state from the training data. As a training sample for the Q-FC-GRU layer, this training sample is input into the observation covariance learning module for training, and the output is the state noise covariance matrix at the corresponding time step. And label it as the real state noise covariance matrix at the corresponding time; S322. Extract the forward evolution difference of the state from the training data. And the state noise covariance matrix of the trained Q-FC-GRU layer output at the corresponding time step. As a training sample for the P-FC-GRU layer, this training sample is input into the observation covariance learning module for training, and the transition matrix at the corresponding time step is output. , and label them as the actual transition matrix at the corresponding time; S323, Extracting new information from training data Observational difference State forward evolution difference , State forward update difference And the state noise covariance matrix of the trained Q-FC-GRU layer output at the corresponding time step. The transition matrix at the corresponding time step of the output of the trained P-FC-GRU layer. Using this data as training samples for the S-FC-GRU layer, the observation covariance learning module is trained to output the observation noise covariance at the corresponding time step. The data is then labeled as the actual observed noise covariance at the corresponding time point.

8. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 1, characterized in that, The step of embedding the trained dual-branch neural network into the interactive multi-model Kalman filter includes: S41, in At that moment, Posterior probability matrices of each sub-model at time step Input transition probability learning module to obtain ;according to get Predicted probability of submodel j at time step ;based on Predicted probability of submodel j at time step ,get Normalized transition confidence of submodel i to submodel j at time step ; New information Observational difference State forward evolution difference , State forward update difference Input the observation covariance learning module to obtain the observation covariance matrix. State noise covariance matrix ; S42, based on Normalized transition confidence of submodel i to submodel j at time step Obtain the initial fusion state of sub-model j Initial fusion covariance of sub-model j ; S43. Predictions for each sub-model ; S44. Based on the state noise covariance matrix Initial fusion covariance of sub-model j Predict the predicted state covariance of sub-model j ; S45, Based on the observation covariance matrix The predicted state covariance of sub-model j The Kalman gain of sub-model j is obtained. ; S46, According to the new information Perform state and covariance updates for each sub-model to obtain the predicted state of sub-model j at time k. The state covariance of submodel j at time k ; S47, Based on the observation covariance matrix Obtain the likelihood function of sub-model j ; S48, according to Predicted probability of submodel j at time step The likelihood function of sub-model j Obtain the posterior probability of sub-model j ; S49. Predicted state of sub-model j at time k posterior probability of sub-model j The filtered states of each sub-model are weighted and fused to obtain the result. Global optimal state estimation at time 1 ;according to Global optimal state estimation at time 1 The optimal state covariance is obtained. .

9. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 8, characterized in that, The The formula for calculating the global optimal state estimate at time t is: ， in, for Global optimal state estimation at time t. Let be the predicted state of sub-model j at time k. Let be the posterior probability of submodel j, where j = 1, 2, ..., n.

10. The method for constructing an interactive multi-model Kalman filter network with unknown prior parameters according to claim 8, characterized in that, The formula for calculating the optimal state covariance is: ， in, For optimal state covariance, Let the state covariance of sub-model j at time k be . Let be the predicted state of sub-model j at time k. for Global optimal state estimation at time t. It is the transpose matrix. The posterior probability of submodel j, j=1,2,…,n.

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