Passive multi-station time difference target positioning and tracking method

Abstract

The invention relates to the technical field of target positioning and tracking, and provides a passive multi-station time difference target positioning and tracking method. Comprising the following steps: performing initialization assignment on an initial algorithm by using an initial state of initialized data and a covariance matrix of a positioning target, inputting a model into an initialized interactive algorithm, and performing model interaction to obtain mixed state estimation and a covariance matrix of the model after interaction; performing state prediction updating by using an improved volume Kalman filter to obtain a model likelihood function; updating the model probability according to the model likelihood function, and obtaining an updated Markov transition probability matrix through an improved IMM algorithm; and calculating state estimation and a covariance matrix which are finally fused by the interactive multi-model to obtain a positioning and tracking result of the target. According to the method, the QS-CKF algorithm is introduced, the IMM algorithm is improved, and the Markov transition probability matrix is dynamically adjusted, so that the problem of filtering divergence or tracking lag is avoided, and the target positioning and tracking performance is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning and tracking, and provides a passive multi-station time difference target positioning and tracking method. Background Art

[0002] In the modern civilian field, target positioning and tracking technology has important application value, especially in a passive multi-station time difference of arrival (TDOA) system. The TDOA system calculates the position information of a target by measuring the time difference of the target signal arriving at multiple receiving stations. However, the high mobility of the target and complex motion patterns make it difficult for traditional positioning and tracking algorithms to meet the requirements of accuracy and real-time performance. The key to accurately tracking a maneuvering target lies in the selection of an appropriate non-linear filter and the optimal design of the tracking model.

[0003] Traditional target tracking algorithms (such as Kalman filtering and its improved algorithms) have the following problems when dealing with non-linear, non-Gaussian noise, and highly maneuverable targets: Non-linear problem: The observation equation of the TDOA positioning system is non-linear, which is difficult to handle by traditional linear filtering algorithms (such as KF). At the same time, traditional non-linear filtering such as EKF (Extended Kalman Filter) will introduce large truncation errors during the Taylor expansion approximation linearization process.

[0004] High mobility problem: The target motion state may change rapidly, and traditional single-model filtering algorithms cannot adapt to this change. Classic target motion models mainly include: CV model (Constant Velocity Model), CA model (Constant Acceleration Model), and CT model (Constant Turn Rate Model). These target dynamic models are used to predict the future position and state of the target in target tracking and provide an estimate of the target motion for the tracker. Which model to use specifically depends on the target motion pattern and task requirements.

[0005] Noise problem: There are various noises in the actual environment (such as measurement noise, process noise), and traditional algorithms have poor robustness to noise.

[0006] Therefore, there is an urgent need for a target positioning and tracking algorithm that can effectively handle non-linearity, high mobility, and noise interference. Summary of the Invention

[0007] The present invention aims to solve at least one of the technical problems existing in the related art. For this purpose, the present invention provides a passive multi-station time difference of arrival (TDOA) target positioning and tracking method, which realizes increasing the transition probability of the matching model and reducing the transition probability of the non-matching model in the model stable stage, and accelerating the model switching speed in the model transition stage, thereby improving the tracking accuracy and response speed for highly maneuverable targets.

[0008] The present invention provides a passive multi-station TDOA target positioning and tracking method, including the following steps: S1: Initialize and assign the initial algorithm using the initial state of the initialization data and the covariance matrix of the positioning target to obtain the initialized algorithm; S2: Input the model into the initialized algorithm to perform model interaction to obtain the mixed state estimation and covariance matrix of the interacted model; S3: Filter the mixed state estimation and covariance matrix of the interacted model, and use Markov transition update for state prediction and update to obtain the likelihood function of the model; S4: Perform model state fusion according to the likelihood function of the model to obtain the target prediction model; S5: Input the model to be predicted into the target prediction model to obtain the positioning and tracking result of the target.

[0009] According to the passive multi-station TDOA target positioning and tracking method provided by the present invention, the model includes a constant velocity model, a constant acceleration model, a turning model, a Singer model, and a Jerk model. According to the passive multi-station TDOA target positioning and tracking method provided by the present invention.

