GMPHD tracking method based on number estimation smoothing

Abstract

The invention relates to the technical field of aquatic target tracking, discloses a GMPHD tracking method based on number estimation smoothing, and aims to solve the problems that initial priori knowledge of a target is unknown and measurement information is uncertain and incomplete in bistatic MIMO sonar multi-target tracking. Performing underwater scene multi-target tracking to obtain a target state estimation and measurement model; 2, introducing a GMPHD algorithm, and performing filtering process propagation in a PHD filtering algorithm by using an approximation method and a posterior intensity function to obtain posterior intensity; and step 3, extracting the target number and the target state according to the posterior strength, adjusting the target number estimation result of the intermediate time node through a target number smoothing method by using the target number estimation of two continuous time points, and outputting the target estimation values of all time nodes.

Description

Technical Field

[0001] The present invention relates to a GMPHD tracking method based on number estimation smoothing, and belongs to the technical field of aquatic target tracking. Background Art

[0002] In a marine environment, the state estimation of a target is affected by factors such as environmental noise, reverberation, and interference, resulting in uncertainty and errors in target tracking. In a target tracking system, generally, the estimation of target motion parameters is achieved through filtering techniques, and the accuracy of target tracking is also affected by the performance of the filtering estimation algorithm.

[0003] In 1955, Wax proposed the concept of multi-target tracking technology. In 1960, Kalman first proposed the Kalman filtering method, which is based on the optimal filtering theory to achieve the optimal filtering effect and belongs to an estimation algorithm based on the minimum mean square error. To solve the above-mentioned non-linear tracking problem, in 1971, Bucy and Sunahara et al. proposed the non-linear extended Kalman filter, which realizes the approximate linearization of the non-linear system by performing Taylor series expansion on the non-linear equation and ignoring the quadratic and higher-order terms. The extended Kalman filter is similar to the Kalman filter in terms of iterative calculation performance, and the algorithm is prone to divergence when the non-linearity is high. To solve the divergence problem caused by high non-linearity, in 1999, Julier et al. proposed the unscented Kalman filter, which filters each sampling point through the unscented sampling method and finally obtains the final filtering result through weighted processing. The unscented Kalman filter has better stability and higher accuracy compared with the extended Kalman filter, but filtering each sampling point and finally weighting results in a lower calculation speed than the extended Kalman filter. Y Luo et al. proposed an interactive multi-model cubature Kalman filtering algorithm. The simulation results show that compared with the single-model CKF and IMM-UKF, the IMM-CKF has higher tracking accuracy and stronger model adaptability. Sahab Edrisi et al. proposed an extended Kalman filter based on Monte Carlo (MC) for the two-dimensional bearing-only tracking problem (BOT) to estimate the position and velocity of the target, and its performance was proven by comparison with the unscented Kalman filtering algorithm. Ye Jin and her colleagues aimed at the slow model switching and low tracking accuracy of the interactive multi-model, defined a posterior information correction factor, and combined it with the interactive multi-model algorithm based on the unscented Kalman filter to achieve the effect of increasing the model matching probability and filtering tracking accuracy. Researchers such as Shi Guixin estimated the bias coefficient introduced by the non-linear approximate linearization as part of the state estimation, and combined the probabilistic unscented Kalman filter and cubature Kalman filter algorithms to effectively improve the tracking accuracy with similar computational complexity. Jing Qi and her research team combined the interactive multi-model with the adaptive Kalman filtering technology to improve the accuracy of target tracking and the matching efficiency of the motion model. Other researchers have also explored the possibility of applying the extended Kalman filtering technology to underwater target tracking.

[0004] Facing a complex underwater environment, such as reverberation, noise, and other forms of interference, sonar systems often receive a dataset containing clutter interference during measurement. Therefore, effectively extracting the true measurement information of the target from the clutter has become a key research area. In single / multi-target tracking systems, the technology to accurately associate measurement information with the target is crucial.

