Pulse signal source tracking method based on robust Kalman filter
By employing a robust Kalman filter and an adaptive high-order volumetric sampling method, the problem of stable tracking of underwater non-cooperative pulse signal sources was solved, achieving high-precision target tracking under outlier interference.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-02-13
- Publication Date
- 2026-05-08
AI Technical Summary
In the tracking of non-cooperative underwater targets, traditional Kalman filters are affected by outlier interference when estimating the frequency and azimuth of pulse signals, resulting in inaccurate parameter estimation results. This is especially true under conditions of non-uniform ocean waveguides and ocean background noise, making it difficult to achieve stable target tracking.
A robust Kalman filter-based approach is adopted, which updates the parameter estimates through an adaptive high-order volumetric sampling method. Combining the receiving frequency and the azimuth of arrival, the target state vector and the error covariance matrix are iteratively calculated, and a stable target state is output when the iteration terminates.
Stable tracking of underwater non-cooperative pulse signal sources was achieved under outlier interference, improving tracking accuracy and reducing computational costs.
Smart Images
Figure CN121995384A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a pulse signal source tracking method based on a robust Kalman filter, belonging to the field of underwater acoustic signal target localization and tracking. Background Technology
[0002] Underwater acoustic passive localization technology has always been a hot research topic in the field of underwater acoustics, especially in the tracking of non-cooperative underwater targets. Based on the Doppler-azimuth target motion analysis theory, the tracking of non-cooperative underwater targets can be achieved by utilizing the signal receiving frequency and the azimuth of arrival.
[0003] In the pursuit of moving targets, the Kalman filter is widely used in engineering practice due to its good balance between estimation accuracy and real-time computational performance. However, achieving stable state tracking with the Kalman filter requires accurate prior information, such as the statistical characteristics of process noise and observation noise. Inaccurate filter parameters can not only severely degrade filter performance but also cause the filter to diverge. To address this issue, maximum likelihood estimation methods generally rely on extracting innovation or residual sequences through time windows to achieve accurate estimation of the observation noise covariance matrix, ultimately obtaining stable target tracking results.
[0004] However, underwater observations of non-cooperative targets involve various signal types, including line spectrum and broadband components of ship radiated noise, as well as pulse signals actively emitted by non-cooperative targets. Regarding the frequency estimation of pulse signals, their transient and short-duration characteristics make it difficult to achieve time accumulation effects during processing, resulting in limited frequency estimation resolution. Furthermore, waveform distortion during propagation in non-uniform ocean waveguide channels leads to drift and deviation in the frequency estimation of the received signal. In pulse signal azimuth estimation, underwater propagation elevation coupling and sonar array distortion cause deviations in the azimuth estimation results. Simultaneously, ocean background noise places pulse signal parameter estimation under unfavorable low signal-to-noise ratio conditions. The combined effect of these underwater engineering scenario factors results in parameter estimation results being affected by outliers. Traditional adaptive Kalman filtering methods theoretically do not consider outliers in the observations of non-cooperative pulse signal source tracking.
[0005] To address the issue of anomalous filter noise, researchers have proposed several improved adaptive Kalman filter schemes, with variational Bayesian inference being one of the most efficient methods. Early variational Bayesian frameworks used the Inverse Wishart distribution to construct the noise covariance matrix model, which could not handle the complex noise environments in real-world engineering scenarios, such as outlier interference with observations. Furthermore, common pulse signal parameter observations are nonlinear functions of motion states. While nonlinear Kalman filters can achieve state tracking through integral sampling methods, general integral sampling methods suffer from errors in expectation calculations under outlier perturbations, reducing the accuracy of motion state estimation. Therefore, achieving low-cost and high-precision tracking of underwater non-cooperative pulse signal sources under observation noise conditions including outliers has significant theoretical and practical value. Summary of the Invention
[0006] Technical Problem: This invention proposes a pulse signal source tracking method based on a robust Kalman filter, achieving accurate estimation of the motion state of underwater non-cooperative pulse signal sources under complex noise conditions with outliers. Simulation data processing results show that, compared with the traditional adaptive Kalman filter tracking method, this method solves the interference of outliers in nonlinear observation systems and achieves stable tracking of underwater non-cooperative pulse signal sources.
