A high-speed maneuvering target tracking method based on a random process of continuous space-time trajectory function

Abstract

The present invention relates to a high-speed maneuvering target tracking method based on a continuous space-time trajectory function random process, and relates to the field of target tracking. The method comprises: modeling the continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model as a random process based on a continuous-time trajectory function; modeling the mean function of the target trajectory random process as a continuous space-time trajectory function; and fitting and estimating the continuous space-time trajectory function to output the target state. The method of the present invention can achieve higher-precision real-time target tracking in complex maneuvering scenarios, overcoming the shortcomings of existing random process target tracking methods, which often add a constant mean function and rely solely on covariance kernel function representation for trajectory estimation.

Description

Technical Field

[0001] The present invention relates to the field of target tracking, and in particular to a high-speed maneuvering target tracking method based on a continuous space-time track function random process, which is applicable to a series of high-speed moving targets such as unmanned aerial vehicles (UAVs). Background Art

[0002] In recent years, with the continuous development of modern computer and communication technologies, high-precision data acquisition and real-time information transmission have become increasingly convenient. Target tracking technology has become indispensable for its application and has clear technical requirements. Researchers from all walks of life, both domestically and internationally, have conducted extensive and in-depth research on this topic, and numerous tracking theories and methods have been proposed. However, existing mainstream target tracking methods model dynamic state systems as hidden Markov models. In the case of target maneuvers, the system must identify changes in the dynamic system model in real time; otherwise, the filter / tracker will diverge or even fail completely. In actual tracking tasks, high-value threats often exploit this circumstance by maneuvering at high speeds and frequently, making it difficult for early warning and surveillance systems to form effective and accurate track estimates, greatly exacerbating the difficulty of positioning and tracking. Classic filter model-driven tracking methods can rapidly deteriorate due to inaccurate prior knowledge and complex real-world system models. Therefore, model-driven filter tracking algorithms face increasing challenges in meeting practical applications and requirements, while data-driven methods, characterized by learning, are gradually demonstrating increasing advantages.

[0003] The paper "A Gaussian Process Regression Approach for Point Target Tracking" proposes a data-driven Gaussian Process Motion Tracker (GPMT), demonstrating its effectiveness in target tracking. This method models the target state as a function of time based on a Gaussian process (GP) prior. The parameters of this Gaussian process are iteratively updated and learned using time-series measurement data, enabling real-time estimation and prediction of the target state. However, this work and its subsequent developments are all based on solutions using a zero-mean Gaussian process function, learning the unknown target dynamic model solely through a covariance kernel function. Although this is interpreted as "lacking prior information about the average behavior of the modeled function" (obviously, this does not mean that the mean function is constant or zero, but rather that its form should be determined by learning from data), this method lacks the ability to characterize time-varying data trends, as required by mean function learning. Furthermore, the parameters of the covariance kernel function used are often time-invariant, effectively assuming that the target motion trajectory is a stationary process, which is inconsistent with most practical target tracking scenarios. In actual target tracking scenarios, the target track has a non-zero mean, and its fluctuations are often non-stationary, corresponding to a non-stationary random process. Moreover, if the mean function is fixed as a constant, the covariance learning and characterization capabilities are limited. When the target undergoes high-speed and large maneuvers, and the track shows a trend of large changes in the mean, the adjustment of the covariance is difficult to fully characterize the randomness of the track, resulting in large tracking errors or even loss of tracking. In response to the above-mentioned Gaussian process modeling problem of high-speed maneuvering targets, how to model the mean function of the Gaussian process and reasonably integrate possible additional system constraint information to give full play to the Gaussian process's ability to characterize dynamic systems is the main starting point of the present invention. Summary of the Invention

[0004] The technical problems to be solved by the present invention are:

[0005] In response to the problems that existing classical methods heavily rely on precise prior knowledge of target motion and that Gaussian process tracking methods are insufficient in characterizing the time-varying trends of data, the present invention proposes a data-driven maneuvering target tracking method based on a random process of continuous space-time trajectory functions to solve the problem of maneuvering target tracking in complex maneuvering scenarios.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A high-speed maneuvering target tracking method based on a continuous space-time track function random process is characterized by comprising:

[0008] The continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model is modeled as a random process based on a continuous-time trajectory function.

[0009] The mean function of the target track random process is modeled as a continuous space-time track function;

[0010] Fit and estimate the continuous space-time trajectory function and output the target state.