[0010] According to the passive multi-station TDOA target positioning and tracking method provided by the present invention, step S1 includes: S11: Calculate the state initial mean according to the initial state, and perform QR decomposition on the covariance matrix to obtain the covariance square root; S12: Perform time update according to the state initial mean and the covariance square root to obtain the state mean after time update and the covariance square root after time update; S13: Perform measurement update on the state mean after time update and the covariance square root after time update to obtain the state estimation of the initialized algorithm and the covariance matrix square root of the initialized algorithm.

[0011] According to the passive multi-station TDOA target positioning and tracking method provided by the present invention, step S13 includes: S131: Calculate the cubature points according to the state mean after time update and the covariance square root after time update; S132: Calculate the measurement prediction value according to the cubature points; S133: Calculate the square root of the measurement one-step prediction error covariance matrix and the cross-covariance based on the measured predicted value; S134: Perform SVD decomposition on the cross-covariance to obtain the autocorrelation covariance; S135: Calculate the gain matrix based on the autocorrelation covariance, the square root of the measurement one-step prediction error covariance matrix, and the cross-covariance; S136: Calculate the state estimate of the initialization algorithm based on the autocorrelation covariance and the gain matrix; S137: Calculate the square root of the covariance matrix of the initialization algorithm based on the autocorrelation covariance.

[0012] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S2 includes: S21: Calculate the mixing probability of the model; S22: Calculate the mixed state estimate of the model based on the mixing probability and the state estimate of the initialization algorithm; S23: Calculate the covariance matrix of the model based on the mixing probability and the square root of the covariance matrix of the initialization algorithm.

[0013] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S3 includes: S31: Update the model based on the mixed state estimate and covariance matrix of the post-interaction model to obtain the updated model probability; S32: Update the updated model probability using Markov transition to obtain the normalized probability model probability; S33: Perform secondary correction on the normalized probability model probability to obtain the diagonal elements of the normalized TPM; S34: Input the diagonal elements of the normalized TPM as the transition probability for the next moment, and continue to update the model corresponding to the normalized probability model until the model converges to obtain the likelihood function of the model.

[0014] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S31 includes: S311: Calculate the likelihood function corresponding to the model based on the mixed state estimate of the model and the covariance matrix polarity model of the model; S312: Update the model based on the likelihood function corresponding to the model to obtain the updated model probability.

[0015] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S32 includes: S321: Obtain the change amount of the model probability at different moments based on the updated model probability; S322: Calculate the model probability change amount between different models at the same time according to the model probability change amounts at different times; S323: Perform probability transfer correction on the model probability change amount between different models at the same time according to the correction function to obtain the normalized probability model probability.

[0016] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S33 includes: S331: Normalize the likelihood function corresponding to the model to obtain a normalized likelihood function; S332: Calculate the likelihood function change amount according to the normalized likelihood function; S333: Calculate the prediction error according to the likelihood function change amount and normalize it to obtain a normalized prediction error; S334: Determine whether to enter the model transfer stage according to the normalized prediction error. If entering the model transfer stage, execute step S335. If not entering the model transfer stage, return to step S331; S335: Calculate the diagonal elements of the TPM according to the prediction error and normalize the calculation result to obtain the normalized diagonal elements of the TPM.

[0017] According to a passive multi-station time difference target positioning and tracking method provided by the present invention, step S4 includes: S41: Update the probability of the model according to the likelihood function of the model to obtain an updated model probability; S42: Dynamically correct the Markov transition matrix according to the updated model probability using a correction coefficient to adjust the model strategy; S43: According to the updated model probability, fuse the mixed state estimation of the model to obtain a target prediction model.

[0018] One or more of the above technical solutions in the embodiments of the present invention have at least one of the following technical effects: A passive multi-station time difference target positioning and tracking method provided by the present invention significantly improves the numerical stability and computational efficiency of non-linear filtering by introducing the QS-CKF algorithm based on QR decomposition and SVD decomposition, and solves the problems of ill-conditioned covariance matrix and high computational complexity of the traditional CKF (Cubature Kalman Filter) in high-dimensional systems. At the same time, the improved IMM (Interacting Multiple Model Algorithm) algorithm dynamically adjusts the Markov transition probability matrix (TPM), increases the transition probability of the matching model and reduces the transition probability of the non-matching model in the model stable stage, and speeds up the model switching speed in the model transition stage, thereby improving the tracking accuracy and response speed of high-maneuver targets. In addition, the algorithm combining QS-CKF and the improved IMM shows stronger robustness and stability in complex environments, avoids the common problems of filtering divergence or tracking lag in traditional algorithms, and significantly improves the performance of target positioning and tracking.

