A target tracking method and system based on unscented Kalman filter

Abstract

The application discloses a target tracking method and system based on an unscented Kalman filter, and the method comprises the following steps: based on an elliptic model, the motion state and shape of a tracking target are parameterized to obtain the motion state parameters and shape parameters of the tracking target and to construct a system model; according to the system model, the motion state parameters and shape parameters of the tracking target are iteratively updated by using an unscented Kalman filter to obtain the updated motion state parameters and shape parameters. By using the application, the tracking precision of the target can be improved while the calculation process is simplified. The application can be widely applied to the technical field of target tracking as a target tracking method and system based on an unscented Kalman filter.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of target tracking, and particularly relates to a target tracking method and system based on unscented Kalman filtering. BACKGROUND

[0002] Target tracking is a process of determining the motion state of a moving target based on a measurement containing noise. Most target tracking algorithms are based on a point target model, that is, a target generates only one measurement value in each sampling period. With the development of sensor technology, the resolution accuracy of sensors is getting higher and higher, and a target can return multiple measurement values in each sampling period. Such a target is called an extended target. In recent years, the extended target tracking problem has been increasingly applied to maritime surveillance and automatic driving and other fields. By fully utilizing the multiple measurement information of an ET, the target motion state is tracked and the parameter information of the target is identified at the same time. An extended Kalman filter is usually used for tracking. However, due to the high nonlinearity of the problem, the estimation results of standard estimation techniques such as the extended Kalman filter, the second-order extended Kalman filter and the unscented Kalman filter are not ideal. Therefore, the existing extended Kalman filter estimator is combined with a constructed pseudo-measurement to detect and track the target. However, the calculation amount of the algorithm is too large, resulting in a relatively large final error obtained by calculation, and the algorithm also has certain limitations on tracking accuracy. SUMMARY

[0003] To solve the above technical problems, the purpose of the present application is to provide a target tracking method and system based on unscented Kalman filtering, which can simplify the calculation process while improving the tracking accuracy of the target.

[0004] The first technical solution adopted by the present application is: a target tracking method based on unscented Kalman filtering, comprising the following steps:

[0005] Based on an elliptical model, the motion state and shape of the tracking target are parameterized to obtain the motion state parameters and shape parameters of the tracking target and construct a system model;

[0006] According to the system model, the motion state parameters and shape parameters of the tracking target are iteratively updated by an unscented Kalman filter to obtain updated motion state parameters and shape parameters.

[0007] Further, the step of parameterizing the motion state and shape of the tracking target based on an elliptical model to obtain the motion state parameters and shape parameters of the tracking target and construct a system model specifically comprises:

[0008] Based on the elliptical model, the motion state and shape of the tracking target are parameterized to obtain the motion state parameter and shape parameter of the tracking target, and the motion state of the tracking target includes the center position of the tracking target and the velocity of the tracking target.

[0009] By introducing multiplicative noise and combining the motion state parameter and shape parameter of the tracking target, a system model is constructed.

[0010] Further, the elliptical model is specifically as follows:

[0011]

[0012] In the above formula, m k represents the center position of the elliptical model, r k represents the velocity of the elliptical model, p k represents the shape parameter of the elliptical model, x k represents the state variable of the elliptical model, and k represents the time step.

[0013] Further, the measurement equation is specifically as follows:

[0014]

[0015] In the above formula, represents the measurement equation, S k represents the motion direction and axis length of the elliptical model, represents multiplicative noise, represents measurement noise.

[0016] Further, the state equation is specifically as follows:

[0017] x k+1 =A k *x k +w k

[0018] In the above formula, A k represents the process matrix, w k represents zero-mean Gaussian process noise, x k+1 represents the updated elliptical model state variable.

[0019] Further, according to the system model, the motion state parameter and shape parameter of the tracking target are updated by the unscented Kalman filter to obtain the updated motion state parameter and shape parameter, and this step specifically includes:

[0020] Obtaining the measurement value of the tracking target by a sensor;

[0021] In combination with the measurement value, the motion state parameter and the shape parameter of the tracked target are updated by a measurement equation of the unscented Kalman filter to obtain an updated estimation value;

[0022] The updated estimation value is time-updated by a state equation of the unscented Kalman filter to obtain the updated motion state parameter and the updated shape parameter.

