Target tracking method for robust continuous discrete TPHD filtering under disordered measurement

Abstract

The invention discloses a target tracking method for performing out-of-order measurement (OOSM) updating by using a continuous discrete model, and aims to solve the problems that communication delay exists in a sensor tracking scene, the target detection probability is unknown, the clutter rate is unknown, and the filtering precision is reduced due to the fact that a traditional target tracking technology cannot perform accurate tracking. According to the method, on the basis of beta-Gaussian mixed trajectory probability hypothesis density (TPHD) filtering, trajectory information is added to disordered measurement time steps, backtracking under continuous time is executed, discretization updating is carried out on a trajectory through obtained disordered measurement, finally, the trajectory information of the disordered measurement time steps is marginalized, and the trajectory information of the disordered measurement time steps is obtained. Only track information on sequential sampling time is reserved, and the detection probability, the clutter rate and the multi-track posterior probability density are estimated in a self-adaptive mode at the same time. According to the method, on the basis of trajectory probability hypothesis density filtering, the problems of disordered measurement updating and unknown detection background parameters are mainly solved while each target trajectory is distinguished.

Description

Technical Field

[0001] The present invention belongs to the fields of Bayesian filtering technology and radar data processing technology, and specifically relates to a target tracking method using a continuous discrete model for disordered measurement updates, which can be applied to radar systems such as air warning, road monitoring and ocean detection. Background Art

[0002] Multi-target tracking technology is gaining more and more attention. However, in real-world environments, multi-target tracking systems are subject to many uncertainties, leading to the following difficulties: (1) Due to different time delays in transmission, measurement scans may be received out of order, i.e., out-of-order measurement (OOSM); (2) Due to differences in tracking environments and sensors, the target detection profiles and clutter counts in the detection scene are unknown; (3) When the time interval between measurement scans is not fixed, directly using traditional tracking algorithms will lead to a decrease in the tracking accuracy of multiple targets.

[0003] Traditional multi-target tracking technology uses data association techniques based on single-target Bayesian filtering. However, computational explosion is inevitable when the number of targets and clutter is large, and there is also a limitation that the number of targets must be known. The introduction of random finite sets has opened up new avenues for track association and new target confirmation. The subsequent Probability Hypothesis Density (PHD) filter applies multi-target tracking to a similar single-target filter and performs Bayesian recursion on the entire system, resulting in a closed-form solution and a Gaussian mixture implementation in a linear Gaussian environment. Considering that conventional PHD filters cannot distinguish the trajectories of individual targets, Angel et al. proposed the Trajectory Probability Hypothesis Density (TPHD) filter, which uses trajectories instead of point targets as the research object, thus addressing the shortcomings of PHD filters. Currently, PHD filters are applied to continuous-discrete models, allowing them to infer the occurrence time and state of trajectories in continuous time, without being constrained to discrete time steps. Summary of the Invention

[0004] Technical problem solved: To address the communication delays and unknown target detection probabilities and clutter rates in sensor tracking scenarios, traditional target tracking technologies cannot accurately track, resulting in reduced filtering accuracy. The present invention provides a target tracking method that uses a continuous discrete model to perform out-of-order measurement updates. The core technology is to add trajectory information to the time steps of out-of-order measurements and perform backtracking in continuous time based on Beta-Gaussian mixture trajectory probability hypothesis density (TPHD) filtering. The trajectory is discretized and updated using the acquired out-of-order measurements. Finally, the trajectory information of the out-of-order measurement time steps is marginalized, retaining only the trajectory information at sequential sampling times, thereby achieving simultaneous adaptive estimation of detection probability, clutter rate, and multi-trajectory posterior probability density.

[0005] Technical solution:

[0006] A target tracking method using a continuous discrete model for out-of-order measurement updates, the target tracking method comprising the following steps:

[0007] S1, when the initial time k=0, initialization is performed; the initialization process includes the following sub-steps:

[0008] S11, initialize the survival trajectory X = (k s , x 1：l )'s basic state ω k , Gaussian distribution Where x refers to a single target, k s is the starting time of the trajectory, l is the duration of the trajectory, and are the mean and covariance matrices of trajectory states within the duration, ω k is the weight of the Gaussian component; the trajectory window length is set to L, and the filtering per unit time is the prediction and update of the trajectory with no more than L steps;