[0007] Technical Solution: The purpose of this invention is to address the problems of high nonlinearity and outlier disturbances in underwater acoustic pulse signals by providing a pulse signal source tracking method based on a robust Kalman filter. This method uses the target state vector and state error covariance matrix from the previous time step, along with the pulse signal receiving frequency and azimuth of arrival at the current time step, and the coordinate vector of the receiving station, to obtain sampling weights and sampling point vectors using an adaptive high-order volumetric sampling method. This yields the target predicted state vector and prediction error covariance matrix for the current time step. Subsequently, parameters and the target state vector and state error covariance matrix from the previous iteration are initialized. Based on the distribution model of parameters such as scaling factors, indications, and mixing coefficients, the estimation results of each parameter are updated, and the prediction error covariance matrix and observation noise covariance matrix are iteratively calculated. Finally, based on the Kalman filter framework, the target state vector and state error covariance matrix for the current iteration are obtained. The iteration terminates when the change in the target state vector from the previous iteration is less than a tolerance, and the final result is output. Thus, stable tracking of underwater non-cooperative pulse signal sources is achieved based on nonlinear observation results under outlier disturbances.
[0008] To achieve the above objectives, the present invention employs a method for tracking pulse signal sources based on a robust Kalman filter, comprising the following steps:
[0009] (1) Read in the target state vector and error covariance matrix and observation noise covariance matrix of the previous time step, and use the adaptive high-order volume sampling method and state transition model to calculate the target prediction state vector and prediction error covariance matrix of the current time step.
[0010] (2) Initialize variational Bayesian parameters (scaling factor, indicator and mixing coefficient), target state vector and error covariance matrix before iteration.
[0011] (3) At the start of the iteration, based on the target state vector and state error covariance matrix of the previous iteration, the quadratic sufficient statistics of observation error and prediction error are calculated using the adaptive high-order volume sampling method.
[0012] (4) Update variational Bayes parameters (scaling factor, indicator and mixing coefficient).
[0013] (5) Update the forecast error covariance matrix and the observation noise covariance matrix.
[0014] (6) Based on the target state prediction vector and the prediction error covariance matrix of this iteration, the adaptive high-order volume sampling method is used to calculate the target state vector and error covariance matrix of this iteration.
[0015] (7) The iteration ends when the change between the target state vector in this iteration and the target state vector in the previous iteration is less than the tolerance, and the target state vector, error covariance matrix, and observation noise covariance matrix at the current moment are output; otherwise, return to step (3).
[0016] As a further improvement to the present invention, step 1 specifically includes the following steps:
[0017] (1.1) Set the arrival time of the pulse signal during the tracking process as... Read in the previous moment, that is... Target state vector at time 1 State error covariance matrix The degrees of freedom describing the observation noise covariance matrix at the previous time step. With scale matrix , The coordinate vector of the receiving station at that moment With the observed vector The superscript 't' indicates a physical quantity related to the target, and the superscript 'o' indicates a physical quantity related to the receiving array. It is an identifier for the physical quantity estimation results; read in the forgetting factor to adjust the observation noise covariance matrix. Adjusting the parameters of the forecast error covariance matrix Set the initial coefficients for the i-th gamma distribution. and , , The number of gamma distributions and the initial values of the gamma distribution mixing coefficients. Maximum number of iterations tolerance ;
[0018] (1.2) Based on Target state vector at time 1 With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. The weight of each sampling point is ; calculated using the state transition model Time-based target prediction state vector With the forecast error covariance matrix :
[0019]
[0020]
[0021] in, It is a state transition function. It is the process noise covariance matrix. It is the transpose of the matrix.
[0022] Step 2 specifically includes the following steps:
[0023] (2.1) Initialize variational Bayes parameters (scaling factor, indicator and mixing coefficient) before iteration
[0024] Initialize scaling factor Expectations The expectation of its natural logarithm :
[0025]
[0026] in, It is the expected value.