[0005] In 1971, Singer introduced the Nearest Neighbor Data Association (NNDA). By calculating the weighted Euclidean distance within the association threshold, the measurement with the smallest distance from the predicted measurement is taken as the associated measurement. The advantage of this algorithm is its small computational complexity, but the disadvantage is that it is prone to incorrect associations in the case of a large amount of clutter and multi-target measurement intersections. In 1975, Bar-Shalom proposed the Probabilistic Data Association (PDA). By calculating the posterior probability of each element in the measurement set as the association value, the target state can be estimated through each measurement value and weighted combination to achieve the estimation of the target state. This algorithm can achieve the association of single-target measurements in a clutter environment, but it cannot be used in the association of multi-target measurements. Further, Fortmann, Bar-Shalom, etc. introduced the Joint Probabilistic Data Association (JPDA). This method identifies various possible events by constructing and decomposing the association matrix of the multi-target measurement set, calculates the posterior probability of these events and the association probability of the measurement values, and realizes the effective association of multi-target measurements. Although its calculation is relatively complex and depends on the prior knowledge of the number of target movements. Scholars such as Guo Longxiang combined JPDA, the Hungarian algorithm, and convex combination fusion technology in a complex underwater environment with a high clutter density, significantly improving the accuracy and reliability of the tracking system and effectively achieving multi-target underwater tracking. Zhang Jun et al. used a method combining joint JPDA and YOLO target detection technology to enhance the association between trajectory matching and observation data, demonstrating the practicality of the algorithm. Bi Wenhao et al. proposed a Joint Probabilistic Data Association algorithm based on maximum entropy fuzzy clustering (MEFC-JPDA). The membership degree obtained through maximum entropy fuzzy clustering preliminarily characterizes the association probability between the target and the effective measurement, and it is corrected by the measurement correction factor, showing a significant improvement in performance compared with the existing two association algorithms.

[0006] Recently, Mahler deduced that the probability hypothesis density (PHD) is the best approximate expression of the multi-target tracking posterior probability based on the random finite set (RFS) for multi-target tracking. Vo B N et al. proposed the Gaussian mixture probability hypothesis density (GMPHD) algorithm to address the target tracking problem in non-linear models. Xue Qiutiao and his team integrated the jump Markov model with the PHD filter and developed an advanced track-before-detect method. Without knowing the number and motion patterns of maneuvering targets, this method successfully tracked weak targets by analyzing the measurement data of infrared sensors. Zhu Hongpeng et al. combined the GMPHD algorithm with the smoothing recursive technique, improving the estimation efficiency at the cost of the estimation accuracy. Especially in a low signal-to-noise ratio environment, the estimation accuracy of the target state was significantly improved, which is particularly suitable for weak target tracking scenarios. T Kropfreiter et al. proposed an effective multi-target tracking algorithm based on the random finite set (RFS), where the target state is modeled by a combination of a labeled multi-Bernoulli (LMB) RFS and a Poisson RFS, promoting the continuity of the trajectory and achieving the characteristic of reduced complexity. In addition, other researchers also used the probability hypothesis density filter to achieve reliable filtering and tracking of targets.

[0007] In summary, the traditional bistatic MIMO sonar multi-target tracking system can no longer meet the requirements of complex underwater acoustic target tracking environments. To solve problems such as unknown initial prior knowledge of targets, uncertain and incomplete measurement information, it is particularly important to study the improvement of multi-target tracking performance under unknown initial states. Summary of the Invention

[0008] To solve the problems of unknown initial prior knowledge of targets, uncertain and incomplete measurement information in bistatic MIMO sonar multi-target tracking, the present invention further proposes a GMPHD tracking method based on number estimation smoothing.

[0009] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0010] Step 1: Introduce the random finite set theory into the PHD filtering algorithm to perform multi-target tracking in underwater scenarios and obtain the state estimation and measurement model of the targets.

[0011] Step 2: Introduce the GMPHD algorithm, use the approximation method and the posterior intensity function to propagate the filtering process in the PHD filtering algorithm to obtain the posterior intensity.

[0012] Step 3: Extract the number of targets and the target states based on the posterior intensity, and adjust the estimated result of the number of targets at the intermediate time nodes by using the method of smoothing the number of targets with the estimation of the number of targets at two consecutive time points, and output the estimated values of the targets at all time nodes.

[0013] Preferably, step 1 specifically includes:

[0014] Step 1.1: Set the target state at time k to include the survival, evolution, and natural birth of the target state at time k-1, and construct a transition model of the random finite set;

[0015] Step 1.2: Construct a measurement model of the target based on the random finite set state model;

[0016] The expression of the random finite set state model is:

[0017]

[0018] In formula (1), X k is the state random set at time k, representing the M k estimated states at time k, that is, X i,k , i = 1, 2,..., M k , is the state that has survived to time k, is the state at time k-1 transferred to time k, Γ k is the state of new birth at time k;

[0019] The expression of the measurement model is:

[0020]

[0021] In formula (2), Z k represents that there are N k measurement values at time k, that is, Z j,k , j = 1, 2,..., N k , N k is the pure noise measurement set at time k, Θ k (X k ) is the measurement of the true target of state X k .