[0023] Further, in combination with the measurement value, the motion state parameter and the shape parameter of the tracked target are updated by a measurement equation of the unscented Kalman filter to obtain an updated estimation value, and the step specifically comprises:

[0024] The measurement value is obtained based on a sensor and is processed by a Kronecker product operation to construct a pseudo-measurement equation;

[0025] The motion state parameter and the shape parameter of the tracked target are parameter-extended and discretized to obtain Sigma points;

[0026] The Sigma points are substituted into the pseudo-measurement equation to obtain observation prediction values of the Sigma points;

[0027] Based on the observation prediction values of the Sigma points, the mean value and the covariance value of the measurement value are obtained by weighted summation processing;

[0028] The Kalman filter gain is calculated based on the mean value and the covariance value of the measurement value to obtain a Kalman filter gain value;

[0029] The motion state parameter and the shape parameter of the system model are updated based on the Kalman filter gain value to obtain the updated estimation value.

[0030] Further, the updated estimation value is time-updated by a state equation of the unscented Kalman filter to obtain the updated motion state parameter and the updated shape parameter, and the step specifically comprises:

[0031] The Sigma points are obtained based on the mean value and the covariance value of the motion state parameter and the shape parameter of the tracked target, and the Sigma points are UT-transformed to obtain predicted Sigma points;

[0032] The updated estimation value is updated by a state equation of the unscented Kalman filter based on the predicted Sigma points to obtain the updated motion state parameter and the updated shape parameter.

[0033] The second technical solution adopted by the application is a target tracking system based on an unscented Kalman filter, which comprises:

[0034] A construction module parameterizes the motion state and the shape of the tracked target based on an elliptical model to obtain the motion state parameter and the shape parameter of the tracked target and construct a system model.

[0035] updating the model, for updating the motion state parameters and the shape parameters of the tracked target according to the system model through the unscented Kalman filter to obtain updated motion state parameters and shape parameters.

[0036] The method and system have the advantages that: by parameterizing the state variables of the target and combining with multiplicative noise, the calculation amount of the system can be reduced, the tracking efficiency of the target is further improved, by using the measurement equation to update the parameterized state variables of the target based on the unscented Kalman filter, the updating error of the system can be reduced, and the tracking accuracy of the target is further improved. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a step flow chart of a target tracking method based on an unscented Kalman filter according to the present application;

[0038] Figure 2 is a structure block diagram of a target tracking system based on an unscented Kalman filter according to the present application;

[0039] Figure 3 is a measurement equation schematic diagram based on an elliptical model constructed according to the present application;

[0040] Figure 4 is a tracking result schematic diagram under low noise based on three different filters in simulation experiment one according to the present application;

[0041] Figure 5 is a tracking result schematic diagram under high noise based on three different filters in simulation experiment one according to the present application;

[0042] Figure 6 is a tracking center position error comparative analysis diagram under low noise based on three different filters in simulation experiment one according to the present application;

[0043] Figure 7 is a tracking center position error comparative analysis diagram under high noise based on three different filters in simulation experiment one according to the present application;

[0044] Figure 8 is a tracking axis length error comparative analysis diagram under low noise based on three different filters in simulation experiment one according to the present application;

[0045] Figure 9 is a tracking axis length error comparative analysis diagram under high noise based on three different filters in simulation experiment one according to the present application;

[0046] Figure 10 is a tracking direction error comparative analysis diagram under low noise based on three different filters in simulation experiment one according to the present application;

[0047] Figure 11 is a tracking direction error comparison analysis diagram based on three different filters under high noise of the simulation experiment one of the present application;

[0048] Figure 12 is a tracking result schematic diagram based on three different filters of the simulation experiment two of the present application;

[0049] Figure 13 is a tracking center position error comparison analysis diagram based on three different filters of the simulation experiment two of the present application;

[0050] Figure 14 is a tracking axis length error comparison analysis diagram based on three different filters of the simulation experiment two of the present application;

[0051] Figure 15 is a tracking direction error comparison analysis diagram based on three different filters of the simulation experiment two of the present application. DETAILED DESCRIPTION