[0009] S12, initialize the survival trajectory X = (k s , x 1：l ) follows the Beta distribution detection probability parameter β(u; n k , v k ), where n k and v k are the shape parameters of the Beta distribution, represents the enhanced trajectory with detection parameters;

[0010] S13, initialize the basic state of the clutter component (ω c,k ,n c,k ,v c，k ), where ω c，k is the weight of the beta component, n c，k and v c，k are the shape parameters of the Beta distribution. c represents the clutter state, Indicates the enhanced clutter state with detection parameters;

[0011] S14, initialize the basic parameters of the scene: set the beta factor k β ; Initialize the state transfer matrix F (·) , process noise covariance matrix Q (·) , measurement model function h, measurement noise covariance matrix R, the survival probability of the target at the moment of sequential measurement Clutter survival probability Unknown detection probability p d , the unknown clutter rate μ in the scene FAand the clutter distribution f FA (·);

[0012] S2: If the timestamp of the acquired measurement set is greater than the current time step, it is considered as a sequential measurement and processed by conventional trajectory probability hypothesis density filtering; otherwise, it goes to step S3;

[0013] S3, backtracking the trajectory probability hypothesis density under the continuous time model, specifically includes the following sub-steps:

[0014] S31, the starting time step k of the trajectory X that survived at time k s and the unordered measurement set Z τ The next time step k of the timestamp τ o Make comparisons;

[0015] S32, for the starting time step k s >k o The trajectory contains the detected Beta distribution and no backtracking is performed, and the label o=0 is set;

[0016] S33, for the starting time step k s <k o The trajectory contains the detected Beta distribution and performs the corresponding backtracking operation, setting the label o = 1;

[0017] S34, for the starting time step k s =k o The trajectory contains the detected Beta distribution, which is labeled o=0 and o=1 respectively, and only the trajectory component with o=1 is backtracked;

[0018] S35, label the new target o=1 and combine it with k in S34 s =k o The trajectories are merged;

[0019] S36, performing a backtracking operation on the clutter component at time k according to the properties of the Beta distribution and merging it with the newly generated clutter component;

[0020] S4, measuring and updating the trajectory probability hypothesis density under the discrete time model, specifically includes the following sub-steps:

[0021] S41, update the missed detection of the trajectory set according to the label o of the trajectory;

[0022] S42, based on the trajectory label o, use the received measurement set Z with timestamp τ τ Perform measurement updates on the backtracked trajectory sets respectively;

[0023] S43, combining the update results of step S41 and step S42 into a final update result;

[0024] S5, marginalize the trajectory probability hypothesis density under the discrete time model and only retain the trajectory state to the current time step;

[0025] S6, according to the trajectory weight ω k , perform probability hypothesis density pruning absorption of trajectories under the continuous discrete model, set the Mahalanobis distance threshold, and directly absorb and merge the components whose weight is less than the distance threshold; set the weight threshold, and directly delete the components whose weight is less than the weight threshold;

[0026] S7, extract the trajectory probability hypothesis density state and calculate the trajectory weight and N k|τ Extract the N with the highest weight k|τ Gaussian components and extract the estimated detection probability p d，k|τ and the clutter rate μ FA,k|τ If it is within the filtering time, go to step S2; if it exceeds the filtering time, the target tracking ends.

[0027] Furthermore, in step S14, the continuous discrete model of the target is described using the following formula:

[0028] Assume that the discrete model is from to t k-1 Evolved to t k , Δt k =t k -t k-1 The survival probability p of a single target s,k and the transfer density f(·|·) is calculated as follows:

[0029]

[0030] The target lifespan is independently modeled using an exponential distribution with parameter μ, and the target motion follows a linear time-invariant stochastic differential equation: A and ρ are the magnitudes of The matrix of , dx(t) is The differential of is a Wiener process (Brownian motion). Other relevant parameter definitions can be found in step S1.

[0031] The new target strength of the continuous-discrete model is calculated as follows:

[0032]

[0033] Among them, the time when the target appears is expressed with parameter λ ω The Poisson process model of the target is an independent Gaussian distribution. represents the set [0, Δt k ) indicator function, if t∈[0,Δtk )but otherwise Other relevant parameter definitions can be found in step S1.