[0011] A further technical solution of the present invention is to model the continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model as a random process based on a continuous-time trajectory function, specifically:

[0012] Based on the continuous time trajectory function T-FoT, the continuous space-time trajectory f(t) of a high-speed maneuvering target with an unknown motion model is modeled as a random process specified by the parameter Θ Then any target track is a sample of the random process, that is, the continuous time-space domain track function f(t) satisfies:

[0013]

[0014] Where, represents time, x t represents the target state at time t, and m(t) is the mean function of the random process;

[0015] The target trajectory random process is modeled by GP as:

[0016]

[0017] in, represents the GP random process, k(t, t′) represents the covariance kernel function with parameters.

[0018] A further technical solution of the present invention is that the continuous space-time trajectory adopts a two-dimensional trajectory generation method based on a state space model to construct two motion model trajectory libraries of uniform linear motion CV and uniform circular motion CT and combine them to simulate the trajectory of a real maneuvering target.

[0019] A further technical solution of the present invention is to model the mean function of the target track random process as a continuous space-time track function, specifically:

[0020] The target track mean function m(t) is parameterized as F(t;C), which is determined by the parameter C:

[0021] F(t;C)=m(t)

[0022] By estimating the parameter C in real time, the target track mean function m(t) can be obtained; assuming that the parameter of the track mean function estimated at time k is C k ,but

[0023] F(t;C k )=c0+c1t+…+c γ t γ

[0024] Among them, C k ={c i} i＝0，1，…，γ represents the polynomial track coefficient, γ represents the polynomial order, c0 corresponds to the initial position of the target, c1 corresponds to the velocity, and c2 corresponds to the acceleration.

[0025] A further technical solution of the present invention is to optimize and estimate the continuous space-time trajectory function and output the target state, specifically:

[0026] Estimate the target mean function parameters and states

[0027] Establishing sensor measurement model:

[0028] z t =h t (f(t))+v t Where z t represents the measurement value of the target at time t, which is used to calculate and update the system state value; h(·) represents the measurement function; v t represents the observation noise at time t, which is assumed to be Gaussian noise;

[0029] Select the polynomial order to fit the target mean function of the corresponding time window, and estimate the coefficient parameter C based on the least squares fitting residual k :

[0030]

[0031] In the formula, ||ab|| represents a certain distance between a and b, z t Represents the observation data at time t, when t=k, z k =h(x k , v k ), h(x k , v k ) represents the measurement function, v k Represents the observation error; obtain the target mean function state estimate at the corresponding sampling moment by determining the mean function order and coefficient;

[0032] Use GP to compensate for the residual function of the mean function fitting and obtain the target state estimate at the current moment:

[0033]

[0034] in, It is the state estimate of the fitted residual function e(t) at the current moment.

[0035] A further technical solution of the present invention is to use the root mean square error (RMSE) as a comparison indicator and define the target position RMSE at time t as:

[0036]

[0037] Where x t and y t is the true state of the target, and is the state estimate of the output.

[0038] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0039] A computer-readable storage medium is characterized by storing computer-executable instructions, which are used to implement the above method when executed.

[0040] A computer program product, characterized by comprising computer executable instructions, wherein the instructions are used to implement the above method when executed.

[0041] The beneficial effects of the present invention are:

[0042] The present invention provides a high-speed maneuvering target tracking method based on a continuous space-time track function random process. Focusing on the difficulties faced by high-speed maneuvering targets such as high speed and large maneuvers, the method analyzes their dynamic motion mechanism and the space-time variation law of the track. Based on the long-range time series angle rather than the single point state at each moment, a continuous space-time function track random process model is constructed. That is, the mean function of the target track random process is modeled as a continuous space-time track function, which is learned and acquired through time series measurement data, and the adaptive hierarchical Gaussian process is used to further obtain an accurate estimate of the maneuvering target state.

[0043] The method of the present invention can achieve higher-precision real-time tracking of targets in complex maneuvering scenarios, breaking through the shortcomings of existing random process target tracking methods that often add a constant mean function and rely solely on the covariance kernel function representation for track estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0045] Figure 1 It is a flow chart of the method of the present invention.

[0046] Figure 2 This is the target simulation scenario of the method of the present invention.

[0047] Figure 3 This is the target tracking simulation result of the method of the present invention.

[0048] Figure 4 This is the simulation accuracy result of the method of the present invention. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0050] The present invention provides a high-speed maneuvering target tracking method based on a continuous space-time track function random process. The target track mean function is constructed using a polynomial T-FoT. The fitting residual function of the mean function is compensated by GP to obtain an accurate state estimation of the maneuvering target at the current moment using pure measurement information.

[0051] like Figure 1 As shown, the present invention includes the following steps:

[0052] Step 1: Establish the target continuous space-time trajectory function.