[0052] The present application will be further described below in conjunction with the drawings and specific embodiments. For the step numbers in the following embodiments, only the setting for facilitating the description is provided, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0053] Referring to Figure 1 , the present application provides a target tracking method based on unscented Kalman filtering, which comprises the following steps:

[0054] S1, based on an elliptical model, parameterizing the motion state and shape of the tracking target to obtain the motion state parameters and shape parameters of the tracking target and construct a system model;

[0055] S11, based on an elliptical model, parameterizing the motion state and shape of the tracking target to obtain the motion state parameters and shape parameters of the tracking target, wherein the motion state of the tracking target includes the center position of the tracking target and the velocity of the tracking target;

[0056] Specifically, the state variables of the tracking target are parameterized and set to construct an elliptical model, and the parameterized setting is specifically as follows:

[0057]

[0058] In the above formula, m k represents the center position of the elliptical model, r k represents the velocity of the elliptical model, p k represents the shape parameter of the elliptical model, x krepresents the state variables of the elliptic model, and k represents the time step;

[0059] The shape parameters of the ellipse model specifically include the following parameters:

[0060]

[0061] In the above formula, α k This indicates the direction at time step k, and α k ∈[0,2π],l k,1 The length of the semi-major axis of the ellipse, l k,2 This indicates the length of the semi-minor axis of the ellipse.

[0062] S12. A system model is constructed by introducing multiplicative noise and combining the motion state parameters and shape parameters of the tracked target.

[0063] S121. During the construction of the elliptical model, the tracking target will generate a different number of independent Cartesian measurements.

[0064] Specifically, the Cartesian measurement is as follows:

[0065]

[0066] In the above formula, y represents the i-th measurement value acquired by the sensor at time step k. k Let n represent the set of all measurements acquired by the sensor at time step k. k This indicates the number of measurements acquired by the sensor at time step k;

[0067] Each individual measurement Source of measurement Among them, the measurement source Additive Gaussian measurement noise with covariance R Damaged, each measurement source It depends on the range of the target being tracked and follows a uniform spatial distribution;

[0068] S122. Based on the Gaussian distribution, multiplicative noise is introduced, and the motion state parameters and shape parameters of the tracked target are combined to construct the measurement equation and the state equation.

[0069] Specifically, refer to Figure 3 This method uses a Gaussian spatial distribution to approximate a uniform spatial distribution. A key step is constructing the measurement equation, which uses a multiplicative noise h to handle the relationship between the measurement source and the target state. This equation is then modeled as an axial ellipse located at the origin, with semi-axis lengths l1 and l2. Any multiple measurement sources z located on this ellipse... (i) It can be written as follows:

[0070]

[0071] In the above formula, l1 represents the semi-major axis of the ellipse, l2 represents the semi-minor axis of the ellipse, h (i) represents multiplicative noise;

[0072] In the constructed ellipse model, the time step flag k and the measurement flag i are omitted, and the position of the target is m = [m1, m2] T , and the shape parameter of the target is p k = [a k , l k，1 , l k，2 ] T , the measurement y is the measurement source z destroyed by the measurement noise v, the measurement source z is associated with p through multiplicative noise h = [h1, h2] T , further, the coordinate system of the ellipse model is rotated by an angle a, in order to describe the measurement source distributed on the ellipse, it is assumed that the random variable h (i) is zero mean and is distributed on a unit circle, by rotating and translating z (i) , the measurement source equation is constructed:

[0073]

[0074] In the above formula, m represents the center position of the ellipse model, and S represents the motion direction and axis length of the ellipse model;

[0075] Further, the time flag and the sensor noise are added to the measurement source equation to obtain the measurement equation, which is specifically as follows:

[0076]

[0077] In the above formula, represents the measurement value, S k represents the motion direction and axis length of the ellipse model, represents multiplicative noise, specifically C h represents the covariance of the multiplicative noise, and represents the measurement noise, specifically , and R represents the covariance of the measurement noise.

[0078] The state equation of the system model is specifically represented as follows:

[0079] x k+1 = A k *x k +w k

[0080] In the above formula, Ak represents a process matrix, w k represents a zero-mean Gaussian process noise with covariance Q.