[0022] Preferably, step 2 specifically includes:

[0023] Step 2.1: Obtain all the measurement sets Z 1:k by the Bayesian formula and predict the probability density of the state X k at time k and update it;

[0024] ​Step 2.2: Assume that the distribution of parameters follows a Gaussian distribution, where the posterior intensity in the distribution assumption is the first-order matrix of the probability statistics of the target state appearance;

[0025] Step 2.3: Assume that the transition model and measurement model obtained in Step 1 follow a Gaussian distribution, the measurements generated by each target are independent of each other during evolution, and the clutter during the propagation process follows a Poisson distribution and is independent of the measurements of the target;

[0026] Step 2.4: Based on the settings in Step 2.3, convert the continuous integral into a discrete summation and perform Gaussian mixture to obtain the posterior intensity v k-1 (x);

[0027] All measurement sets Z 1:k The predicted state X at time k k The expression of the probability density is:

[0028] p k|k-1 (X k |Z 1:k-1 ) = ∫f k|k-1 (X k |X)p k-1 (X|Z 1:k-1 )μ S (dX) (3);

[0029] The update expression is:

[0030]

[0031] In formulas (3) and (4), f k|k-1 (X k |X) is the probability density of the state X at time k-1 transitioning to the state X at time k k p k (X k |Z 1:k ) is the probability density of inferring the state X at time k from all measurement sets Z 1:k μ k is the appropriate parameter, and g S (Z k |X k ) is the likelihood function of inferring the measurement Z k from the state X k , and its expression is: k In formula (5), Pr

[0032]

[0033] is the detection probability, and g(Z|X) is the target likelihood function; D ​

[0034] The expression of the first-order matrix for the statistical probability of the target state is as follows:

[0035] ∫|X∩S|p(dX) = ∫ S v(x)(dx) (6);

[0036] In formula (6), |X∩S| is the Boolean value of the intersection of state X and state set S, p is the posterior probability of state X, and v is the posterior intensity of the states in state set S.

[0037] Preferably, step 2.4 specifically includes:

[0038] Step 2.4.1: Obtain the one-step prediction intensity v k|k-1 and the one-step posterior intensity v k ;

[0039] Step 2.4.2: Combine the set conditions in step 2.3, convert the continuous integral into a discrete summation, and perform Gaussian mixture on the discrete summation result to obtain the posterior intensity v k-1 (x);

[0040] The expression of the one-step prediction intensity v k|k-1 and the one-step posterior intensity v k is as follows:

[0041] v k|k-1 (x) = ∫p S,k (ζ)f k|k-1 (x|ζ)v k-1 (ζ)(dζ) (7);

[0042]

[0043] In formulas (7) and (8), f k|k-1 (x|ζ) and g k (z|x) are obtained by combining the first set condition in step 2.3 and the target state model, and their expressions are as follows:

[0044]

[0045] g k (z|x) = N(z; H k x, R k )(10);

[0046] The expression of the discrete summation is as follows:

[0047]

[0048] In formulas (11) and (12), J γ,k is the number of newborn states, is the weight of the set newborn state, is the prior probability of state x with mean and covariance ;

[0049] The expression of Gaussian mixture is:

[0050]

[0051] In formula (13), J k-1 is the number of target states at time k-1, is the mean of the j-th state, is the covariance of the j-th state.

[0052] Preferably, step 3 specifically includes:

[0053] After obtaining the estimated number at the current time point through step 2, perform pairwise subtraction on the target number estimates of three adjacent time nodes k-2, k-1, and k;

[0054] On the basis of the moving average SMA, set the correction value U c as the threshold. If both subtraction results are not equal to the threshold, the target data estimate at the k-2 node is the mean of the target estimates at the other two times; if both subtraction results are equal to the threshold, take the mean of the target number estimates at the k-2, k-1, and k time nodes;

[0055] When both subtraction results are not equal to the threshold, the expression of the adjusted estimated number at the intermediate node k-1 is:

[0056]

[0057] When both subtraction results are equal to the threshold, the expression of the adjusted estimated number at the intermediate node k-1 is:

[0058]

[0059] The beneficial effects of the present invention are:

[0060] 1. The present invention introduces the random finite set theory. Without complex measurement-target association processing, by only updating the first moment of the target number, the multi-target tracking problem of target number change and track intersection can be solved.

