CN-119846638-B - Underwater target tracking method based on multivariable bias Laplace distribution

CN119846638BCN 119846638 BCN119846638 BCN 119846638BCN-119846638-B

Abstract

The invention discloses an underwater target tracking method based on multivariate bias Laplace distribution modeling, which adopts a sonar sensor mode to collect motion state data of an underwater target and adopts a coordinate system conversion mode to obtain target position measurement information, establishes a motion model of the underwater target, determines a state space equation of the underwater target, analyzes mathematical characteristics of underwater noise, establishes a measurement model of the target under non-Gaussian noise, models the non-Gaussian noise based on multivariate bias Laplace distribution, solves mixed parameters, shape parameters and a scale matrix of the noise under a variational Bayesian framework, iteratively updates a target state and a noise covariance matrix, iteratively updates an estimated target motion state by Kalman filtering, and outputs an estimated value of the position and the speed of the underwater target and an estimated value of the covariance matrix after the iteration times are reached. The method has better robustness and estimation precision, does not need to select a degree of freedom parameter, and can be better applied to tracking of the target.

Inventors

Wu panlong
ZHAO BAOCHEN
HE SHAN
KONG LINGQI
WANG KE

Assignees

南京理工大学

Dates

Publication Date: 20260512
Application Date: 20241226

Claims (7)