[0027] Initialize indicator Expectations :
[0028]
[0029] Initialize the mixing coefficients expect The expectation of its natural logarithm :
[0030]
[0031] Initialize the degrees of freedom of the observation noise covariance matrix at the current time without observation correction. Initialize the scaling matrix of the observation noise covariance matrix that has not been corrected at the current time. .
[0032]
[0033]
[0034] in, It is the dimension of the observation vector.
[0035] Initialize the degrees of freedom of the forecast error covariance matrix at the current time without observation corrections. The scaling matrix is initialized to the forecast error covariance matrix that has not been corrected for observations at the current time. .
[0036]
[0037]
[0038] in, It is the dimension of the target state vector.
[0039] (2.2) According to Time-prediction state vector With the forecast error covariance matrix Initialize the target state vector before iteration With the state error covariance matrix : , .
[0040] Expectation of the inverse of the initial observation noise covariance matrix : .
[0041] As a further improvement to the present invention, step 3 specifically includes the following steps:
[0042] (3.1) Let the previous iteration be the th iteration. This iteration is the [number]th. Next. Based on the target state vector of the previous iteration. With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of sampling points is , No. The weight of each sampling point is Calculate the quadratic sufficient statistic of the observation error. With the quadratic sufficient statistic of forecast error :
[0043]
[0044]
[0045] in, It is the first The posterior observation mean of the next iteration It is the observation function.
[0046] As a further improvement to the present invention, step 4 specifically includes the following steps:
[0047] (4.1) Update the scaling factor that follows a gamma distribution. posterior distribution Update Shape parameters with rate parameter :
[0048]
[0049]
[0050] in, It is the trace of the matrix. It is the first Indicator during the next iteration Expected value It is the expected value. It is the first The expected result of observing the inverse of the noise covariance matrix in the next iteration.
[0051] Therefore, we obtain the first... During the next iteration Expectation calculation Its natural logarithm expected result :
[0052]
[0053] in, It is the digamma function.
[0054] (4.2) Update the indicator that follows a multinomial distribution posterior distribution Update parameters :
[0055]
[0056] in, Coefficients before normalization The calculation formula is:
[0057]
[0058] in, It is the gamma function. It is the first The mixing coefficient at the next iteration The expected result of the natural logarithm.
[0059] Therefore, we obtain the first... During the next iteration Expected calculation result:
[0060]
[0061] (4.3) Update the mixing coefficients that follow a Dirichlet distribution. posterior distribution Update coefficient The formula for calculating this coefficient is:
[0062]
[0063] Therefore, we obtain the first... During the next iteration Expected results Its natural logarithm expected result :
[0064]
[0065] As a further improvement to the present invention, step 5 specifically includes the following steps:
[0066] (5.1) Update description The degrees of freedom of the prediction error covariance matrix in the next iteration With scale matrix :
[0067]
[0068]
[0069] Therefore, we obtain the first... The prediction error covariance matrix at the next iteration :
[0070]
[0071] (5.2) Update description The degrees of freedom of the observation noise covariance matrix in the next iteration With scale matrix :
[0072]
[0073]
[0074] Therefore, we obtain the first... The observation noise covariance matrix at the next iteration :
[0075]
[0076] As a further improvement to the present invention, step 6 specifically includes the following steps:
[0077] (6.1) Based on the target prediction state vector at the current moment With the The prediction error covariance matrix of the next iteration The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. Each sampling weight is Calculate the first The mean of the target state vector at the next iteration with the mean of the observed vector :
[0078]
[0079]
[0080] Therefore, the first... The observation autocovariance matrix at the next iteration The cross-covariance matrix between target state and observed quantities and Kalman gain :
[0081]
[0082]
[0083]
[0084] Final calculation The target state vector for the next iteration With the state error covariance matrix :
[0085]
[0086]
[0087] Step 7 specifically includes the following steps:
[0088] (7.1) When the change in the target state vector of the current iteration relative to the target state vector of the previous iteration is greater than the tolerance, i.e. Then, return to step (3.1) to proceed to the next iteration, where, It is the L2 norm of the vector; when the change in the target state vector in the current iteration relative to the target state vector in the previous iteration is less than the tolerance, i.e. When the iteration ends, output the target state vector, error covariance matrix, and observation noise covariance matrix at the current time step, along with related parameters: , , and .