[0034] Furthermore, in step S3, the starting time step k of the trajectory X that survives at time k is s and the unordered measurement set Z τ The next time step k of the timestamp τ o Compare and then use the following formula to backtrack:

[0035]

[0036] in, is the density of the given trajectory to be backtracked, φ τ|k (o, X|X) refers to the transition density of the trajectory, and δ[o] is the label indicator function. o , Δt o，1 and Δt o，2 are the sampling time intervals between adjacent time steps of timestamp τ, the sampling time interval between timestamp τ and the previous time step, and the sampling time interval between timestamp τ and the next time step. Refers to the time-dependent probability of trajectory survival.

[0037]

[0038] When the trajectory initial time k s >k o hour

[0039]

[0040] When the trajectory initial time k s <k o hour

[0041]

[0042] ω τ|k,i =ω k|k,i

[0043]

[0044] When the trajectory initial time k s =k o hour

[0045]

[0046] Among them, according to k s With k o By comparing the k-time posterior trajectory components, the k-time posterior trajectory components can be divided into The trajectory of newborns Refers to the sum of the three types of trajectory intensities after backtracking, n x refers to the target state dimension, F (·) With Q (·) are the state transfer matrix and process noise covariance related to the time interval, and are the mean and covariance of the Gaussian components of the trajectories before and after backtracking, respectively. are the moments of the new target under the continuous discrete model.

[0047] The beta component of the target is calculated as follows:

[0048]

[0049] Among them, n k|k,i 、v k|k,i With n τ|k,i 、v τ|k,i are the parameters of the beta components of the trajectories before and after backtracking, respectively.

[0050] And the clutter component at time k is backtracked and merged with the new clutter component:

[0051]

[0052] Among them, the clutter component of the posterior at time k is J c，k|k , the new clutter component n c，k|k,j 、v c，k|k,j With n c，τ|k,j 、v c,τ|k,j are the parameters of the clutter beta component before and after backtracking, Refers to the time-dependent probability of clutter survival.

[0053] Furthermore, in step S4, the following formula is used to update the unordered measurement value of the trajectory probability hypothesis density under the discrete time model according to the label o of the trajectory:

[0054] Perform missed detection updates on the backtracked trajectory set and clutter set:

[0055]

[0056] Among them, B(n, v) refers to the beta function The relevant parameter definitions are shown in step S1.

[0057] Perform measurement updates on the backtracked trajectory set and clutter set:

[0058]

[0059] in, is a parameter The trajectory mean and covariance after Kalman update, and other related parameter definitions can be found in step S1 and above.

[0060] Furthermore, in step S5, the trajectory is marginalized using the following formula:

[0061]

[0062] The relevant parameter definitions can be found in step S1 and above.

[0063] Furthermore, in step S6, a distance threshold U is set, if the component satisfies the following conditions: Then the component where the trajectory is located is absorbed (Absorption), where represents different trajectory means, represents the trajectory covariance.

[0064] Furthermore, in step S7, the detection probability p is calculated using the following formula: d，k|τ and the clutter rate μ FA,k|τ Extraction:

[0065]

[0066] Among them, the weight of the enhanced trajectory and the weight of enhanced clutter as well as v k|τ，i 、n c,k|τ，j and v c,k|τ，j is the updated beta parameter.

[0067] The present invention is based on continuous discrete trajectory probability hypothesis density filtering. While distinguishing each target trajectory, it focuses on solving the problems of disordered measurement updates and unknown detection probability and clutter rate in the scene.

[0068] Beneficial effects:

[0069] (1) The target tracking method of the present invention using a continuous discrete model for disordered measurement updates is based on the continuous discrete trajectory probability hypothesis density filtering, which can estimate the occurrence time and state of the trajectory in continuous time without being constrained to a discrete time step.

[0070] (2) The target tracking method of the present invention uses a continuous discrete model for disordered measurement update, which adaptively models the target detection probability and the clutter, and solves the problem of mismatch between unknown detection probability and clutter rate in the scene.

[0071] (3) The target tracking method of the present invention using a continuous discrete model for disordered measurement updates adds trajectory information to the time step of the disordered measurement and performs backtracking in continuous time, uses the obtained disordered measurement to discretize and update the trajectory, and finally marginalizes the trajectory information of the time step of the disordered measurement, retaining only the trajectory information at the sequential sampling time, thereby achieving effective update of the sequential trajectory posteriori using the disordered measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 Flowchart of a target tracking method using a continuous-discrete model for out-of-order measurement updates according to an embodiment of the present invention.