[0061] 2. The present invention introduces the GMPHD algorithm. Since the multi-target posterior density is not propagated during the filtering process, the present invention adopts an approximate method to propagate with the posterior intensity function, that is, the first moment of the posterior density, with small computational amount and low complexity.

[0062] 3. The present invention adjusts the estimated number of targets at the intermediate time point by introducing a method for smoothing the number of targets and using the estimated number of targets at two consecutive time points, and adds a correction value U on the basis of the moving average SMA to solve the problem of isolated points. c , to solve the problem of isolated points. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 FIG. is a schematic flowchart of a GMPHD tracking method based on number estimation smoothing provided by the present invention;

[0064] Figure 2 FIG. is a schematic flowchart of the GMPHD algorithm provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] Combined with Figure 1 and Figure 2 to illustrate this embodiment. As Figure 1 shown, the steps of a GMPHD tracking method based on number estimation smoothing described in this embodiment include:

[0066] S1: Generate state estimation and measurement models of targets based on the theory of random finite sets;

[0067] For a filtering algorithm based on the theory of random finite sets, the PHD filtering algorithm can complete the tracking of multiple moving targets. It represents a further extension of the concept of random variables in probability theory, and the probability set involved is a set of random elements with finite values, that is, a random finite set; in this framework, the state of a single target defines the state space, and the set of measurements generated by the target and interference forms the observation vector space; based on this, the state and observation models of multiple targets can be described in the form of random sets, including the following steps:

[0068] S101: Assume that the target state at time k consists of the survival, evolution, and natural birth of the target state at time k-1. The state model of the random finite set can be expressed as:

[0069]

[0070] In formula (1), X k is the state random set at time k, representing the M k estimated states at time k, that is, X i,k , i = 1, 2,..., M k , is the state surviving to time k, is the state at time k-1 transferred to time k, and Γ k is the state of new birth at time k;

[0071] S102: Construct a measurement model for the target based on the random finite set state model. The measurement information is also limited, and the measurement model is as follows:

[0072]

[0073] In formula (2), Z k represents that there are N k measurement values at time k, that is, Z j,k , j = 1, 2,..., N k , N k is the pure noise measurement set at time k, and Θ k (X k ) is the measurement of the true target of state X k .

[0074] This embodiment introduces the random finite set theory. Without complex measurement-target association processing, by only updating the first-order moment of the number of targets, the multi-target tracking problem of target number change and track intersection can be solved.

[0075] S2: GMPHD predicts, updates, and Gaussian mixes the state estimation and measurement model of S1, and extracts the number of targets and target states;

[0076] As Figure 2 shown, S2 includes the following steps:

[0077] S201: Obtain all measurement sets Z 1:k through the Bayesian formula and predict the probability density of state X k at time k and update it;

[0078] The expression for the probability density of all measurement sets Z 1:k predicting state X k at time k is:

[0079] p k|k-1 (X k |Z 1:k-1 ) = ∫f k|k-1 (X k |X)p k-1 (X|Z 1:k-1 )μ S (dX)(3);

[0080] The update expression is:

[0081]

[0082] In formulas (3) and (4), f k|k-1 (X k |X) is the state X at time k - 1 transferring to state X at time kk The probability density, p k (X k |Z 1:k ) is for all measurement sets Z 1:k to infer the state X at time k k The probability density, μ S is the appropriate parameter, g k (Z k |X k ) is the likelihood function for inferring the measurement Z from the state X k and its expression is: k In formula (5), Pr

[0083]

[0084] is the detection probability, and g(Z|X) is the target likelihood function; D In formula (5), Pr

[0085] As can be seen from formula (5), Pr D is the detection probability, and g(Z|X) is the target likelihood function. It can be seen from the formula that the joint likelihood function grows geometrically with the increase in the number of targets and is computationally difficult. Therefore, the GMPHD method is used for simplified calculation.

[0086] The premise for using the JPDA algorithm is that prior knowledge of the targets needs to be known, such as the number of targets and the association matrix. However, in actual multi-target tracking, there will be situations where the above conditions are unknown. Therefore, the JPDA algorithm is not applicable in some actual underwater tracking scenarios. To address the above problems, the probability density hypothesis algorithm is combined with the random finite set to track multi-targets and complete the estimation of the number and state of moving targets.