[0053] Based on the continuous time trajectory function (T-FoT), the continuous spatiotemporal trajectory f(t) of a high-speed maneuvering target with an unknown motion model is modeled as a random process specified by the parameter Θ. Then any target track is a sample of the random process, that is, the continuous time-space domain track function f(t) satisfies:

[0054]

[0055] Where, represents time, x t represents the target state at time t, and m(t) is the mean function of the random process.

[0056] The target trajectory random process is modeled by GP as:

[0057]

[0058] in, represents a GP random process, k(t, t′) represents a process with parameters (variance ∑m and length scale ζ).

[0059] Step 2: Establish the objective function random process mean function.

[0060] A trajectory model (i.e., polynomial T-FoT) that can approximate any continuous trajectory curve in time and space with arbitrary accuracy is used to parameterize the target trajectory mean function m(t) into F(t; C), which is determined by the parameter C.

[0061] F(t;C)=m(t) (3)

[0062] By estimating the parameter C in real time, the target track mean function m(t) can be obtained. Assume that the parameter of the track mean function estimated at time k is C k ,

[0063]

[0064] Among them, C k ={c i} i＝0，1，…，γ represents the polynomial track coefficient, γ represents the polynomial order, c0 corresponds to the initial position of the target, c1 corresponds to the velocity, and c2 corresponds to the acceleration.

[0065] Step 3: Continuous space-time trajectory function parameter estimation and target state estimation.

[0066] In order to avoid the track function being too complicated due to a large time span, the estimation of track parameters is generally based on a time window of appropriate length, which is denoted as follows: k =[kd, k-d+1, ..., k-1] T , where d is the sliding window length. For formula (2), it is necessary to jointly identify the hyperparameters online in and ζ k is the sliding window t corresponding to time k k The GP covariance kernel parameters in are given in detail in Equation (8). However, due to the difficulty of solving non-convex problems and the tendency to fall into local minima, the above GP online fitting is transformed into hierarchical GP modeling of the residual function e(t) fitted by the mean function, and the joint learning of hyperparameters is decomposed into two stages to seek a suboptimal solution:

[0067]

[0068] Where O represents a zero vector / matrix of appropriate dimension.

[0069] Step 3-1: Target mean function parameter estimation and state estimation.

[0070] The sensor measurement model is modeled as:

[0071] z t =h t (f(t))+v t (6)

[0072] Where z t represents the measurement value of the target at time t, which is used to calculate and update the system state value; h(·) represents the measurement function; v t represents the observation noise at time t, which is assumed to be Gaussian noise.

[0073] Select the appropriate polynomial order to fit the target mean function of the corresponding time window, and estimate the coefficient parameter C based on the least squares fitting residual k :

[0074]

[0075] In the formula, ||ab|| represents a certain distance between a and b (when it is agreed to be the 2 norm or Mahalanobis distance, that is, least squares (LS) or weighted least squares), z t Represents the observation data at time t, when t=k, z k =h(x k , v k ), h(x k , v k ) represents the measurement function, v k Represents the observation error. The target mean function state estimate at the corresponding sampling moment is obtained by determining the mean function order and coefficient.

[0076] Step 3-2: Use GP to compensate for the residual function of the mean function fitting, obtain the target state estimate at the current moment, and obtain the fitting uncertainty, thereby obtaining the GP closed-form solution of the target track function random process.

[0077] The present invention uses the squared exponential kernel (SE) for GP analysis, and the calculation formula is as follows:

[0078]

[0079] In the formula, the hyperparameter ∑ m and ζ denote the variance and length scale of the covariance kernel, respectively.

[0080] On the one hand, hyperparameter optimization models are often non-convex and prone to falling into local minima. On the other hand, in the absence of prior information, unknown parameters, and even time-varying synchronous parameter identification, are extremely difficult. Therefore, this paper assumes unknown hyperparameters and conducts online learning within a state-space framework to reduce latency and improve identification accuracy.

[0081]

[0082] y k =A k x k-1 +v k (10)

[0083]

[0084] Among them, x k-1 represents the state vector; y k is an enhancement vector consisting of the state vector and the function prediction at the measurement position; θ k =[η k ,∑] T represents the hyperparameter vector, ∑ represents the observation noise v t The covariance of k Represents the hyperparameter vector of the GP modeling covariance function; e k and They represent the sliding windows corresponding to the k moment [kd, k-d+1,…, k+1] T And the function evaluation value at the current moment; A k is the state update matrix, is the mean gain matrix, K tt′ is the covariance matrix between the data at time t and t′, which is calculated by k(t, t′); v k is an additive Gaussian noise vector with independent and identically distributed (iid) elements, with the following parameters:

[0085]

[0086] in, Represents the mean state estimate of the modeling residual function e(t) at time k, Represents the joint GP mean estimation of the modeling residual function e(t) within the sliding window corresponding to time k; represents the covariance gain.