[0073] Figure 2 It is a real trajectory diagram of simulation 1 in an embodiment of the present invention.

[0074] Figure 3 1 is a time difference diagram of the sampling time intervals of simulation 1 in an embodiment of the present invention.

[0075] Figure 4 1 is an average detection probability estimation diagram of 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.

[0076] Figure 5 1 is an average clutter rate estimation diagram obtained by performing 200 Monte Carlo experiments in simulation 1 according to an embodiment of the present invention.

[0077] Figure 6 3 is a comparison diagram of the total root mean square error of the trajectory metric after 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.

[0078] Figure 7 3 is a comparison diagram of the root mean square error of the target position after 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.

[0079] Figure 8 3 is a comparison diagram of the root mean square error of missed detection targets after 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.

[0080] Figure 9 3 is a comparison diagram of the root mean square error of the misdetected targets after 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.

[0081] Figure 10 3 is a comparison diagram of the root mean square error of the trajectory crossover of 200 Monte Carlo experiments in simulation 1 of the embodiment of the present invention. DETAILED DESCRIPTION

[0082] The following examples may enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0083] This embodiment adopts a multi-target tracking method based on trajectory probability hypothesis density filtering, which uses a continuous discrete model to model the target's motion equation and the intensity of the new target and performs recursive iterative adaptive estimation of the detection probability and the clutter rate.

[0084] The target tracking method using a continuous-discrete model for out-of-order measurement updates is as follows: based on the Beta-Gaussian mixture TPHD filter under the continuous-discrete model, trajectory information is added to the time step of the out-of-order measurement and backtracking is performed in continuous time. The obtained out-of-order measurements are used to discretize the trajectory and update it. Finally, the trajectory information of the time step of the out-of-order measurement is marginalized, and only the trajectory information at the sequential sampling time is retained. This method realizes the simultaneous adaptive estimation of the detection probability, clutter rate and multi-trajectory posterior probability density.

[0085] See also Figure 1 This embodiment discloses a target tracking method using a continuous discrete model for disordered measurement update, the multi-target tracking method comprising the following steps:

[0086] Step 1: Initialize the specific content at the initial time k=0:

[0087] (1a) Initialize the survival trajectory X = (k s , x 1:l )'s basic state ω k , Gaussian distribution Where x refers to a single target, k s is the starting time of the trajectory, l is the duration of the trajectory, and are the mean and covariance matrices of trajectory states within the duration, ω k is the weight of the Gaussian component; the trajectory window length is set to L, and the filtering per unit time is the prediction and update of the trajectory with no more than L steps;

[0088] (1b) Initialize the survival trajectory X = (k s , x 1：l ) follows the Beta distribution detection probability parameter β(u; n k , v k ), where n k and v k are the shape parameters of the Beta distribution, represents the enhanced trajectory with detection parameters;

[0089] (1c) Initialize the basic state of the clutter component (ω c,k ,n c,k ,v c，k ), where ω c，k is the weight of the beta component, n c，k and v c，kare the shape parameters of the Beta distribution. c represents the clutter state, Indicates the enhanced clutter state with detection parameters;

[0090] (1d) Initialize the basic parameters of the scene: set the beta factor k β ; Initialize the state transfer matrix F (·) , process noise covariance matrix Q (·) , measurement model function h, measurement noise covariance matrix R, the survival probability of the target at the moment of sequential measurement Clutter survival probability Unknown detection probability p d , the unknown clutter rate μ in the scene FA and the clutter distribution f FA (·);

[0091] The continuous-discrete model of the target is described by the following formula:

[0092] Assume that the discrete model is from to t k-1 Evolved to t k , Δt k =t k -t k-1 The survival probability p of a single target s,k and the transfer density f(·|·) is calculated as follows:

[0093]

[0094] The target lifespan is independently modeled using an exponential distribution with parameter μ, and the target motion follows a linear time-invariant stochastic differential equation: A and ρ are respectively the size of n x ×n x and The matrix of , dx(t) is The differential of is the Wiener process (Brownian motion). Other relevant parameter definitions can be found in step 1.