[0081] S2, updating the motion state parameters and the shape parameters of the tracked target by a unscented Kalman filter according to a system model, to obtain updated motion state parameters and shape parameters;

[0082] S21, obtaining a measurement value of the tracked target by a sensor;

[0083] Specifically, based on n k measurement values obtained at time step k, and adding them to the measurement equation for iterative updating, first, represents the updated parameter estimation obtained by adding i-1 measurement values at time k to the updated state parameters at time k-1; represents the updated state parameter covariance matrix obtained by adding i-1 measurement values at time k to the updated state parameter covariance matrix at time k-1; then adding the measurement value at time k to the updated state parameter estimation and the corresponding covariance matrix before the update, to obtain updated estimation value and According to the above expression, the prediction estimation at time k is recorded as The measurement values of a single scan are combined in any order, and different ordering may result in slightly different results.

[0084] S22, combining the measurement values, updating the motion state parameters and the shape parameters of the tracked target by the measurement equation of the unscented Kalman filter to obtain updated estimation value;

[0085] S221, obtaining measurement values at different times and constructing a second estimator by Kronecker product operation processing;

[0086] Specifically, for an axis-aligned ellipse, the best linear estimator is not feasible for a multiplicative noise model, that is, in the Kalman filter framework, using a single measurement to update the shape parameters, the shape parameters will not change, therefore, a second estimator is constructed by obtaining the measurement value and the Kronecker product to form a pseudo measurement value, which is specifically as follows:

[0087]

[0088] S222, constructing a pseudo measurement equation according to the second estimator;

[0089] ​Specifically, in order to avoid numerical problems caused by squaring, the estimated target center point Moving to the origin, and all transitions do not change the original likelihood function, therefore, the constructed pseudo-measurement is:

[0090]

[0091] Further reconstruct the pseudo-measurement equation, as shown below:

[0092]

[0093] In the above formula, Indicates the target center position before moving.

[0094] S223, the motion state parameter and shape parameter of the tracking target are parameter expanded and discretized to obtain Sigma points;

[0095] Specifically, in order to realize more compact covariance update and improve the tracking accuracy of the target, the state parameter is expanded, and the multiplicative noise h and the measurement noise v k When the parameter is processed, therefore, the state variable parameter of the elliptical model is:

[0096]

[0097] The corresponding covariance matrix is specifically represented as follows:

[0098]

[0099] Obtain Sigma points, and the Sigma is shown as follows:

[0100]

[0101] In the above formula, c represents the weight coefficient;

[0102] Where c=n+λ, parameter λ=α 2 (n+k)-n is a scaling parameter to reduce the total prediction error, the selection of α controls the distribution state of the sampling points, generally α=1, k is a parameter to be selected, and generally there is no limit to the specific value, but generally it should be ensured that the matrix Is a semi-definite matrix;

[0103] S224, substitute the Sigma points into the pseudo-measurement equation to obtain the observation prediction value of the Sigma points;

[0104] S225, based on the observation prediction value of the Sigma points, the mean and covariance values of the motion state parameter and the shape parameter are obtained by weighted calculation and summation processing;

[0105] Specifically, the obtained Sigma points are substituted into the pseudo measurement equation to obtain the observation prediction value of the Sigma point set, and the mean value and covariance of the predicted observation value are obtained by weighted summation. The specific substitution process is as shown below:

[0106]

[0107] The mean value is further shown as follows:

[0108]

[0109] In the above formula, w m represents the weight coefficient of the mean value, represents the mean value of the system prediction;

[0110] The covariance is further shown as follows:

[0111]

[0112]

[0113] In the above formula, w c represents the weight coefficient of the covariance, represents the covariance of the state variable and the pseudo measurement, represents the covariance of the pseudo measurement;

[0114] The to-be-selected parameter β≥0 is a non-negative weight coefficient, which can combine the variance of the high-order term in the equation, so that the influence of the high-order term can be included. Generally, β=2, and the specific process is as shown below:

[0115]

[0116] S226, calculate the Kalman filter gain based on the related covariance value of the observation prediction value, to obtain a Kalman filter gain value; specifically, the Kalman filter gain value is as shown below:

[0117]

[0118] In the above formula, K (i) represents the Kalman filter gain value.