[0089] This invention discloses a pulse signal source tracking method based on a robust Kalman filter. The method uses the target state vector and state error covariance matrix from the previous time step, along with the pulse signal reception frequency and azimuth of arrival at the current time step, and the coordinates of the receiving station. An adaptive high-order volumetric sampling method is employed to obtain sampling weights and sampling point vectors, resulting in the target predicted state vector and prediction error covariance matrix for the current time step. Subsequently, parameters are initialized, along with the target state vector and state error covariance matrix from the previous iteration. Based on the distribution model of parameters such as scaling factors, indications, and mixing coefficients, the estimation results of each parameter are updated, and the prediction error covariance matrix and observation noise covariance matrix are iteratively calculated. Finally, the target state vector and state error covariance matrix for the current iteration are obtained according to the Kalman filter framework. The iteration terminates when the change in the target state vector from the previous iteration is less than a tolerance, and the final result is output. Thus, stable tracking of underwater non-cooperative pulse signal sources is achieved based on nonlinear observation results under outlier interference.
[0090] Beneficial effects: Compared with the prior art, the method disclosed in this invention has the following advantages: Compared with the existing traditional adaptive Kalman filter and variational Bayesian filter modeled with a simple inverse Wishart distribution, the method proposed in this invention achieves stable tracking of underwater non-cooperative pulse signals by utilizing the receiving frequency and azimuth of arrival under complex noise conditions containing outliers; Compared with deterministic integral sampling methods, the method proposed in this invention achieves higher tracking accuracy with lower computational cost by using adaptive volumetric sampling. Attached Figure Description
[0091] Figure 1. Flowchart of the implementation of the method of the present invention;
[0092] Figure 2. Target state vector-coordinate RMSE in a complex observation noise perturbation scenario containing outliers;
[0093] Figure 3. Target state vector-velocity RMSE in a complex observation noise perturbation scenario containing outliers;
[0094] Figure 4. Target state vector-frequency RMSE in a complex observation noise perturbation scenario containing outliers;
[0095] Figure 5. Angle term of the observation noise covariance matrix in a complex observation noise perturbation scenario containing outliers;
[0096] Figure 6. Frequency term of the observation noise covariance matrix in a complex observation noise disturbance scenario containing outliers. Detailed Implementation
[0097] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:
[0098] This invention utilizes the receiving frequency and arrival direction of underwater acoustic pulse signals to achieve stable tracking of non-cooperative underwater targets. Based on the target state vector, state error covariance matrix, and observation noise covariance matrix of the previous moment, and combined with the state transition function, an adaptive high-order volumetric sampling method is used to calculate the target prediction state and prediction error covariance matrix at the current moment. During the iteration process, parameters following different distributions are updated to obtain the prediction error covariance matrix and observation noise covariance matrix for this iteration. From this, the target state vector and state error covariance matrix at the current moment are estimated, and finally, stable tracking of the target state vector is achieved through recursion.
[0099] Example 1:
[0100] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.
[0101] The parameters are set as follows: In the motion state setting, the northeast-central coordinate system is used, the sonar array is set at the origin, the target's initial coordinates are (7000, 3873), the speed is 8 knots, the heading is 194.5°, the single-frequency transmission signal frequency is 6500Hz, and the pulse signal period is 10s. The simulation example uses 400 pulse signal groups. Target state vector. Including the target in the Coordinates and velocity at time 1 and the source frequency of this pulse signal Dimension of the target state vector The target motion state transition function is 5. for:
[0102]
[0103] Set acceleration in the due east and due north directions and The standard deviation of all values is 0.001 m / s. 2 Source frequency disturbance The standard deviation is 0.1 Hz, thus constituting the first... Process noise vector per pulse Based on the state transition model of uniform linear motion, its noise driving matrix is:
[0104]
[0105] This gives the process noise covariance matrix. .