[0095] The new target strength of the continuous-discrete model is calculated as follows:

[0096]

[0097] Among them, the time when the target appears is expressed with parameter λ ω The Poisson process model of the target is an independent Gaussian distribution. represents the set [0, Δt k ) indicator function, if t∈[0,Δt k )but otherwise Other relevant parameter definitions can be found in step 1.

[0098] Step 2: If the timestamp of the acquired measurement set is greater than the current time step, it is considered as a sequential measurement and processed according to the conventional trajectory probability hypothesis density filtering. Otherwise, go to step 3.

[0099] Step 3: Backtrack the trajectory probability hypothesis density under the continuous time model. Specific steps:

[0100] (3a) The starting time step k of the trajectory X that survived at time k is s and the unordered measurement set Z τ The next time step k of the timestamp τ o Make comparisons;

[0101] Use the following formula for backtracking:

[0102]

[0103] in, is the density of the given trajectory to be backtracked, φ τ|k (o, X|X) refers to the transition density of the trajectory, and δ[o] is the label indicator function. o , Δt o，1 and Δt o，2 are the sampling time intervals between adjacent time steps of timestamp τ, the sampling time interval between timestamp τ and the previous time step, and the sampling time interval between timestamp τ and the next time step. Refers to the time-dependent probability of trajectory survival.

[0104]

[0105] (3b) For the starting time step k s >k o The trajectory contains the detected Beta distribution and no backtracking is performed, and the label o=0 is set;

[0106] When the trajectory initial time k s >k o hour

[0107]

[0108] (3c) For the starting time step k s <k o The trajectory contains the detected Beta distribution and performs the corresponding backtracking operation, setting the label o = 1;

[0109] When the trajectory initial time k s <k o hour

[0110]

[0111] ω τ|k,i =ω k|k，i

[0112]

[0113] (3d) For the starting time step k s =k o The trajectory contains the detected Beta distribution, which is labeled o=0 and o=1 respectively, and only the trajectory component with o=1 is backtracked;

[0114] When the trajectory initial time k s =k o hour

[0115]

[0116] Among them, according to k s With k o By comparing the k-time posterior trajectory components, the k-time posterior trajectory components can be divided into The trajectory of newborns Refers to the sum of the three types of trajectory intensities after backtracking, n x refers to the target state dimension, F (·) With Q (·) are the state transfer matrix and process noise covariance related to the time interval, and are the mean and covariance of the Gaussian components of the trajectories before and after backtracking, respectively. are the moments of the new target under the continuous discrete model.

[0117] The beta component of the target is calculated as follows:

[0118]

[0119]

[0120] Among them, n k|k,i 、v k|k，l With n τ|k,i 、v τ|k,i are the parameters of the beta components of the trajectories before and after backtracking, respectively.

[0121] (3e) Label the new target o = 1 and compare it with k in step (3d) s =k o The trajectories are merged;

[0122] (3f) The clutter component at time k is back-traced according to the properties of the Beta distribution and merged with the newly generated clutter component;

[0123]

[0124] Among them, the clutter component of the posterior at time k is J c，k|k , the new clutter component n c，k|k,j 、v c，k|k，j With n c,τ|k,j 、v c，τ|k,j are the parameters of the clutter beta component before and after backtracking, Refers to the time-dependent probability of clutter survival.

[0125] Step 4: Update the trajectory probability hypothesis density under the discrete time model. Specific steps:

[0126] (4a) Update the missed detection of the trajectory set according to the trajectory label o;

[0127] Perform missed detection updates on the backtracked trajectory set and clutter set:

[0128]

[0129] Among them, B(n, v) refers to the beta function The relevant parameter definitions are given in step 1.

[0130] (4b) Based on the label o of the trajectory, use the received measurement set Z with timestamp τ τ Perform measurement updates on the backtracked trajectory sets respectively;

[0131] Perform measurement updates on the backtracked trajectory set and clutter set:

[0132]

[0133] in, is a parameter The trajectory mean and covariance after Kalman update, and other related parameter definitions can be found in step 1 and above.

[0134] (4c) merging the update results of step (4a) and step (4b) into a final update result;

[0135] Step 5: Marginalize the trajectory probability hypothesis density under the discrete time model and only retain the trajectory state to the current time step;

[0136] The trajectory is marginalized using the following formula:

[0137]

[0138] The relevant parameter definitions can be found in step 1 and above.