[0119] S227, update the motion state parameter and the shape parameter of the system model based on the Kalman filter gain value, to obtain an updated estimation value.

[0120] Specifically, the update formula of the state variable and the covariance matrix of the ellipse model is as shown below:

[0121]

[0122] For the above 11-dimensional state variables and covariance, take the first 7 dimensions, and add the original movement to the center point, that is

[0123]

[0124] In summary, the state variable updated at time step k is expressed as The updated covariance is

[0125] S23, the state equation of the unscented Kalman filter is used to perform time update processing on the updated estimate, to obtain updated motion state parameters and shape parameters.

[0126] S231, based on the motion state parameters and shape parameters of the tracking target and the Sigma points obtained by combining the mean and covariance values of the updated estimate, UT transformation processing is performed on the Sigma points to obtain predicted Sigma points;

[0127] Specifically, since the time update of the motion state and the shape parameters both follow a linear model, the standard unscented Kalman filter time update formula can be used for time update to obtain 2n+1 Sigma points, as follows:

[0128]

[0129] UT transformation is performed on the obtained Sigma points, as follows:

[0130]

[0131] S232, based on the predicted Sigma points, the state equation of the unscented Kalman filter is used to perform update processing on the updated estimate, to obtain updated motion state parameters and shape parameters.

[0132] The initial state and covariance update formula at time step k+1 is as follows:

[0133]

[0134]

[0135] S3, target tracking is realized based on the system model.

[0136] Specifically, the target maneuverability is increased by changing the motion speed of the target, and the advantages of the algorithm are evaluated. Finally, under different noise, the tracking accuracy and error of the algorithm are evaluated, and the decoupled distance evaluation method is used to evaluate the position, direction, and long and short axis errors of the target. The specific calculation is as follows:

[0137] Position error:

[0138]

[0139] Direction error:

[0140]

[0141] Axis length error:

[0142]

[0143] Wherein, the position of the real ellipse is The direction is alpha, and the axis length is The position of the tracked ellipse is The direction is The axis length is

[0144] Referring to Figure 2 A target tracking system based on unscented Kalman filter, comprising:

[0145] A construction module, based on an ellipse model, parameterizes the motion state and shape of the tracked target, obtains the motion state parameters and shape parameters of the tracked target, and constructs a system model;

[0146] An update model for updating the motion state parameters and shape parameters of the tracked target through an unscented Kalman filter according to the system model, to obtain updated motion state parameters and shape parameters.

[0147] The simulation experiment of the application is as follows:

[0148] Simulation experiment one:

[0149] According to the derived closed-form measurement update unscented Kalman filter, in order to focus on measurement update, first consider tracking an extended target modeled as an ellipse on the ground. It is located at m k =[0 0], rotate 45 degrees counterclockwise from the x-axis, i.e. Length l k =[70 40], same as the previous model, multiplicative noise Its covariance is And On the interval [-1, 1], independently and uniformly distributed, the unscented Kalman filter, the new extended Kalman filter and the second-order extended Kalman filter are used to track under high and low Gaussian white noise, the measurement noise covariance R is diag([1 1]) under low noise, and the measurement noise covariance R is diag([100 100]) under high noise, and the Monte Carlo algorithm is run 100 times.

[0150] Referring toFigure 4 , the measurement value of the target tracking of the three Kalman filters under low noise and the real value;

[0151] Reference Figure 5 , the measurement value of the target tracking of the three Kalman filters under high noise and the real value;

[0152] Reference Figure 6 , the error comparison of the center position of the target tracking of the three Kalman filters under low noise;

[0153] Reference Figure 7 , the error comparison of the center position of the target tracking of the three Kalman filters under high noise;

[0154] Reference Figure 8 , the error comparison of the axis length of the target tracking of the three Kalman filters under low noise;

[0155] Reference Figure 9 , the error comparison of the axis length of the target tracking of the three Kalman filters under high noise;

[0156] Reference Figure 10 , the error comparison of the direction of the target tracking of the three Kalman filters under low noise;

[0157] Reference Figure 11 , the error comparison of the direction of the target tracking of the three Kalman filters under high noise;

[0158] The specific simulation data is shown in the following table:

[0159] The average tracking error of 100 times of MC

[0160]