[0106] Set observations for:
[0107]
[0108] Dimension of the observation vector The value is 2, where, It is the observation function. It is the first The azimuth angle of arrival of each pulse signal at any given time:
[0109]
[0110] It is the first The receiving frequency at each pulse signal moment:
[0111]
[0112] in, It is the first The coordinates and velocity of the observation station at each pulse signal moment. It is the speed of sound in seawater, usually taken as 1500 m / s.
[0113] Set a baseline value for the observation noise covariance matrix. :
[0114]
[0115] Among them, the standard deviation of azimuth observation noise Set as Standard deviation of frequency observation noise The frequency is set to 5Hz. Based on the baseline value of the observation noise covariance matrix, an observation noise covariance matrix containing outliers is defined. :
[0116]
[0117] in, It is a random number that is uniformly distributed between 0 and 1.
[0118] In the graphs of the observation noise covariance matrix, OTNVBAKF presents the results estimated by the algorithm proposed in this invention, while True presents the set true value.
[0119] A pulse signal source tracking method based on a robust Kalman filter, such as Figure 1 , Figure 2 As shown, it includes the following steps:
[0120] Step 1 is as follows:
[0121] (1.1) Set the arrival time of the pulse signal during the tracking process as... Read in the previous moment, that is... Target state vector at time 1 State error covariance matrix .make hour, This represents the actual state at the initial moment. for ; Read in the scalar of degrees of freedom describing the observation noise covariance matrix from the previous time step. With scale matrix , for , Calculated from the identity matrix, the receiving station remains stationary at the origin, and its coordinate vector... , The observation of time is The superscript 't' indicates a physical quantity related to the target, and the superscript 'o' indicates a physical quantity related to the receiving array. This is an identifier for the physical quantity estimation results. It reads in the forgetting factor to adjust the observation noise covariance matrix. Adjusting the parameters of the forecast error covariance matrix Forgetting factor for e is the natural constant, and the parameter Set the initial coefficient of the gamma distribution to 5; for , yes Number of mixed distributions The initial value of the gamma distribution mixing coefficient is 4. for Maximum number of iterations 100, tolerance 10 -10 .
[0122] (1.2) Based on Target state vector at time 1 With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. The weight of each sampling point is ; calculated using the state transition model Time-based target prediction state vector With the forecast error covariance matrix :
[0123]
[0124]
[0125] in, It is a state transition function. It is the process noise covariance matrix. It is the transpose of the matrix.
[0126] Step 2 is as follows:
[0127] (2.1) Initialize variational Bayes parameters (scaling factor, indicator and mixing coefficient) before iteration
[0128] Initialize scaling factor Expectations The expectation of its natural logarithm :
[0129]
[0130] in, It is the expected value.
[0131] Initialize indicator Expectations :
[0132]
[0133] Initialize the mixing coefficients expect The expectation of its natural logarithm :
[0134]
[0135] Initialize the degrees of freedom of the observation noise covariance matrix at the current time without observation correction. Initialize the scaling matrix of the observation noise covariance matrix that has not been corrected at the current time. .
[0136]
[0137]
[0138] Initialize the degrees of freedom of the forecast error covariance matrix at the current time without observation corrections. The scaling matrix is initialized to the forecast error covariance matrix that has not been corrected for observations at the current time. .
[0139]
[0140]
[0141] (2.2) According to Time-prediction state vector With the forecast error covariance matrix Initialize the target state vector before iteration With the state error covariance matrix : , .
[0142] Expectation of the inverse of the initial observation noise covariance matrix : .
[0143] Step 3 specifically involves:
[0144] (3.1) Let the previous iteration be the th iteration. This iteration is the [number]th. Next. Based on the target state vector of the previous iteration. With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of sampling points is , No. The weight of each sampling point is Calculate the quadratic sufficient statistic of the observation error. With the quadratic sufficient statistic of forecast error :
[0145]
[0146]
[0147] in, It is the first The posterior observation mean of the next iteration.
[0148] Step 4 specifically involves:
[0149] (4.1) Update the scaling factor that follows a gamma distribution. posterior distribution Update Shape parameters with rate parameter :
[0150]
[0151]
[0152] in, It is the trace of the matrix. It is the first Indicator during the next iteration Expected value It is the expected value. It is the first The expected result of observing the inverse of the noise covariance matrix in the next iteration.