[0087] Model the mean state of GP at time t=k As the mean function fitting error compensation, the target track function at time t = k is expressed as follows:

[0088]

[0089] in, represents the gain matrix; and They represent the predicted covariance and mean of e(t) at time k, It represents the joint GP estimated covariance of the modeling residual function e(t) in the sliding window corresponding to the k-1 moment; and denote prediction and estimate, respectively.

[0090] The estimated covariance of the GP model at time k is taken as the covariance of the fitting error of the time series trajectory random process, which is expressed as follows:

[0091]

[0092] In order to enable those skilled in the art to better understand the present invention, the present invention is described in detail below with reference to specific embodiments.

[0093] 1. Set up the simulation scene.

[0094] The simulation scenario uses a two-dimensional trajectory generation method based on the state space model to construct two motion model trajectory libraries of constant velocity (CV) and constant circular motion (CT) and combine them to simulate the trajectory of a real maneuvering target. The state of the target at time step k is included in the two-dimensional Cartesian coordinate system x k and y k The position in the coordinate system, and the speed towards these coordinate axes and Therefore, the state vector can be expressed as:

[0095]

[0096] Among them, the dynamic model of CV is:

[0097]

[0098] Among them, q k-1 is a Gaussian process noise with zero mean

[0099]

[0100] Wherein, q is the spectral density of the noise, which is set to q = 0.1 in the simulation.

[0101] In the dynamic modeling of CT, the turning rate parameter ω is used to enhance the state vector, so the joint system vector is expressed as:

[0102]

[0103] in, is the univariate Gaussian white process noise of the turning rate parameter, set ∑ ω =0.1.

[0104] The observation equations of CV and CT are:

[0105]

[0106] in, To observe the noise, set ∑ = 0.1.

[0107] The system is simulated for 200 time steps with a step size of Δt = 0.1. The target's motion process is as follows:

[0108] Target speed Start from the origin.

[0109] After 4 seconds, the target begins to turn left at a rate of ω = 1.

[0110] After 9 seconds, the target stops turning and moves straight ahead at a constant speed for 2 seconds.

[0111] After 11 seconds, the target begins to turn right at a rate of ω = -1.

[0112] After 16 seconds, the target stops rotating and moves straight ahead at the same speed for 4 seconds.

[0113] The sensor generating the position measurement value is located at (s x , s y )=(-0.5, 3.5). The specific target trajectory and the measurement data obtained by the sensor are as follows Figure 2 shown.

[0114] 2. Fit the target mean function based on the polynomial T-FoT method.

[0115] The sliding window size d=5 is set, and the polynomial T-FoT method (fitting order is second order) is applied to estimate the target mean function parameters, and the estimated value of the mean function at the current moment is obtained.

[0116] 3. Use GP to compensate for the fitting residual function of the mean function, obtain the target state estimate at the current moment, and obtain the fitting uncertainty.

[0117] 3-1: GP modeling initialization.

[0118] Use the measurement data in the initial sliding window to initialize the GP model. Use the first d measurement samples to establish the initial sliding window, and use GP regression to fit the target track function in the initial sliding window, that is, to obtain the mean and covariance of the joint Gaussian to which the target track belongs in the first sliding window, which is in the form of:

[0119]

[0120] Where p(·) is the probability density function; Indicates that the mean is μ and the covariance is Gaussian distribution; and They represent the GP mean and covariance of the measurement data set within the initial sliding window, respectively. The specific expressions are as follows:

[0121]

[0122] Determine the initial distribution of the hyperparameter vector, which is of the form:

[0123]

[0124] in, and denote the GP mean and covariance of the initial hyperparameter vector respectively.

[0125] 3-2: Target state estimation.

[0126] First, according to formula (5), the GP modeling mean estimate and covariance estimate of the mean function fitting residual function e(t) at time t = k are obtained. The GP mean estimate is used as the state estimate of the fitting residual function e(t) at the current moment. Then, the target state estimation at the current moment is obtained according to formula (13).

[0127]

[0128] 3-3: Calculate tracking uncertainty and measure tracking accuracy.

[0129] The GP covariance estimate is used as the covariance estimate of the fitted residual function e(t) at the current moment. Since the covariance term is not included in the mean function fitting process, the target tracking uncertainty can be obtained according to Equation (14), thereby obtaining the GP closed-form solution of the target track function random process.

[0130] 4. Comparison of performance indicators.