[0019] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. Brief Description of the Drawings

[0020] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] Figure 1 It is a schematic flow chart of a passive multi-station time difference target positioning and tracking method provided by the present invention.

[0022] Figure 2 It is a comparison chart of RMSE between the present invention and other methods.

[0023] Figure 3 It is a comparison chart of the average filtering error between the present invention and other methods. Detailed Embodiments

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0025] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the embodiments of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0026] The following is combined with Figures 1 to 3 to describe the present invention.

[0027] Embodiment As Figure 1 shown, Figure 1 is a schematic flow diagram of a passive multi-station time difference target positioning and tracking method provided by the present invention. Specifically, it includes: S1: Initialize and assign the initial algorithm using the initial state of the initialization data and the covariance matrix of the positioning target to obtain the initialized algorithm; S2: Input the model into the initialized algorithm, perform model interaction to obtain the mixed state estimation and covariance matrix of the model after interaction; S3: Filter the mixed state estimation and covariance matrix of the model after interaction, use Markov transfer update for state prediction and update to obtain the likelihood function of the model; S4: Perform model state fusion according to the likelihood function of the model to obtain the target prediction model; S5: Input the model to be predicted into the target prediction model to obtain the positioning and tracking result of the target.

[0028] Specifically, the model includes a uniform motion model, a uniform acceleration model, a turning model, a Singer model, and a Jerk model.

[0029] Specifically, step S1 includes: S11: Calculate the state initial mean according to the initial state, and perform QR decomposition on the covariance matrix to obtain the covariance square root. The specific process is as follows: The state initial mean is , and the error covariance is . Perform decomposition on through QR decomposition to obtain the following square roots: Among them, is the square root of the covariance obtained by performing QR decomposition on the covariance , is the expected predicted value of is the function for obtaining the expectation represents the matrix transpose

[0030] S12: Perform time update based on the initial state mean and the square root of the covariance to obtain the state mean after time update and the square root of the covariance after time update. The specific process is as follows: Calculate the cubature points: Among them, is the state mean corresponding to the th cubature point for the th time update is the th cubature point is the th expected predicted value for time update is the dimension of the state variable is the identity matrix

[0031] Propagate the cubature points: Among them, is the state mean after propagating the cubature points is the time update propagation function Calculate the state predicted value: is the corresponding state predicted value Calculate the square root of the state one-step prediction error covariance matrix : Among them, is the QR decomposition method is the square root of the process noise covariance matrix, and the first weighted central matrix is: S13: Perform measurement update on the state mean after time update and the square root of the covariance after time update to obtain the state estimate of the initialization algorithm and the square root of the covariance matrix of the initialization algorithm. Step S13 includes: S131: Calculate the cubature points based on the state mean updated according to the time and the square root of the covariance updated according to the time; is the state mean for the th cubature point corresponding to the th measurement update; S132: Calculate the measurement prediction value based on the cubature points; where is the mean of the measurement state after propagating the cubature points, is the measurement propagation function, is the measurement prediction value of the measurement propagation.

[0032] S133: Calculate the square root of the measurement one-step prediction error covariance matrix and the cross-covariance based on the measurement prediction value: In the formula, is the square root of the one-step prediction error covariance matrix, is the cross-covariance, and the second weighted central matrix is: S134: Perform SVD decomposition (Singular Value Decomposition) on the cross-covariance to obtain the autocorrelation covariance: where is the left singular matrix, is the diagonal singular matrix, is the right singular matrix, is the singular value decomposition.

[0033] S135: Calculate the gain matrix based on the first weighted central matrix and the second weighted central matrix; S136: Calculate the state estimate of the initialization algorithm based on the autocorrelation covariance and the gain matrix ; .

[0034] S137: Calculate the square root of the covariance matrix of the initialization algorithm based on the autocorrelation covariance, the square root of the measurement one-step prediction error covariance matrix, and the cross-covariance.

[0035] Among them, is the state prediction value at the end of the update, is the gain matrix after the update ends.

[0036] Specifically, step S2 includes: S21: Calculate the mixing probability of the model; S22: Calculate the mixed state estimate of the model after interaction according to the mixing probability and the state estimate of the initialization algorithm; S23: Calculate the covariance matrix of the model after interaction according to the mixing probability and the square root of the covariance matrix of the initialization algorithm.