[0087] S202: The Gaussian distribution is adopted as the main assumed distribution of the parameters, and the posterior intensity, which is the first-order statistical matrix of the target state occurrence probability, is:

[0088] ∫|X∩S|p(dX) = ∫ S v(x)(dx) (6);

[0089] In formula (6), |X∩S| is the Boolean value of the intersection of state X and state set S, p is the posterior probability of state X, and v is the posterior intensity of the states in state set S;

[0090] As can be seen from formula (6), the predicted number of elements in state set S is v. Considering all potential state sets comprehensively, let the total number of elements in set X be N = ∫v(x)(dx). In short, the intensity v represents the possibility of a specific set occurring, and by integrating the predicted values of the elements in all sets, the number of targets can be estimated.

[0091] S203: Make the following assumptions:

[0092] (1) The state transition equation and measurement equation of the target both follow Gaussian distributions;

[0093] (2) The measurements generated by each target are independent of each other in terms of evolution;

[0094] (3) The clutter follows a Poisson distribution and is independent of the target measurements.

[0095] According to formula (1), introduce the following parameters:

[0096] γ k (·) is the state newly born at time k, that is, the Γ part in formula (1) k β k|k-1 (·|ζ) is the intensity of the state transition of state ζ at time k - 1, that is, the B part in formula (1) k|k-1 p S,k (ζ) is the probability of state ζ surviving at time k, p D,k (ζ) is the probability of state ζ being detected at time k, n k (·) is the intensity of the clutter part in the measurement at time k, that is, the N part in formula (2) k part.

[0097] Combining the prediction and update formulas, the one-step prediction intensity v k|k-1 and the posterior intensity v k are

[0098] v k|k-1 (x) = ∫p S,k (ζ)f k|k-1 (x|ζ)v k-1 (ζ)(dζ)(7);

[0099]

[0100] According to assumption (1) and the target state model, we can obtain:

[0101]

[0102] g k (z|x) = N(z; H k x, R k )(10);

[0103] Through the assumption that the target state set has only a finite number and is discrete, the continuous integral can be transformed into a discrete sum, and we can obtain:

[0104]

[0105] In formulas (11) and (12), Jγ,k is the number of newborn states, is the weight of the set newborn state, is the prior probability that state x is at the mean and covariance ;

[0106] S204: Based on the setting in step S203, convert the continuous integral into a discrete sum and perform Gaussian mixture to obtain the posterior intensity v k-1 (x);

[0107]

[0108] In formula (13), J k-1 is the number of target states at time k - 1, is the mean of the j-th state, is the covariance of the j-th state.

[0109] This embodiment introduces the GMPHD algorithm. Since the multi-target posterior density is not propagated during the filtering process, the present invention uses an approximation method, propagating with the posterior intensity function, i.e., the first moment of the posterior density, which has a small computational amount and low complexity.

[0110] S3: Based on the method of smoothing the target number, adjust the target number estimation result at the intermediate time node and output the target estimation values at all time nodes;

[0111] This embodiment uses the target number estimations at two consecutive time points to adjust the target number estimation result at the intermediate time point. Based on the simple moving average (SMA), a correction value U c is added to solve the problem of isolated points, specifically including:

[0112] Based on the simple moving average (SMA), set the correction value U c as the threshold. If the results of both differences are not equal to the threshold, the target number estimation at the k - 2 node is the mean of the target estimations at the other two moments; if the results of both differences are equal to the threshold, take the mean of the target number estimations at the k - 2, k - 1, and k time nodes;

[0113] When the results of both differences are not equal to the threshold, the expression for the adjusted target estimation at the intermediate node k - 1 is:

[0114]

[0115] When the results of both differences are equal to the threshold, the expression for the adjusted target estimation at the intermediate node k - 1 is:

[0116]

[0117] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the above-disclosed technical content within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modifications, equivalent replacements, and improvements made to the above embodiments within the spirit and principles of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A GMPHD tracking method based on number estimation smoothing, characterized in that, The steps of the GMPHD tracking method based on number estimation smoothing include: Step 1: Introduce the random finite set theory into the PHD filtering algorithm to perform multi-target tracking in the underwater scenario, and obtain the state estimation and measurement model of the target. Step 2: Introduce the GMPHD algorithm, use the approximation method and the posterior intensity function to propagate the filtering process in the PHD filtering algorithm to obtain the posterior intensity, where the GMPHD algorithm is the Gaussian mixture probability hypothesis algorithm. Step 3: Extract the target number and target state according to the posterior intensity, and use the target number estimation at two consecutive time points to adjust the target number estimation result at the intermediate time node by smoothing the target number method, and output the target estimation values at all time nodes.