1. An underwater target tracking method based on multivariable bias Laplace distribution modeling is characterized by comprising the following steps: step 1, acquiring motion state data of an underwater target by adopting a sonar sensor, wherein the motion state data comprises a radial distance and an azimuth angle, and converting the radial distance and the azimuth angle of the underwater target acquired by the sensor from a ball/polar coordinate system to a Cartesian coordinate system by adopting a coordinate system conversion mode to obtain target position measurement information; Step 2, establishing a motion model of the underwater target, determining a state space equation of the underwater target, analyzing mathematical characteristics of underwater noise, and establishing a measurement model of the target under non-Gaussian noise; and 3, modeling non-Gaussian noise based on multivariate bias laplace distribution, solving a mixed parameter, a shape parameter and a scale matrix of noise under a variational Bayesian framework, iteratively updating a target state and a noise covariance matrix, iteratively updating an estimated target motion state by using Kalman filtering, and outputting estimated values of the underwater target position and speed and the estimated values of the covariance matrix after the number of iterations is reached.
2. The method for tracking the underwater target based on the multivariable skew Laplace distribution modeling according to claim 1, wherein the method is characterized in that step 1, the motion state data of the underwater target is collected by adopting a sonar sensor, wherein the motion state data comprises a radial distance and an azimuth angle, the radial distance and the azimuth angle of the underwater target collected by the sensor are converted from a polar coordinate system to a Cartesian coordinate system by adopting a coordinate system conversion mode, and target position measurement information is obtained, wherein: assumed point The positions of the Cartesian coordinate system are recorded as The position in the polar coordinate system is recorded as The transformation relation from the polar coordinate system to the rectangular coordinate system is as follows: 。
3. the method for tracking the underwater target based on the multivariate bias Laplace distribution modeling of claim 2, wherein the method is characterized by comprising the following steps of establishing a motion model of the underwater target, determining a state space equation of the underwater target, analyzing mathematical characteristics of underwater noise, and establishing a measurement model of the target under non-Gaussian noise, wherein: establishing a motion model of an underwater target, and determining a state space equation of the underwater target; ; Wherein, the The position and velocity of the target at time k, Is a sequence of process noise at k-time subject to gaussian distribution, the process noise is zero-mean gaussian noise with covariance, expressed as: ; The K distribution is adopted to simulate the non-Gaussian noise under water, and the probability density function of the K distribution is as follows: ; Wherein, the For the shape factor, a is the scale factor, Is that Step(s) Class(s) The function of the function is that, Is that A function; The measurement model of the target under non-Gaussian noise is as follows: ; Wherein, the Measuring a target at the moment k, wherein the target comprises a distance and an azimuth angle; noise is measured for a non-gaussian distribution of K.
4. The method for tracking the underwater target based on the multivariate bias Laplace distribution modeling according to claim 2, wherein the step 3 is characterized in that modeling is performed on non-Gaussian noise based on the multivariate bias Laplace distribution, the mixing parameters, the shape parameters and the scale matrix of the noise are solved under a variational Bayesian framework, the target state and the noise covariance matrix are updated in an iteration mode, the estimated target motion state is updated in an iteration mode through Kalman filtering, and after the iteration times are reached, the estimated values of the position and the speed of the underwater target and the estimated values of the covariance matrix are output, wherein: The measured noise has thick tail or thick tail skew distribution, and modeling is performed on non-Gaussian noise based on multivariate skew laplace distribution; ; Wherein, the Is the measurement noise of a non-gaussian distribution, Is the mean value of Covariance is Is a function of the gaussian probability density of (c), Representing the parameters as Is a function of the exponential probability density of (c), 、、 And Respectively representing a mixing parameter, a shape parameter, a scale matrix and a rate parameter of the measurement noise; according to the Chapman-Komlogorov equation, the probability density function is predicted in one step Expressed as: ; Wherein, the And Respectively represent State one-step prediction of time and corresponding prediction error covariance matrix, From time 1 to time A measurement value of time; Likelihood PDF Expressed as: ; adopting inverse Wishare distribution as conjugate prior distribution of a scale matrix; ; Wherein, the Is a degree of freedom parameter of The inverse scale matrix is An inverse Wishart probability density function; nominal measurement noise covariance matrix The method comprises the following steps: ; Wherein m is the dimension of the measurement vector; The prior distribution of shape parameters is chosen to be gaussian, i.e.: ; Wherein the method comprises the steps of Representing a nominal shape parameter of the measured noise, Representing the confidence in the nominal shape parameters, Is a unit matrix; jointly deducing the mixing parameters, shape parameters and scale matrix by using the variational Bayesian method, i.e. ; Obtaining using a variational Bayesian method Has an approximate posterior probability density function in free decomposition form, namely: ; Wherein, the An approximation of the true posterior probability density function with free form decomposition, the optimal solution satisfying the following equation ; Wherein the method comprises the steps of Is that Is a combination of any of the elements of the formula, As the remaining elements of the composition, Is a constant term; conditional independence of building a layered Gaussian state space model, then joint probability density functions Is decomposed into: ; Wherein, the Representing a known state transition matrix of the type, Representation of The prediction error covariance matrix of the moment in time, Is a measurement matrix; taking logarithms from two sides simultaneously to obtain: ; Wherein, the Representing a nominal shape parameter of the measured noise, For characterizing the confidence level for the nominal parameters; (1) Solving state variables Posterior distribution of (2) Order the Substituted into the following formula: ; the logarithmic expression for the resulting state posterior distribution is: ; Wherein, the Represent the first One type of iterative true posterior probability density function has an approximation in free decomposition form, Representation of The inverse of the prediction error covariance matrix of the instant, Is a constant term; defining a modified measurement noise mean vector Covariance matrix The method comprises the following steps: ; ; using Bayesian criteria Updated as a gaussian probability density function, namely: ; wherein the state estimate and covariance are as follows: ; Wherein the method comprises the steps of Is the first Multiple iterations A state estimate of the time of day, Represent the first Multiple iterations The error covariance matrix of the time instant, Is the first Multiple iterations The kalman gain at the moment in time, Is a matrix of units which is a matrix of units, For the corrected measurement noise mean vector, A corrected measurement noise covariance matrix; (2) Updating posterior distribution of mixing parameters Order the Substituted into the following ; The logarithmic expression of the posterior distribution of the resulting states is: ; Wherein the method comprises the steps of Is that ; By matching the parameters, the posterior distribution is found to be still generalized inverse Gaussian distribution, namely: ; defining relevant parameters The method comprises the following steps of: ; according to the generalized inverse gaussian distribution property, The method comprises the following steps: ; (3) Updating posterior distribution of shape parameters Order the , Written in the form: ; Wherein the method comprises the steps of Is a constant term which is used to determine the degree of freedom, ; Wherein the method comprises the steps of , Updating to Gaussian distribution ; Wherein the mean vector and covariance matrix are as follows: ; (4) Updating posterior distribution of scale matrix Order the , Written in the form: ; ; Wherein the method comprises the steps of Is a constant term which is used to determine the degree of freedom, ; ; ; By the nature of IW distribution, there are: ; Thus, the VB-based hidden variable iteration solving process is completed, and the estimated value of the target state can be obtained after a plurality of iterations.
5. An underwater target tracking system based on multivariable bias Laplace distribution modeling is characterized in that the underwater target tracking method based on multivariable bias Laplace distribution modeling according to any one of claims 1-4 is implemented to realize the underwater target tracking based on multivariable bias Laplace distribution modeling, and the method is divided into three modules to respectively execute steps 1-3.
6. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of underwater target tracking based on multivariate bias Laplace distribution modeling of any of claims 1-4 when the computer program is executed, to implement underwater target tracking based on multivariate bias Laplace distribution modeling.
7. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method for underwater target tracking based on multivariate bias Laplace distribution modeling of any of claims 1 to 4, enabling underwater target tracking based on multivariate bias Laplace distribution modeling.