[0139] Step 6: According to the trajectory weight ω k , perform probability hypothesis density pruning absorption of trajectories under the continuous discrete model, set the Mahalanobis distance threshold, and directly absorb and merge the components whose weight is less than the distance threshold; set the weight threshold, and directly delete the components whose weight is less than the weight threshold;

[0140] Set the distance threshold U, if the component meets the following conditions: Then the component where the trajectory is located is absorbed (Absorption), where represents different trajectory means, represents the trajectory covariance.

[0141] Step 7: Extract the trajectory probability hypothesis density state and calculate the trajectory weight and N k|τ Extract the N with the highest weight k|τ Gaussian components and extract the estimated detection probability p d，k|τ and the clutter rate μ FA,k|τ If it is within the filtering time, go to step 2; if it exceeds the filtering time, the target tracking ends.

[0142] The detection probability p is calculated using the following formula: d，k|τ and the clutter rate μ FA，k|τ Extraction:

[0143]

[0144] Among them, the weight of the enhanced trajectory and the weight of enhanced clutter as well as n k|τ，i 、v k|τ,i 、n c,k|τ，j and v c,k|τ，j is the updated beta parameter.

[0145] The algorithm and processing method of the present invention have been verified and achieved satisfactory application results:

[0146] 1. Experimental conditions: Assume that there are multiple targets moving in a uniform linear motion on the horizontal rectangular coordinate system XY plane. The target's motion state can be expressed as {x, v x ,y,v y}, where {x, y} are the position information of the target in the X and Y directions in the horizontal rectangular coordinate system, {v x , v y} are the speed information of the target in the X and Y directions in the horizontal rectangular coordinate system. Initialize the state transfer matrix Process noise Measurement transfer matrix h, the survival probability of the target at the sequential measurement moment Clutter survival probability Unknown detection probability p d , the unknown clutter rate and distribution in the scene are μ FA and f FA (·).

[0147]

[0148] I d is the unit matrix (d=2).

[0149] λ ω =0.12s -1 , μ=0.02s -1 .

[0150]

[0151] R k =diag(25,(0.5π / 180) 2 ).

[0152]

[0153] P d =0.95.

[0154] μ FA =10,f FA =300π.

[0155] Evaluation parameters are p=2, c=10, and γ=1.

[0156] Beta factor k β is 1.1.

[0157] The window length of TPHD is L=2,5.

[0158] Beta parameters for setting new targets in Scenario 1 In addition, the beta parameter of the new clutter

[0159] 2. Simulation content:

[0160] Simulation 1: Assume that the prior moment of the target at the initial moment is in According to the exponential distribution measurement results of the parameters, the sampling is performed at 200 time intervals. Among them, a random number λ with a parameter of 1 and a Poisson distribution is determined every 5 intervals. n , measuring delay λ ntime intervals. The proposed OOSM-TPHD filter is compared with several variants of the continuous-discrete TPHD filter. In scenarios without out-of-order measurements, the continuous-discrete TPHD filter will be referred to as the baseline algorithm, namely the ISM-TPHD filter. Therefore, the continuous-discrete TPHD filter is considered to be updated using the most recent out-of-order measurement timestamp where out-of-order measurements are present. The last variant of the continuous-discrete TPHD filter that does not handle out-of-order measurements, i.e., simply discards them, can be named the (D)OOSM-TPHD filter. Figure 2 This is the actual trajectory diagram of this scene. The solid circle indicates the starting point of the trajectory, and the position of every 10 time steps is marked with a circle. Figure 3 This is a time difference diagram of the sampling time intervals in this scenario. The time intervals when out-of-order measurements are received are negative and marked with red crosses. Figure 4 It is the average detection probability estimation graph of this scene. Figure 5 is an estimate of the average clutter rate for this scene. Figure 6 This is a comparison chart of the total error of the root mean square trajectory measurement of the above four filters in this scenario. Figure 7 This is a comparison chart of the root mean square error of the target position of the above four filters in this scene. Figure 8 This is a comparison chart of the root mean square error of missed targets of the above four filters in this scenario. Figure 9 This is a comparison chart of the root mean square error of the above four filters for this scenario. Figure 10 This is a comparison chart of the root mean square error of the four filter trajectory switching in this scenario. Figures 3 to 10 The horizontal axis is the measurement number on the time axis, and the vertical axis is the comparison index of the picture.