[0037] Assume there are N models, and the mixing probability of model j is: where represents the Markov transition probability of the model from to at time , that is, the th row and the th column of the Markov transition matrix. represents the probability that model is the matching model at time , is the mixed normalization constant, and N is the total number of input models in the interactive multiple model algorithm.

[0038] Calculate the mixed state estimate and covariance matrix of model using the state estimate and covariance matrix of the previous model : is the state estimate of model at time , is the state estimate of model at time , is the covariance matrix of model at time .

[0039] Specifically, step S3 includes: S31: Update the model based on the mixed state estimate and covariance matrix of the post-interaction model to obtain the updated model probability, including: S311: Calculate the likelihood function corresponding to the model according to the mixed state estimate of the model and the covariance matrix polarity model of the model; Calculate the likelihood function of the th model: .

[0040] Among them, is the likelihood function of the th model, is the prediction difference, is the measurement propagation value at the end of the update.

[0041] S312: Update the model according to the likelihood function corresponding to the model to obtain the updated model probability Among them, is the model probability of the th model after update, is the normalization constant, is the normalization weighting coefficient, represents the transition probability from model to model .

[0042] S32: Use Markov transition to update the updated model probability to obtain the normalized probability model probability, including: S321: Obtain the change amount of the model probability at different times according to the updated model probability; Calculate the change amount of the model probability at different times : Among them represents the posterior probability of the th model, represents the prior probability of the th model, is the trend variable.

[0043] When the model j matches, is positive, otherwise it is negative. Therefore The values are defined as follows S322: Calculate the model probability change amount between different models at the same time according to the obtained model probability change amounts at different times; Calculate the model probability change amount between different models at the same time: where is the model compared with the model The model probability change amount between them, is the exponential parameter, represents the posterior probability of the th model.

[0044] When the model is more matched than the model , that is, at time k , then When the model is more matched than the model , that is , then It realizes reducing the probability of the matching model transferring to the non - matching model and increasing the transfer of the non - matching model to the matching model.

[0045] S323: Perform probability transfer correction on the model probability change amount between different models at the same time according to the correction function to obtain the normalized probability model probability.

[0046] Comprehensively use the above two correction functions to correct each element of the probability transfer matrix: where represents the element in the th row and th column of the transition probability matrix at time the th row, the th column element, represents the modified transition probability at time. At the same time, the elements in the transition probability matrix are non - negative. Due to the property of the time - homogeneous Markov chain, the sum of all elements in each row is equal to 1.

[0047] where is normalized to: where is the normalized .

[0048] S33: Perform a secondary correction on the probabilities of the normalized probability model to obtain the diagonal elements of the normalized TPM, including: Therefore, set limits for the main diagonal elements . When , perform a secondary correction as where represents the element in the th row and th column of the time transition probability matrix at time

[0049] S331: Normalize the likelihood function corresponding to the model to obtain a normalized likelihood function; First, calculate the likelihood function of the model and normalize it: is the likelihood function of the th model, is the normalized likelihood function.

[0050] S332: Calculate the change in the likelihood function based on the normalized likelihood function; When calculating the change in the likelihood function of model : where is the normalized likelihood function before update.

[0051] S333: Calculate the prediction error based on the change in the likelihood function and normalize it to obtain a normalized prediction error; Then, for each model, calculate its prediction error : where is the system measurement value at the current time, is the th corresponding state prediction value of the model, represents the modulo operation.

[0052] Normalize the prediction error: where is the normalized prediction error.

[0053] S334: Determine whether to enter the model transfer phase based on the normalized prediction error. If entering the model transfer phase, execute step S335; if not, return to step S331. By setting a first threshold and a second threshold to determine whether to enter the model transfer phase: where is the maximum value function, is the minimum value function, is the mean value function, is the standard deviation calculation function.

[0054] If one of the following conditions is met, enter the model transfer phase: where is to take the absolute value.

[0055] S335: Calculate the diagonal elements of the TPM based on the prediction error and normalize the calculation result to obtain the normalized diagonal elements of the TPM.

[0056] Dynamically adjust the main diagonal elements of the TPM: where is the element of the main diagonal at the current moment, is the element of the main diagonal at the previous moment. is the adjustment factor that controls the overall adjustment amplitude and is usually set to . is the first weight coefficient, is the second weight coefficient, which respectively control the influence of the prediction error and the change amount of the likelihood function on the adjustment.

