CN-121995384-A - Pulse signal source tracking method based on robust Kalman filter

CN121995384ACN 121995384 ACN121995384 ACN 121995384ACN-121995384-A

Abstract

The invention discloses a pulse signal source tracking method based on a robust Kalman filter, which comprises the following steps of reading in a target state vector and an error covariance matrix at the previous moment, observing a noise covariance matrix, initializing a pre-iteration variable decibel leaf parameter, a target state vector and an error covariance matrix, starting iteration, calculating full statistics of an observed error and a forecast error quadratic form, updating the variable decibel leaf parameter, updating the forecast error covariance matrix and the observed noise covariance matrix, calculating the target state vector and the error covariance matrix of the current iteration, ending the iteration when the change amount of the target state vector and the target state vector of the last iteration is smaller than a tolerance, and outputting the target state vector and the error covariance matrix at the current moment and the observed noise covariance matrix.

Inventors

WANG XIAOYAN
YE YANG
AN LIANG
CAO HONGLI
LUO HAORAN
YANG ZHENNING

Assignees

东南大学

Dates

Publication Date: 20260508
Application Date: 20260213

Claims (6)

1. A pulse signal source tracking method based on a robust Kalman filter is characterized by comprising the following steps: Step 1, reading in a target state vector, an error covariance matrix and an observation noise covariance matrix at the previous moment, and calculating a target forecast state vector and a forecast error covariance matrix at the current moment by using a self-adaptive high-order volume sampling method and a state transition model; Step 2, initializing a variable decibel leaf parameter (a scaling factor, an indication quantity and a mixing coefficient), a target state vector and an error covariance matrix before iteration; Step 3, starting iteration, and calculating full statistics of the quadratic forms of the observation error and the forecast error by using a self-adaptive high-order volume sampling method based on the target state vector and the state error covariance matrix of the previous iteration; step 4, updating the variable decibel leaf parameters (scaling factors, indication quantity and mixing coefficients); step 5, updating a prediction error covariance matrix and an observation noise covariance matrix; Step 6, calculating a target state vector and an error covariance matrix of the iteration by adopting a self-adaptive high-order volume sampling method based on the target state prediction vector and the prediction error covariance matrix of the iteration; And 7, ending iteration when the change quantity of the target state vector of the current iteration and the target state vector of the last iteration is smaller than the tolerance, outputting the target state vector, the error covariance matrix and the observation noise covariance matrix at the current moment, and otherwise, returning to the step 3.
2. The pulse signal source tracking method based on the robust kalman filter according to claim 1, wherein the step 1 specifically comprises the following steps: Step 1.1, setting the arrival time of the pulse signal in the tracking process as Reading in the previous moment, i.e Time of day target state vector Covariance matrix of state error Describing the degree of freedom of the observed noise covariance matrix at the previous moment And scale matrix , Time of day receiving station coordinate vector Vector of observational quantity Wherein the superscript t is an identification of a physical quantity related to the target, the superscript o is an identification of a physical quantity related to the receiving array, Is the identification of the estimation result of the physical quantity, reads in the forgetting factor for adjusting the covariance matrix of the observation noise And adjusting parameters of the prediction error covariance matrix Setting the initial coefficient of the ith gamma distribution And (3) with , , Is the number of gamma distributions, and the initial value of the gamma distribution mixing coefficient Maximum number of iterations Tolerance, tolerance ; Step 1.2 based on Time of day target state vector Covariance matrix of state error The number of sampling points obtained by adopting the self-adaptive high-order volume sampling method is Wherein the first The vector of the sampling points is First, the The weight of each sampling point is And combining the state transition model to calculate Time of day target forecast state vector Covariance matrix of prediction error : , Wherein, the Is a state transfer function that is a function of the state, Is the process noise covariance matrix and, Is a transpose of the matrix.
3. The pulse signal source tracking method based on the robust kalman filter according to claim 1, wherein the step 3 specifically comprises the following steps: Step 3.1, setting the previous iteration to be the first The next time, the current iteration is the first Second time, based on previous iteration target state vector Covariance matrix of state error The number of sampling points obtained by adopting the self-adaptive high-order volume sampling method is Wherein the first The vectors of the sampling points are First, the The weights of the sampling points are as follows Calculating the quadratic form full statistics of the observation errors And forecast error quadratic form full statistics : , Wherein, the Is the first The posterior observed mean value of the multiple iterations, Is an observation function.
4. The pulse signal source tracking method based on the robust kalman filter according to claim 1, wherein the step 4 specifically comprises the following steps: step 4.1, updating the scaling factor obeying the gamma distribution Posterior distribution of (2) I.e. updating Shape parameters of (a) And rate parameter : , Wherein, the Is the dimension of the observation vector and, Is the trace of the matrix, Is the first Indicating quantity at time of iteration Is used as a reference to the desired value of (a), Is a desired value that is to be determined, Is the first Observing the expected result of the noise covariance matrix inverse array in the next iteration; Thereby obtaining the first At the time of iteration Is calculated by the expectation of (a) Expected results from natural logarithms of : , Wherein, the Is digamma function; step 4.2, updating the indication quantity obeying the polynomial distribution Posterior distribution of (2) I.e. updating Parameters of (2) : , Wherein, the Coefficient before normalization The calculation formula of (2) is as follows: , Wherein, the Is a function of the gamma-ray, Is the first Mixing coefficients at multiple iterations Natural log expected results of (a); Thereby obtaining the first At the time of iteration Is a result of the expected calculation of: , step 4.3, updating the mixing coefficients subject to Dirichlet distribution Posterior distribution of (2) I.e. updating Coefficient of (2) The calculation formula of the coefficient is as follows: , Thereby obtaining the first At the time of iteration Is of the desired outcome of (1) Expected results from natural logarithms of : 。
5. The pulse signal source tracking method based on the robust kalman filter according to claim 1, wherein the step 5 specifically comprises the following steps: step 5.1, update description Degree of freedom of prediction error covariance matrix in multiple iterations And scale matrix : , Wherein the method comprises the steps of Is the degree of freedom of the prediction error covariance matrix which is not observed and corrected at the current moment, The scale matrix is a prediction error covariance matrix which is not observed and corrected at the current moment; Thereby obtaining the first Prediction error covariance matrix at multiple iterations : , Wherein, the Is the dimension of the target state vector; Step 5.2, update description Degree of freedom for observing noise covariance matrix in multiple iterations And scale matrix : , Wherein the method comprises the steps of Is the degree of freedom of the observed noise covariance matrix with no observation correction at the current moment, Is a scale matrix of an observation noise covariance matrix which is not observed and corrected at the current moment; Thereby obtaining the first Observed noise covariance matrix at multiple iterations : 。
6. The pulse signal source tracking method based on the robust kalman filter according to claim 1, wherein the step 6 specifically includes the steps of: Step 6.1, target forecast status vector based on the current time And the first Prediction error covariance matrix of secondary iteration The number of sampling points obtained by adopting the self-adaptive high-order volume sampling method is Wherein the first The vector of the sampling points is First, the The sampling weights are Calculate the first Target state vector average at multiple iterations Mean value of observation vector : , Thereby calculating the first Observed quantity auto-covariance matrix at multiple iterations Cross covariance matrix of target state and observed quantity Kalman gain : , , , Final calculation Target state vector for multiple iterations Covariance matrix of state error : 。