Description

Underwater target tracking method based on multivariable bias Laplace distribution Technical Field The invention relates to target tracking, in particular to an underwater target tracking method based on multivariable skew Laplace distribution. Background Underwater target tracking refers to the continuous estimation and prediction of the state (speed, position, etc.) of a target over time by a filtering algorithm using different measured information (distance, azimuth, etc.) obtained by one or more sensors of different kinds. By rapidly acquiring the state information such as the position, the speed, the acceleration and the like of the enemy target, the method can effectively defend and fight against enemy invading ships, torpedoes, submarines, underwater robots and the like During the measurement of underwater, the sensor is susceptible to non-gaussian noise, and the measurement may no longer conform to gaussian distribution, but rather exhibit a skewed heavy tail distribution (SKEW HEAVY TAILED distribution) characteristic. The noise of this distribution has a large extreme value and can negatively impact the performance of the tracking. In practical engineering application, in face of non-gaussian noise problem, relevant scholars propose Student t-based filters (STFs), and model the heavy tail characteristics of noise by utilizing Student t distribution, but with the increase of the degree of freedom parameters, the heavy tail characteristics may be weakened, and estimation accuracy is affected. To overcome this problem, a variable decibels-based student t Kalman filter (VB-STKF) is used to jointly estimate the state and degree of freedom parameters using the variable decibels method. However, for complex thick tail noise and thick tail skew noise conditions, the student t distribution cannot accurately describe the noise model, so that gaussian proportional mixing distribution (Gaussian Scale Mixture, GScM) is provided, noise modeling accuracy better than that of the student t distribution can be obtained through self-adaptive learning of distribution parameters, although the noise distribution can be flexibly modeled, and filtering implementation time is possibly longer due to the fact that the number of iterations is large. The design and selection of these filters should be comprehensively considered according to the system characteristics, noise characteristics and real-time requirements to achieve the optimal state estimation effect. At present, a modeling method based on student t distribution is generally adopted in a target tracking algorithm under non-Gaussian noise, the method needs to select a degree of freedom parameter, more variables need to be modeled, actual application is not facilitated, and errors are larger when the existing algorithm processes non-Gaussian skew heavy tail noise. Disclosure of Invention The invention aims to provide an underwater target tracking method based on multivariable skew Laplace distribution. The technical scheme for realizing the purpose of the invention is that the underwater target tracking method based on multivariable deflection Laplace distribution modeling comprises the following steps: step 1, acquiring motion state data of an underwater target by adopting a sonar sensor, wherein the motion state data comprises a radial distance and an azimuth angle, and converting the radial distance and the azimuth angle of the underwater target acquired by the sensor from a ball/polar coordinate system to a Cartesian coordinate system by adopting a coordinate system conversion mode to obtain target position measurement information; Step 2, establishing a motion model of the underwater target, determining a state space equation of the underwater target, analyzing mathematical characteristics of underwater noise, and establishing a measurement model of the target under non-Gaussian noise; and 3, modeling non-Gaussian noise based on multivariate bias laplace distribution, solving a mixed parameter, a shape parameter and a scale matrix of noise under a variational Bayesian framework, iteratively updating a target state and a noise covariance matrix, iteratively updating an estimated target motion state by using Kalman filtering, and outputting estimated values of the underwater target position and speed and the estimated values of the covariance matrix after the number of iterations is reached. Further, step 1, acquiring motion state data of an underwater target by adopting a sonar sensor, wherein the motion state data comprises a radial distance and an azimuth angle, and converting the radial distance and the azimuth angle acquired by the sensor from a polar coordinate system to a Cartesian coordinate system by adopting a coordinate system conversion mode to obtain target position measurement information, wherein the radial distance and the azimuth angle acquired by the sensor are as follows: Assuming that the position of the point P in the cartesian coordinate sys