[0161] The standard deviation of the tracking error of 100 times of MC

[0162]

[0163] The root mean square of the tracking error of 100 times of MC

[0164]

[0165] In summary, whether under low noise or high noise, the tracking error of the unscented Kalman filter is obviously better than that of the other two algorithms;

[0166] Simulation experiment two:

[0167] Based on simulation experiment one, the scenario considered is tracking an elliptical extended target with unknown extent, whose orientation changes over time, with fixed axis length, assuming low system noise in the semi-axis length and high system noise in the orientation. The axis length of the extended target is 140 meters and 70 meters, which starts from the coordinate origin with a speed of Moving, at each time step, the measurements are uniformly distributed over the elliptical extent, the number of measurements per scan follows a Poisson distribution with mean 5, for the three estimators, the process noise covariance of the state is diag[100, 100, 1, 1, 0.05, 0.001, 0.001], the state prior is [100, 100, 10, -17, -π / 3, 200, 90] T , the covariance prior of the state is diag[900, 900, 16, 16, 0.02, 400, 400], the covariance of the multiplicative noise is diag[0.25, 0.25], the measurement noise covariance is diag[200, 80], and its process matrix is According to the decoupling distance calculation error method, run 100 times of Monte Carlo;

[0168] Referring to Figure 12 , the measurement value and the true value of the three Kalman filters for tracking the fast moving target are compared;

[0169] Referring to Figure 13 , the error comparison of the center position of the three Kalman filters for tracking the fast moving target is compared;

[0170] Referring to Figure 14 , the error comparison of the axis length of the three Kalman filters for tracking the fast moving target is compared;

[0171] Referring to Figure 15 , the error comparison of the direction of the three Kalman filters for tracking the fast moving target is compared;

[0172] In summary, from the figures, it can be seen that the position tracking errors of the three estimators are not much different; for the tracking of the axis length, the tracking error of the unscented Kalman filter is smaller as the number of updates increases; for the tracking of the direction, the tracking error is larger when the direction changes suddenly, and the tracking accuracy of the total unscented Kalman filter is higher;

[0173] Similarly, the running simulation data is shown in the following table:

[0174] The mean tracking error of 100 times of MC

[0175] Algorithm Center position / m Axis length / m Direction / rad EKF 139.0674 21.6430 0.1170 SOEKF 138.8565 10.0983 0.1142 EKF* 138.9365 10.2469 0.1127 UKF 138.8217 11.0598 0.0685

[0176] The standard deviation of the tracking error of 100 times of MC

[0177] Algorithm Center position / m Axis length / m Direction / rad EKF 10.3633 14.0503 0.0369 SOEKF 11.0641 12.9418 0.0362 EKF* 10.9658 13.2024 0.0354 UKF 10.0505 9.4162 0.0437

[0178] Root mean square of tracking error for 100 runs of MC

[0179] Algorithm Center position / m Axis length / m Direction / rad EKF 139.4501 25.7749 0.1226 SOEKF 139.2933 16.3770 0.1198 EKF* 139.3653 16.6731 0.1181 UKF 139.1823 14.5023 0.0812

[0180] In summary, it can be seen that for the target with fast motion change, the adaptability of the unscented Kalman filter is stronger, and the tracking accuracy is higher.

[0181] The contents in the method embodiments are applicable to the system embodiments, the system embodiments specifically implement the same functions as the method embodiments, and achieve the same beneficial effects as the method embodiments.