[0057] Adjust the off-diagonal elements: where is the off-diagonal element at the current moment, represents the element in the th row and th column of the transition probability matrix at the current moment.

[0058] Normalize the adjusted TPM: where is the normalized off-diagonal element.

[0059] S34: Input the diagonal elements of the normalized TPM as the transition probability for the next moment, and continue to update the model corresponding to the normalized probability model until the model converges to obtain the likelihood function of the model.

[0060] Specifically, step S4 includes: S41: Update the probability of the model according to the likelihood function of the model to obtain the updated model probability; S42: Dynamically correct the Markov transition matrix according to the updated model probability and adjust the model strategy; S43: According to the updated model probability, fuse the mixed state estimation of the model to obtain the target prediction model.

[0061] Specifically, step S5 includes: Input the model to be predicted into the target prediction model to obtain the target positioning and tracking result. Since the method proposed in the embodiment of the present invention is to predict the model itself to obtain the target tracking result corresponding to the model.

[0062] Next, the method proposed in the present invention is compared with the methods proposed in other inventions, and the results are shown in Table 1: Table 1 Comparison result table

[0063] As shown in Table 1, it can be seen that the RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) of the present invention are both smaller than those of other models, and the switching speed and matching probability of the model are also relatively high.

[0064] As Figure 2 and Figure 3 shown, Figure 2 is the RMSE comparison chart between the present invention and other methods. Among them, Figure 2 in (a) is the RMSE in the X direction, Figure 2 in (b) is the RMSE in the Y direction. It can be seen that the RMSE value of the improved method of this patent is the smallest.

[0065] Figure 3 is the comparison chart of the filtering average error between the present invention and other methods. Among them, Figure 3 in (a) is the filtering average error in the X direction, Figure 3 in (b) is the filtering average error in the Y direction. It can be seen that the filtering average error value of the improved method of this patent is the smallest.

[0066] It can be seen from the above two figures that the RMSE and filtering average error of the present invention are both smaller than those of other methods, and it has better accuracy.

[0067] By introducing the QS-CKF algorithm based on QR decomposition and SVD decomposition, the present invention significantly improves the numerical stability and computational efficiency of nonlinear filtering, and solves the problems of ill-conditioned covariance matrix and high computational complexity of traditional CKF in high-dimensional systems. At the same time, the improved IMM algorithm dynamically adjusts the Markov transition probability matrix (TPM), increases the transition probability of the matching model and reduces the transition probability of the non-matching model during the model stable stage, and speeds up the model switching speed during the model transition stage, thereby improving the tracking accuracy and response speed for highly maneuverable targets. In addition, the algorithm combining QS-CKF and the improved IMM shows stronger robustness and stability in complex environments, avoids the common problems of filtering divergence or tracking lag in traditional algorithms, and significantly improves the performance of target positioning and tracking.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0069] It should be noted that the embodiments of the present disclosure can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic: the software part can be stored in a memory and executed by a suitable instruction execution system such as a microprocessor or dedicated designed hardware. Those skilled in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code is provided on a programmable memory or a data carrier such as an optical or electronic signal carrier.

[0070] In addition, although the operations of the method of the present disclosure are described in a specific order in the drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the steps depicted in the flowchart can change the execution order. Additionally or alternatively, some steps can be omitted, multiple steps can be combined into one step for execution, and / or one step can be decomposed into multiple steps for execution. It should also be noted that the features and functions of two or more devices according to the present disclosure can be embodied in one device. Conversely, the features and functions of one device described above can be further divided and embodied by multiple devices.

[0071] Although the present disclosure has been described with reference to several specific embodiments, it should be understood that the present disclosure is not limited to the specific embodiments disclosed. The present disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A passive multi-station time difference of arrival target positioning and tracking method, characterized in that, It includes the following steps: S1: Initialize and assign the initial algorithm using the initial state of the initialization data and the covariance matrix of the positioning target to obtain the initialized algorithm. Step S1 includes: S11: Calculate the initial state mean according to the initial state, and perform QR decomposition on the covariance matrix to obtain the covariance square root; S12: Perform time update according to the initial state mean and the covariance square root to obtain the state mean after time update and the covariance square root after time update; S13: Perform measurement update on the state mean after time update and the covariance square root after time update to obtain the state estimate of the initialized algorithm and the covariance matrix square root of the initialized algorithm; S2: Input the model into the initialized algorithm, and perform model interaction to obtain the mixed state estimate and covariance matrix of the model after interaction; S3: Filter the mixed state estimate and covariance matrix of the model after interaction, and use Markov transfer update for state prediction and update to obtain the likelihood function of the model; S4: Perform model state fusion according to the likelihood function of the model to obtain the target prediction model; S5: Input the model to be predicted into the target prediction model to obtain the positioning and tracking result of the target.