[0131] To demonstrate the superiority of the proposed method, existing target tracking methods were selected for comparison, including polynomial time trajectory function fitting (fitting order is second order) and target tracking methods based on zero-mean Gaussian process modeling (GPMT). The root mean square error (RMSE) of the target position at time t was defined as:

[0132]

[0133] Where x t and y t is the true state of the target, and is the state estimate of the output.

[0134] Table 1 Average performance of different tracking methods

[0135]

[0136] like Figure 4 As shown in the simulation of the position error between this method and other methods for tracking maneuvering targets, it is clear that this method achieves significantly better results when tracking large maneuvering targets with high turning rates, and the error is significantly smaller than that of other methods at locations where the target undergoes large maneuvers. In particular, after considering the mean function, compared with the existing zero-mean GP-based GPMT method, not only does it achieve higher tracking accuracy, but it also significantly improves tracking stability. The experimental results demonstrate the effectiveness of this method in tracking maneuvering targets.

[0137] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A high-speed maneuvering target tracking method based on a continuous space-time track function random process, characterized in that: include: The continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model is modeled as a random process based on a continuous-time trajectory function. The mean function of the target track random process is modeled as a continuous space-time track function; Fit and estimate the continuous space-time trajectory function and output the target state; The continuous time trajectory function is used to model the continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model as a random process, specifically: Based on the continuous time trajectory function T-FoT, the continuous space-time trajectory of a high-speed maneuvering target with an unknown motion model is converted into a continuous space-time trajectory. Modeled as a parameter Specified random process ; Then any target track is a sample of the random process, that is, the continuous time-space domain track function satisfy: Where, Indicates time, express The target state at all times, is the mean function of the random process; The target trajectory random process is modeled by GP as: in, represents the GP random process, represents the covariance kernel function with parameters; The mean function of the target track random process is modeled as a continuous space-time track function, specifically: The target track mean function Parameterized as , by the parameter Sure: By estimating parameters in real time , the target track mean function can be obtained ; Assumption The parameters of the track mean function estimated at the moment are ,but in, represents the polynomial track coefficients, represents the polynomial order, Corresponding to the initial position of the target, Corresponding speed, Corresponding acceleration; The continuous space-time trajectory function is optimized and estimated to output the target state, specifically: Estimate the target mean function parameters and states Establishing sensor measurement model: Where, Indicates the target is The measured value at each moment is used to calculate and update the system status value; represents the measurement function; Indicates The observation noise at time t is assumed to be Gaussian noise; Select the polynomial order to fit the target mean function of the corresponding time window, and estimate the coefficient parameters based on the least squares fitting residual : Where, express A certain distance between express Observe data at all times, when hour , represents the measurement function, Represents the observation error; obtain the target mean function state estimate at the corresponding sampling moment by determining the mean function order and coefficient; GP is used to compensate for the residual function of the mean function fitting to obtain the target state estimate at the current moment, including: Use the measurement data in the initial sliding window to initialize the GP model, and use the first The initial sliding window is established with measurement samples, and the target track function in the initial sliding window is fitted using GP regression, that is, the mean and covariance of the joint Gaussian to which the target track in the first sliding window belongs are obtained, which is in the form of: in, is the probability density function; Indicates the mean , the covariance is Gaussian distribution; and They represent the GP mean and covariance of the measurement data set within the initial sliding window, respectively. The specific expressions are as follows: Determine the initial distribution of the hyperparameter vector, which is of the form: in, and denote the GP mean and covariance of the initial hyperparameter vector respectively; Use the GP mean estimate as the current moment fitting residual function State estimation , and obtain the target state estimate at the current moment: GP covariance estimation as the current moment fitting residual function The covariance estimation of is used to obtain the GP closed-form solution of the target track function random process.

2. The high-speed maneuvering target tracking method based on a continuous space-time track function random process according to claim 1, characterized in that: The continuous space-time trajectory adopts a two-dimensional trajectory generation method based on a state space model to construct two motion model trajectory libraries of uniform linear motion CV and uniform circular motion CT and combine them to simulate the real maneuvering target trajectory.

3. A performance comparison method for the high-speed maneuvering target tracking method based on a continuous space-time track function random process according to claim 1, characterized in that: Taking the root mean square error RMSE as the comparison indicator, define The RMSE of the target position at each moment is: Where, and is the true state of the target, and is the state estimate of the output.

4. A computer system, characterized in that include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 or 3.

5. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method according to any one of claims 1 or 3.

6. A computer program product, characterized in that The method comprises computer executable instructions, which are used to implement the method according to any one of claims 1 or 3 when being executed.

Images