Description

Pulse signal source tracking method based on robust Kalman filter Technical Field The invention relates to a pulse signal source tracking method based on a robust Kalman filter, and belongs to the field of underwater sound signal target positioning tracking. Background The underwater acoustic passive positioning technology is always a hotspot for research in the field of underwater acoustic, and particularly has been widely focused on tracking underwater non-cooperative targets. Based on Doppler-azimuth target motion analysis theory, the underwater non-cooperative target tracking can be realized by utilizing the signal receiving frequency and the arrival azimuth. On the aspect of realizing the tracking requirement of a moving target, the Kalman filter is widely applied in engineering practice by virtue of the good balance characteristic between the estimation precision and the real-time calculation performance. However, the stable tracking of the state achieved by the kalman filter requires accurate prior information, such as statistical characteristics of process noise and observation noise. Inaccurate filter parameters can severely degrade filter performance and even cause filter divergence. Aiming at the problem, the maximum likelihood estimation method generally relies on a time window to extract innovation or residual sequences so as to realize accurate estimation of an observed noise covariance matrix, and finally a stable target tracking result is obtained. However, observations of underwater non-cooperative targets involve a variety of signal types, including line spectrum and broadband components in ship radiated noise and pulsed signals actively transmitted by non-cooperative targets. Aiming at the problem of frequency estimation of a pulse signal, the transient and short-time characteristics of the pulse signal make it difficult to realize time accumulation effect in processing, so that the frequency estimation resolution is limited, and when the pulse signal propagates in a channel of a non-uniform ocean waveguide, waveform distortion can cause drift and deviation of frequency estimation of a received signal. In the azimuth estimation of the pulse signals, the underwater propagation pitch angle coupling and the underwater array distortion of the sonar array cause the azimuth estimation result to deviate. At the same time, marine background noise places the pulse signal parameter estimation in an unfavorably low signal-to-noise condition. The parameter estimation result is interfered by the outlier due to the combined action of the underwater engineering scene factors, and the outlier in the observation quantity of the non-cooperative pulse signal source tracking process is not considered in theory by the traditional self-adaptive Kalman filtering method. Aiming at the abnormal filter noise condition, scientific researchers propose various improved adaptive Kalman filter schemes, and variational Bayesian inference is one of the efficient methods. Early variational Bayesian frameworks constructed noise covariance matrix models by INVERSE WISHART distributions failed to deal with complex noise environments in actual engineering scenarios, such as outlier-to-observed-quantity interference. In addition, the common pulse signal parameter observed quantity is a nonlinear function of a motion state, and state tracking can be realized by a nonlinear Kalman filter through an integral sampling method, but expected calculation under outlier disturbance in a common integral sampling method has errors, so that motion state estimation precision is reduced. Therefore, the underwater non-cooperative pulse signal source is tracked with low cost and high precision under the condition of observation noise including outliers, and the method has important theoretical significance and application value. Disclosure of Invention The invention provides a pulse signal source tracking method based on a robust Kalman filter, which realizes accurate estimation of the motion state of an underwater non-cooperative pulse signal source under the complex noise condition with outliers. Simulation data processing results show that compared with the traditional self-adaptive Kalman filter tracking method, the method solves the problem of outlier interference under a nonlinear observation system and realizes stable tracking of an underwater non-cooperative pulse signal source. The invention aims to provide a pulse signal source tracking method based on a robust Kalman filter, aiming at the problems of high degree of nonlinearity of parameters of underwater acoustic pulse signals and outlier disturbance. The method is based on a target state vector and a state error covariance matrix at the previous moment, and utilizes the pulse signal receiving frequency and the arrival azimuth at the current moment and the coordinate vector of a receiving station, and adopts a self-adaptive high-order volume sampling method to obtain a sampling wei