2. The passive multi-station time difference of arrival target positioning and tracking method according to claim 1, wherein The model includes a uniform motion model, a uniform acceleration model, a turning model, a Singer model, and a Jerk model.

3. A passive multi-station time difference of arrival target positioning and tracking method according to claim 1, characterized in that Step S13 includes: S131: Calculate the cubature points according to the state mean after time update and the covariance square root after time update; S132: Calculate the measurement prediction value according to the cubature points; S133: Calculate the square root of the measurement one-step prediction error covariance matrix and the cross-covariance according to the measurement prediction value; S134: Perform SVD decomposition on the cross-covariance to obtain the autocorrelation covariance; S135: Calculate the gain matrix according to the autocorrelation covariance, the square root of the measurement one-step prediction error covariance matrix, and the cross-covariance; S136: Calculate the state estimate of the initialized algorithm according to the autocorrelation covariance and the gain matrix; S137: Calculate the covariance matrix square root of the initialized algorithm according to the autocorrelation covariance.

4. A passive multi-station time difference target positioning and tracking method according to claim 1, characterized in that Step S2 includes: S21: Calculate the mixing probability of the model; S22: Calculate the mixed state estimate of the model after interaction according to the mixing probability and the state estimate of the initialized algorithm; S23: Calculate the covariance matrix of the model after interaction according to the mixing probability and the covariance matrix square root of the initialized algorithm.

5. A passive multi-station time difference of arrival target positioning and tracking method according to claim 1, characterized in that Step S3 includes: S31: Update the model according to the mixed state estimate and covariance matrix of the model after interaction to obtain the updated model probability; S32: Use Markov transfer update for the updated model probability to obtain the normalized probability model probability; S33: Perform secondary correction on the normalized probability model probability to obtain the normalized TPM diagonal elements; S34: Input the normalized TPM diagonal elements as the transition probability for the next moment, and continue to update the model corresponding to the normalized probability model until the model converges to obtain the likelihood function of the model.

6. The passive multi-station time difference of arrival target positioning and tracking method according to claim 5, characterized in that, Step S31 includes: S311: Calculate the likelihood function corresponding to the model based on the mixed state estimation of the model and the covariance matrix polarity model of the model; S312: Update the model according to the likelihood function corresponding to the model to obtain the updated model probability.

7. A passive multi-station time difference of arrival target positioning and tracking method according to claim 5, characterized in that Step S32 includes: S321: Obtain the change amount of the model probability at different times according to the updated model probability; S322: Calculate the change amount of the model probability between different models at the same time according to the change amount of the model probability at different times obtained; S323: Perform probability transfer correction on the change amount of the model probability between different models at the same time according to the correction function to obtain the normalized probability model probability.

8. A passive multi-station time difference of arrival target positioning and tracking method according to claim 6, characterized in that Step S33 includes: S331: Normalize the likelihood function corresponding to the model to obtain the normalized likelihood function; S332: Calculate the change amount of the likelihood function according to the normalized likelihood function; S333: Calculate the prediction error according to the change amount of the likelihood function and normalize it to obtain the normalized prediction error; S334: Judge whether to enter the model transfer stage according to the normalized prediction error. If entering the model transfer stage, execute step S335. If not entering the model transfer stage, return to step S331; S335: Calculate the diagonal elements of the TPM according to the prediction error and normalize the calculation result to obtain the normalized diagonal elements of the TPM.

9. A passive multi-station time difference of arrival target positioning and tracking method according to claim 1, characterized in that, Step S4 includes: S41: Update the probability of the model according to the likelihood function of the model to obtain the updated model probability; S42: Dynamically correct the Markov transition matrix according to the updated model probability and adjust the model strategy; S43: Fuse the mixed state estimation of the model according to the updated model probability to obtain the target prediction model.

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