[0182] The above is a specific description of the preferred implementation of the application, but the application is not limited to the embodiments described, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the application. These equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A target tracking method based on unscented Kalman filtering, characterized by, The method comprises the following steps: S1, based on the elliptical model, the motion state and shape of the tracking target are parameterized to obtain the motion state parameters and shape parameters of the tracking target and construct a system model; specifically comprising: S11, based on the elliptical model, the motion state and shape of the tracking target are parameterized to obtain the motion state parameters and shape parameters of the tracking target, and the motion state of the tracking target includes the center position of the tracking target and the speed of the tracking target; The parameterization is specifically as follows: In the above formula, m k represents the center position of the ellipse model, r k represents the velocity of the ellipse model, p k represents the shape parameter of the ellipse model, x k represents the state variable of the ellipse model, and k represents the time step. Wherein, the shape parameters of the elliptical model specifically further include the following parameters: In the above formula, α k represents the direction of the time step at k, and α k ∈ [0, 2π], l k,1 represents the length of the semi-major axis of the ellipse, l k,2 represents the length of the semi-minor axis of the ellipse; S12, a system model is constructed by introducing multiplicative noise and combining the motion state parameters and shape parameters of the tracking target; specifically: S121, in the process of constructing the elliptical model, the tracking target will generate different numbers of independent Cartesian measurements; the Cartesian measurements are specifically as follows: In the above equation, represents the i-th measurement obtained by the sensor at time step k, y k represents the set of all measurements obtained by the sensor at time step k, n k represents the number of measurements obtained by the sensor at time step k; Each individual measurement Originating from a measurement source Wherein the measurement source Is subject to additive Gaussian measurement noise with covariance R Is corrupted, each measurement source Depends on the range of the tracked target and follows a uniform spatial distribution; S122, according to Gaussian distribution, introduce multiplicative noise, combined with the motion state parameters and shape parameters of the tracking target, construct the measurement equation and state equation; Gaussian spatial distribution is used to approximate uniform spatial distribution, and the key step of the method is to construct the formula of the measurement equation, which processes the relationship between the measurement source and the target state through a multiplicative noise h, and then models it as an axial ellipse with its semi-axis length as l1 and l2, and any multiple measurement sources z (i) can be written as shown below: In the above formula, l1 represents a semi-major axis of the ellipse, l2 represents a semi-minor axis of the ellipse, h (i) represents multiplicative noise; In the constructed elliptical model, the time step index k and the measurement index i are omitted, and the position of the target is m = [m1, m2] T , and the shape parameter of the target is p k = [a k , l k,1 , l k,2 ] T , where the measurement y is the measurement source z corrupted by the measurement noise v, the measurement source z is associated with p through multiplicative noise h = [h1, h2] T , and further, the coordinate system of the elliptical model is rotated by an angle a, in order to describe the measurement source distributed on the ellipse, it is assumed that the random variable h (i) is zero mean and is distributed on a unit circle, and the measurement source equation is constructed by rotating and translating z (i) . In the above formula, m represents the center position of the elliptical model, and S represents the motion direction and axis length of the elliptical model; The time tag and sensor noise are added to the measurement source equation to obtain the measurement equation, which is specifically as follows: In the above equation, denotes the measurement value, S j denotes the motion direction and the axis length of the ellipse model, denotes the multiplicative noise, in particular C h denotes the covariance of the multiplicative noise, and denotes the measurement noise, in particular and R denotes the covariance of the measurement noise; The state equation of the system model is specifically represented as follows: x k+1 = A k x k + w k In the above equation, A k represents a process matrix, w k represents a zero-mean Gaussian process noise with covariance Q; S2, according to the system model, the motion state parameters and shape parameters of the tracking target are updated by the unscented Kalman filter to obtain updated motion state parameters and shape parameters; specifically comprising: S21, the measurement value of the tracking target is obtained through the sensor; based on n obtained at time step k k Each measurement value is then incorporated into the measurement equation for iterative updating. Firstly, This represents the parameter estimate obtained after adding i-1 measurements from time k to the state parameters updated at time k-1; This means that the state parameter covariance matrix updated at time k-1 is obtained by adding the i-1 measurements at time k; then the measurements at time k are... Add previously updated state parameter estimation and the corresponding covariance matrix In order to obtain updated estimates and Based on the above expression, the prediction estimate for time k is correspondingly denoted as: The measurements from a single scan are merged in an arbitrary order, and slightly different results may be obtained for different sorting methods. S22, the measurement value is combined to update the motion state parameters and shape parameters of the tracking target through the measurement equation of the unscented Kalman filter to obtain