[0153] Therefore, we obtain the first... During the next iteration Expectation calculation Its natural logarithm expected result :
[0154]
[0155] in, It is the digamma function.
[0156] (4.2) Update the indicator that follows a multinomial distribution posterior distribution Update parameters :
[0157]
[0158] in, Coefficients before normalization The calculation formula is:
[0159]
[0160] in, It is the gamma function. It is the first The mixing coefficient at the next iteration The expected result of the natural logarithm.
[0161] Therefore, we obtain the first... During the next iteration Expected calculation result:
[0162]
[0163] (4.3) Update the mixing coefficients that follow a Dirichlet distribution. posterior distribution Update coefficient The formula for calculating this coefficient is:
[0164]
[0165] Therefore, we obtain the first... During the next iteration Expected results Its natural logarithm expected result :
[0166]
[0167] Step 5 specifically involves:
[0168] (5.1) Update description The degrees of freedom of the prediction error covariance matrix in the next iteration With scale matrix :
[0169]
[0170]
[0171] Therefore, we obtain the first... The prediction error covariance matrix at the next iteration :
[0172]
[0173] (5.2) Update description The degrees of freedom of the observation noise covariance matrix in the next iteration With scale matrix :
[0174]
[0175]
[0176] Therefore, we obtain the first... The observation noise covariance matrix at the next iteration :
[0177]
[0178] Step 6 specifically involves:
[0179] (6.1) Based on the target prediction state vector at the current moment With the The prediction error covariance matrix of the next iteration The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. Each sampling weight is Calculate the first The mean of the target state vector at the next iteration with the mean of the observed vector :
[0180]
[0181]
[0182] Therefore, the first... The observation autocovariance matrix at the next iteration The cross-covariance matrix between target state and observed quantities and Kalman gain :
[0183]
[0184]
[0185]
[0186] Final calculation The target state vector for the next iteration With the state error covariance matrix :
[0187]
[0188]
[0189] Step 7 specifically includes:
[0190] (7.1) When the change in the target state vector of the current iteration relative to the target state vector of the previous iteration is greater than the tolerance, i.e. Then, return to step (3.1) to proceed to the next iteration, where, It is the L2 norm of the vector; when the change in the target state vector in the current iteration relative to the target state vector in the previous iteration is less than the tolerance, i.e. When the iteration ends, output the target state vector, error covariance matrix, and observation noise covariance matrix at the current time step, along with related parameters: , , and .
[0191] The above embodiments demonstrate that the method of the present invention can effectively achieve stable tracking of underwater non-cooperative pulse signal targets under complex observation noise conditions containing outliers, by utilizing the receiving frequency and azimuth of arrival; combined with the adaptive high-order volume sampling method, the method of the present invention achieves high target tracking accuracy with low computational cost.
[0192] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.
Claims
1. A pulse signal source tracking method based on a robust Kalman filter, characterized in that... Includes the following steps: Step 1: Read in the target state vector, error covariance matrix, and observation noise covariance matrix from the previous time step. Calculate the target prediction state vector and prediction error covariance matrix at the current time step using the adaptive high-order volumetric sampling method and state transition model. Step 2: Initialize the variational Bayesian parameters (scaling factor, indicator, and mixing coefficient), target state vector, and error covariance matrix before iteration; Step 3, iteration begins. Based on the target state vector and state error covariance matrix of the previous iteration, the adaptive high-order volumetric sampling method is used to calculate the quadratic sufficient statistics of observation error and prediction error. Step 4: Update the variational Bayes parameters (scaling factor, indicator, and mixing coefficient). Step 5: Update the forecast error covariance matrix and the observation noise covariance matrix; Step 6: Based on the target state prediction vector and the prediction error covariance matrix of this iteration, the adaptive high-order capacitive sampling method is used to calculate the target state vector and error covariance matrix of this iteration. Step 7: The iteration ends when the change between the target state vector in this iteration and the target state vector in the previous iteration is less than the tolerance. Output the target state vector, error covariance matrix, and observation noise covariance matrix at the current moment. Otherwise, return to step (3).