[0161] 3. Analysis of simulation results:

[0162] from Figure 3 and Figure 4 It can be seen that the sampling time of the method proposed in this patent is non-uniform and has a time step lag measurement.

[0163] from Figure 3 and Figure 4 It can be seen that the method proposed in this patent can adaptively estimate the unknown detection probability and clutter rate, and the estimated value converges to the true value.

[0164] from Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10As can be seen, the proposed OOSM-TPHD filter exhibits performance closest to that of the ISM-TPHD filter, while the results of the other filters are unsatisfactory. Compared to the (D)OOSM-TPHD filter and the TPHD filter, the OOSM-TPHD filter has better performance in terms of positioning error, missed target error, false target error, and track switching error, demonstrating the effectiveness and reliability of the present invention. As expected, the cost error of all filters decreases consistently as the time window L increases from 2 to 5, which is a result of the improved estimation of past states using TPHD.

[0165] The simulation results demonstrate the effectiveness of the target tracking method proposed in this patent using a continuous discrete model for disordered measurement updates.

[0166] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A target tracking method using a continuous-discrete model for out-of-order measurement updates, characterized in that: The multi-target tracking method comprises the following steps: S1, when the initial time k=0, initialization is performed; the initialization process includes the following sub-steps: S11, initialize the survival trajectory X = (k s , x 1：l )'s basic state ω k , Gaussian distribution Where x refers to a single target, k s is the starting time of the trajectory, l is the duration of the trajectory, and are the mean and covariance matrices of trajectory states within the duration, ω k is the weight of the Gaussian component; the trajectory window length is set to L, and the filtering per unit time is the prediction and update of the trajectory with no more than L steps; S12, initialize the survival trajectory X = (k s , x 1：l ) follows the Beta distribution detection probability parameter β(u; n k , v k ), where n k and v k are the shape parameters of the Beta distribution, represents the enhanced trajectory with detection parameters; S13, initialize the basic state of the clutter component (ω c,k ,n c,k ,v c,k ), where ω c,k is the weight of the beta component, n c，k and v c,k are the shape parameters of the Beta distribution. c represents the clutter state, Indicates the enhanced clutter state with detection parameters; S14, initialize the basic parameters of the scene: set the beta factor k β ; Initialize the state transfer matrix F (·) , process noise covariance matrix Q (·) , measurement model function h, measurement noise covariance matrix R, the survival probability of the target at the moment of sequential measurement Clutter survival probability Unknown detection probability p d , the unknown clutter rate μ in the scene FA and the clutter distribution f FA (·); S2: If the timestamp of the acquired measurement set is greater than the current time step, it is considered as a sequential measurement and processed by conventional trajectory probability hypothesis density filtering; otherwise, it goes to step S3; S3, backtracking the trajectory probability hypothesis density under the continuous time model, specifically includes the following sub-steps: S31, the starting time step k of the trajectory X that survived at time k s and the unordered measurement set Z τ The next time step k of the timestamp τ o Make comparisons; S32, for the starting time step k s >k o The trajectory contains the detected Beta distribution and no backtracking is performed, and the label o=0 is set; S33, for the starting time step k s <k o The trajectory contains the detected Beta distribution and performs the corresponding backtracking operation, setting the label o = 1; S34, for the starting time step k s =k o The trajectory contains the detected Beta distribution, which is labeled o=0 and o=1 respectively, and only the trajectory component with o=1 is backtracked; S35, label the new target o=1 and combine it with k in S34 s =k o The trajectories are merged; S36, performing a backtracking operation on the clutter component at time k according to the properties of the Beta distribution and merging it with the newly generated clutter component; S4, measuring and updating the trajectory probability hypothesis density under the discrete time model, specifically includes the following sub-steps: S41, update the missed detection of the trajectory set according to the label o of the trajectory; S42, based on the trajectory label o, use the received measurement set Z with timestamp τ τ Perform measurement updates on the backtracked trajectory sets respectively; S43, merging the update results of step S41 and step S42 into a final update result; S5, marginalize the trajectory probability hypothesis density under the discrete time model and only retain the trajectory state to the current time step; S6, according to the trajectory weight ω k , perform probability hypothesis density pruning absorption of trajectories under the continuous discrete model, set the Mahalanobis distance threshold, and directly absorb and merge the components whose weight is less than the distance threshold; set the weight threshold, and directly delete the components whose weight is less than the weight threshold; S7, extract the trajectory probability hypothesis density state and calculate the trajectory weight and N k|τ Extract the N with the highest weight k|τ Gaussian components and extract the estimated detection probability p d,k|τ and the clutter rate μ FA,k|τ If it is within the filtering time, go to step S2; if it exceeds the filtering time, the target tracking ends.

2. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S14, the continuous discrete model of the target is described using the following formula: Assume that the discrete model is from to t k-1 Evolved to t k , Δt k =t k -t k-1 The survival probability p of a single target s,k and the transfer density f(·|·) is calculated as follows: The target lifespan is independently modeled using an exponential distribution with parameter μ, and the target motion follows a linear time-invariant stochastic differential equation: A and ρ are respectively the size of n x ×n x and The matrix dx(t) is The differential of is a Wiener process (Brownian motion). Other relevant parameter definitions can be found in step S1. The new target strength of the continuous-discrete model is calculated as follows: Among them, the time when the target appears is expressed with parameter λ ω The Poisson process model of the target is an independent Gaussian distribution. represents the set [0, Δt k ) indicator function, if t∈[0,Δt k )but otherwise Other relevant parameter definitions can be found in step S1.

3. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S3, the starting time step k of the trajectory X that survives at time k is s and the unordered measurement set Z τ The next time step k of the timestamp τ o Compare and then use the following formula to backtrack: in, is the density of the given trajectory to be backtracked, φ τ|k (o, X|X) refers to the transition density of the trajectory, and δ[o] is the label indicator function. o , Δt o,1 and Δt o，2 are the sampling time intervals between adjacent time steps of timestamp τ, the sampling time interval between timestamp τ and the previous time step, and the sampling time interval between timestamp τ and the next time step. Refers to the time-dependent probability of trajectory survival. When the trajectory initial time k s >k o hour When the trajectory initial time k s <k o hour oh τ|k,i =ω k|k,i When the trajectory initial time k s =k o hour Among them, according to k s With k o By comparing the k-time posterior trajectory components, the k-time posterior trajectory components can be divided into The trajectory of newborns Refers to the sum of the three types of trajectory intensities after backtracking, n x refers to the target state dimension, F (·) With Q (·) are the state transfer matrix and process noise covariance related to the time interval, and are the mean and covariance of the Gaussian components of the trajectories before and after backtracking, respectively. are the moments of the new target under the continuous discrete model. The beta component of the target is calculated as follows: Among them, n k|k,i 、v k|k,i With n τ|k,i 、v τ|k,i are the parameters of the beta components of the trajectories before and after backtracking, respectively. And the clutter component at time k is backtracked and merged with the new clutter component: Among them, the clutter component of the posterior at time k is J c,k|k , the new clutter component n c,k|k，j 、v c，k|k,j With n c，τ|k，j 、v c，τ|k,j are the parameters of the clutter beta component before and after backtracking, Refers to the time-dependent probability of clutter survival.

4. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S4, the following formula is used to update the unordered measurement value of the trajectory probability hypothesis density under the discrete time model according to the label o of the trajectory: Perform missed detection updates on the backtracked trajectory set and clutter set: Among them, B(n, v) refers to the beta function The relevant parameter definitions are shown in step S1 and feature 3. Perform measurement updates on the backtracked trajectory set and clutter set: in, is a parameter The trajectory mean and covariance after Kalman update, and other related parameter definitions can be found in step S1 and feature 3.

5. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S5, the trajectory is marginalized using the following formula: The relevant parameter definitions can be found in step S1 and features 3 and 4.

6. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S6, a distance threshold U is set, if the component meets the following conditions: Then the component where the trajectory is located is absorbed (Absorption), where represents different trajectory means, represents the trajectory covariance.

7. The target tracking method using robust continuous discrete TPHD filtering under disordered measurement according to claim 1, characterized in that: In step S7, the detection probability p is calculated using the following formula: d，k|τ and the clutter rate μ FA，k|τ Extraction: Among them, the weight of the enhanced trajectory and the weight of enhanced clutter as well as n k|τ,i 、v k|τ，i 、n c,k|τ，j and v c,k|τ，j is the updated beta parameter.

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