the updated estimated value; S221, the measurement values at different times are obtained and processed by Kronecker product operation to construct a second estimator; The second estimator is constructed by obtaining the measurement value and the Kronecker product to form a pseudo measurement value, which is specifically as follows: S222, a pseudo measurement equation is constructed according to the second estimator; The estimated target center point is moved to the origin, and all the transitions do not change the original likelihood function, thus the constructed pseudo-measure is: The pseudo measurement equation is constructed again, which is specifically as follows: In the above formula, represents the target center position before moving; S223, the motion state parameters and shape parameters of the tracking target are parameterized and discretized to obtain Sigma points; The multiplicative noise h and the measurement noise v k When the parameters are considered, the state variable parameters of the elliptic model are: The corresponding covariance matrix is specifically represented as follows: The Sigma points are obtained, and the Sigma is as follows: In the above formula, c represents the weight coefficient; where c = n + λ, parameter λ = α 2 (n+k)-n is a scaling parameter to reduce the total prediction error, the selection of α controls the distribution of sampling points, generally α = 1, k is a parameter to be selected, and generally there is no limit to the specific value of k, but generally the matrix should be a semi-positive definite matrix; S224, the Sigma points are substituted into the pseudo measurement equation to obtain the observation prediction value of the Sigma points; S225, based on the observation prediction value of the Sigma points, the mean and covariance of the motion state parameters and shape parameters are obtained by weighted calculation and summation processing; The obtained Sigma points are substituted into the pseudo measurement equation to obtain the observation prediction value of the Sigma point set, and the mean and covariance of the predicted observation value are obtained by weighted summation, and the substitution process is as follows: The mean is as follows: In the above formula, w m a weight coefficient representing the mean value, a mean value predicted by the system; The covariance is as follows: In the above formula, w c a weight coefficient representing a covariance, a covariance of the state variable and the pseudo measurement, a covariance of the pseudo measurement; The to-be-selected parameter β≥0 is a non-negative weight coefficient, which is specifically as follows: S226, the Kalman filter gain is calculated based on the related covariance value of the observation prediction value to obtain the Kalman filter gain value; the Kalman filter gain value is specifically as follows: In the above formula, K (i) denotes the Kalman filter gain value; S227, update the motion state parameter and the shape parameter of the system model based on the Kalman filter gain value, to obtain an updated estimation value; The update formula of the state variable and the covariance matrix of the ellipse model is specifically as follows: For the 11-dimensional state variable and covariance, the first 7 dimensions are taken, and the center point is added to the original movement amount, that is, In summary, the state variable updated at time step k is The updated covariance is S23, perform time update processing on the updated estimation value through the state equation of the unscented Kalman filter, to obtain the updated motion state parameter and shape parameter; S231, based on the Sigma points obtained by combining the mean and covariance values of the updated estimation value and the motion state parameter and the shape parameter of the tracked target, perform UT transformation processing on the Sigma points, to obtain predicted Sigma points; Since the time update of the motion state and the shape parameter both follow a linear model, the standard unscented Kalman filter time update formula is used for time update, to obtain 2n+1 Sigma points, as follows: UT transformation is performed on the obtained Sigma points, as follows: S232, based on the predicted Sigma points, perform update processing on the updated estimation value through the state equation of the unscented Kalman filter, to obtain the updated motion state parameter and shape parameter; The initial state and covariance update formula of the time step k+1 is as follows: S3, realize target tracking based on the system model; By changing the motion speed of the target to increase the maneuverability of the target, and evaluating the advantages of the algorithm, finally under different noises, the tracking accuracy and error of the algorithm are evaluated, the decoupling distance evaluation method is used to evaluate the position error, direction error and axis length error of the target, which is calculated through the following formulas; Position error: Direction error: Axis length error: where the position of the true ellipse is the direction is a, and the axis length is the position of the tracked ellipse is the direction is the axis length is 2. A target tracking system based on unscented Kalman filtering, characterized by, The following modules are included: A construction module, based on the ellipse model, parameterizes the motion state and shape of the tracked target, to obtain the motion state parameter and shape parameter of the tracked target and construct a system model; wherein the motion state parameters comprise a center position m of the elliptic model k and a velocity r k , the shape parameters comprise an orientation angle a of the ellipse k , a semi-major axis l k,1 , and a semi-minor axis l k,2 , and the state variable is represented as the system model comprises the measurement equation and the state equation of claim 1; An update module, configured to update the motion state parameter and shape parameter of the tracked target through the unscented Kalman filter based on the system model, to obtain the updated motion state parameter and shape parameter; the update processing includes the measurement update and time update steps of claim 1.

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