2. The pulse signal source tracking method based on a robust Kalman filter according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1, set the arrival time of the pulse signal during the tracking process as... ; Read in the previous moment, that is The target state vector at time 1 State error covariance matrix The degrees of freedom describing the observation noise covariance matrix at the previous time step. With scale matrix , The receiving station coordinate vector at time With the observed vector The superscript 't' indicates a physical quantity related to the target, and the superscript 'o' indicates a physical quantity related to the receiving array. It is an identifier for the physical quantity estimation results; read in the forgetting factor to adjust the observation noise covariance matrix. Adjusting the parameters of the forecast error covariance matrix ; Set the initial coefficients of the i-th gamma distribution and , , The number of gamma distributions and the initial values of the gamma distribution mixing coefficients. Maximum number of iterations tolerance ; Step 1.2, based on The target state vector at time 1 With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. The weight of each sampling point is ; calculated using the state transition model Time-based target prediction state vector With the forecast error covariance matrix : ， in, It is a state transition function. It is the process noise covariance matrix. It is the transpose of the matrix.
3. The pulse signal source tracking method based on a robust Kalman filter according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3.1, set the previous iteration as the... This iteration is the [number]th iteration. Next; based on the target state vector of the previous iteration With the state error covariance matrix The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of sampling points is , No. The weight of each sampling point is Calculate the quadratic sufficient statistic of the observation error. Sufficient statistics of quadratic form of forecast error : ， in, It is the first The posterior observation mean of the next iteration It is the observation function.
4. The pulse signal source tracking method based on a robust Kalman filter according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1, update the scaling factor that follows a gamma distribution. posterior distribution Update Shape parameters with rate parameter : ， in, It is the dimension of the observation vector. It is the trace of the matrix. It is the first Indicator during the next iteration Expected value It is the expected value. It is the first The expected result of the inverse of the observed noise covariance matrix in the next iteration; Therefore, we obtain the first... During the next iteration Expectation calculation Its natural logarithm expected result : ， in, It is the digamma function; Step 4.2, update the indicator that follows a multinomial distribution. posterior distribution Update parameters : ， in, Coefficients before normalization The calculation formula is: ， in, It is the gamma function. It is the first The mixing coefficient at the next iteration The expected result of the natural logarithm; Therefore, we obtain the first... During the next iteration Expected calculation result: ， Step 4.3, update the mixing coefficients that follow a Dirichlet distribution. posterior distribution Update coefficient The formula for calculating this coefficient is: ， Therefore, we obtain the first... During the next iteration Expected results Its natural logarithm expected result : 。 5. The pulse signal source tracking method based on a robust Kalman filter according to claim 1, characterized in that, Step 5 specifically includes the following steps: Step 5.1, update the description. The degrees of freedom of the prediction error covariance matrix in the next iteration With scale matrix : ， in These are the degrees of freedom of the forecast error covariance matrix at the current moment before observation corrections. It is the scaling matrix of the forecast error covariance matrix at the current time without observation correction; Therefore, we obtain the first... The prediction error covariance matrix at the next iteration : ， in, It is the dimension of the target state vector; Step 5.2, update the description. The degrees of freedom of the observation noise covariance matrix in the next iteration With scale matrix : ， in These are the degrees of freedom of the observation noise covariance matrix at the current moment before any observation corrections have been made. It is the scaling matrix of the observation noise covariance matrix at the current moment before observation correction is performed; Therefore, we obtain the first... The observation noise covariance matrix at the next iteration : 。 6. The pulse signal source tracking method based on a robust Kalman filter according to claim 1, characterized in that, Step 6 specifically includes the following steps: Step 6.1, based on the target prediction state vector at the current moment With the The prediction error covariance matrix of the next iteration The number of sampling points obtained by using the adaptive higher-order volumetric sampling method is , of which The vector of each sampling point is , No. Each sampling weight is Calculate the first The mean of the target state vector at the next iteration with the mean of the observed vector : ， Therefore, the first... The observation autocovariance matrix at the next iteration The cross-covariance matrix between target state and observed quantities and Kalman gain : ， ， ， Final calculation The target state vector for the next iteration With the state error covariance matrix : 。
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