2. The GMPHD tracking method based on number estimation smoothing according to claim 1, wherein Step 1 specifically includes: Step 1.1: Set that the target state at time k includes the survival, evolution, and natural birth of the target state at time k - 1, and construct the transition model of the random finite set. Step 1.2: Construct the measurement model of the target based on the random finite set state model. The expression of the random finite set state model is: In formula (1), X k is the state random set at time k, representing the M k estimated states at time k, that is is the state surviving to time k, is the state at time k - 1 transferred to time k, Γ k is the newly born state at time k; The expression of the measurement model is: In formula (2), Z k represents that there are N k measurement values at time k, i.e., Z j,k , j = 1, 2,..., N k , and N k is the set of pure noise measurements at time k, and Θ k (X k ) is the measurement of the true target of state X k .

3. A GMPHD tracking method based on number estimation smoothing according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Obtain all measurement sets Z through Bayes' formula 1:k Predict the state X at time k k and update its probability density; Step 2.2: Use the Gaussian distribution as the distribution hypothesis of the parameters, where the posterior intensity in the distribution hypothesis is the first-order matrix of the target state appearance probability statistics. Step 2.3: Set that the transition model and measurement model obtained in Step 1 conform to the Gaussian distribution, the measurements generated by each target are independent of each other during evolution, and the clutter during the propagation process follows the Poisson distribution and is independent of the measurements of the target. Step 2.4: Based on the setting in Step 2.3, convert the continuous integral into a discrete summation and perform Gaussian mixture to obtain the posterior intensity v k-1 (x); All measurement sets Z 1:k The predicted state X at time k k The expression for the probability density is as follows: p k|k-1 (X k |Z 1:k-1 ) = ∫ f k|k-1 (X k |X) p k-1 (X|Z 1:k-1 ) μ S (dX)(3); The expression of the update is: In formulas (3) and (4), f k|k-1 (X k |X) is the state X at time k-1 and transfers to the state X at time k k The probability density, p k (X k |Z 1:k ) is the set of all measurements Z 1:k Infer the state X at time k k The probability density of S is an appropriate parameter, g k (Z k |X k ) is from state X k Inferred measurement Z k The likelihood function of is expressed as: In formula (5), Pr D is the detection probability, and g(Z|X) is the target likelihood function; The expression of the first-order matrix of the target state appearance probability statistics is: ∫|X∩S|p(dX) = ∫ S v(x)(dx) (6); In formula (6), |X ∩ S| is the Boolean value of the intersection of state X and state set S, p is the posterior probability of state X, and v is the posterior intensity of the state in state set S.

4. A GMPHD tracking method based on number estimation smoothing according to claim 3, characterized in that Step 2.4 specifically includes: Step 2.4.1: Obtain the one-step prediction intensity v by combining the prediction and update expressions in Step 1.3 k|k-1 and the one-step posterior intensity v k ; Step 2.4.2: Combine the set conditions in Step 2.3, convert the continuous integral into a discrete summation, perform Gaussian mixture on the discrete summation result, and obtain the posterior intensity v k-1 (x); One-step predicted intensity v k|k-1 and one-step posterior intensity v k are expressed as follows: v k|k-1 (x) = ∫ p S,k (ζ) f k|k-1 (x|ζ) v k-1 (ζ) (dζ) (7); In Formulas (7) and (8), f k|k-1 (x|ζ) and g k (z|x) are obtained by combining the first set condition in Step 2.3 and the target state model, and their expressions are as follows: g k (z|x) = N(z; H k x, R k )(10); The expression of the discrete summation is: In Formulas (11) and (12), J γ,k is the number of newborn states, is the weight of the set newborn states, is the prior probability that state x is at the mean and covariance ; The expression of the Gaussian mixture is: In formula (13), J k-1 is the number of target states at time k-1, is the mean of the j-th state, is the covariance of the j-th state.

5. A GMPHD tracking method based on number estimation smoothing according to claim 1, characterized in that, Step 3 specifically includes: After obtaining the estimated number at the current time point through Step 2, take the pairwise differences of the target number estimations at three adjacent time nodes k - 2, k - 1, and k. Based on the simple moving average (SMA), a correction value U is set. c As a threshold, if both of the difference results are not equal to the threshold, the estimated target number at the k - 2 node is the average of the target estimates at the other two times; if both of the difference results are equal to the threshold, the average of the target number estimates at the k - 2, k - 1, and k time nodes is taken. When both of the two difference results are not equal to the threshold, the expression of the adjusted target estimation number at the intermediate node k - 1 is: When both of the two difference results are equal to the threshold, the expression of the adjusted target estimation number at the intermediate node k - 1 is:

Images