CN107831490A

CN107831490A - A kind of improved more extension method for tracking target

Info

Publication number: CN107831490A
Application number: CN201711249650.XA
Authority: CN
Inventors: 吴盘龙; 邓宇浩; 何山; 王雪冬; 肖仁强; 曹竞丹
Original assignee: Nanjing University of Science and Technology
Current assignee: Nanjing University of Science and Technology
Priority date: 2017-12-01
Filing date: 2017-12-01
Publication date: 2018-03-23

Abstract

The invention discloses a kind of improved more extension method for tracking target.This method step is：Clustering, and the probability hypothesis density of initialized target and gesture distribution are carried out to the metric data collection of sensor first；Then dbjective state collection is predicted and updated in probability hypothesis density and the gesture distribution of subsequent time, obtain probability hypothesis density and the gesture distribution at this moment；Then trimming merging is carried out to the Gaussian term of the intensity function of target, extracts Target state estimator, carry out Performance Evaluation；Repeat forecast updating and trimming merges, tracking target disappears until target.The present invention improves the target tracking accuracy under clutter environment, loss of significance caused by reducing radar shadown, reduces the amount of calculation of wave filter, is advantageous to the engineer applied of GM CPHD wave filters.

Description

Improved multi-extension target tracking method

Technical Field

The invention belongs to the field of target tracking, and particularly relates to an improved multi-extension target tracking method.

Background

With the widespread application of high-resolution sensors, the research of Extended Target Tracking (ETT) technology has become a hot spot. In particular, with the increasing resolution of radar, multiple measurements of different equivalent scattering centers of the same target can be received at each time, and at this time, the target is not a point target any longer, but an extended target. In recent years, professor Ronald p.s.mahler has proposed a Probabilistic Hypothesis Density (PHD) filtering algorithm based on the Random Finite Set (RFS) theory, which can simultaneously achieve the estimation of the target number and the target state without considering data correlation. It first tracks the entire target population and then goes to detect each variable. However, the PHD filtering has the problems of sensitive omission and infinite distribution. In order to solve the problems, a potential probability hypothesis density (CPHD) filter is generated, and compared with a PHD filter, the CPHD filter can update the potential distribution of the target, and is particularly suitable for the problem of multi-extended target tracking (METT).

Measurement set division is one of the key problems to be solved in multi-extended target tracking, and theoretically, an extended target filter based on RFS needs to consider all possible divisions of a measurement set, but the number of all possible divisions increases rapidly with the increase of the number of targets. Granstrm et al have first proposed partitioning measurement sets using methods such as distance partitioning, K-means, predictive partitioning, and expected maximum partitioning, but these methods all have some problems. The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a classic representation Based on a Density algorithm, can divide areas with high enough Density into clusters, can find clusters with any shapes in a Noise Spatial database, and is suitable for extended target tracking in a clutter environment.

In the actual radar measurement information, especially when the target is extended to track, a doppler blind area inevitably exists and causes the loss of part of the target measurement information, thereby affecting the filtering precision. Therefore, it is necessary to maintain the filtering accuracy in the case of target measurement data loss (radar blind area); secondly, while the tracking precision is improved, the computation complexity of the CPHD filter is much greater than that of the PHD filter, so that the computation complexity of the algorithm needs to be optimized; finally, the problem of combining the DBSCAN algorithm with the CPHD filter also needs to be solved. In summary, in the actual radar measurement information, there are problems of multiple extended target measurement set division, measurement data loss and complex calculation,

disclosure of Invention

The invention aims to provide an improved multi-extension target tracking method with simple calculation and high precision, thereby improving the multi-extension target tracking performance.

The technical solution for realizing the purpose of the invention is as follows: an improved multi-extension target tracking method comprises the following steps:

step 1, clustering: clustering and dividing a measurement data set of the sensor;

step 2, initialization: probability hypothesis density of initial target D ₀ (x) And potential distribution p ₀ (n)；

Step 3, prediction updating: for target state set X _k Predicting and updating the probability hypothesis density and the potential distribution at the moment k +1 to obtain the probability hypothesis density D at the moment _k+1 (x) And potential distribution p _k+1 (n), wherein k is not less than 1;

step 4, pruning and combining: pruning and merging Gaussian terms of the intensity function of the target, extracting target state estimation and performing performance evaluation;

and 5, repeating the steps 3-4, and tracking the target until the target disappears.

Further, the clustering division of the measurement data set of the sensor in step 1 specifically includes the following steps:

1.1 Two parameters of the DBSCAN algorithm are initialized: radius parameter Be and neighborhood density threshold MinPts;

δ neighborhood of subject p: for a data space, that is, any data object p in the measured data set, its σ neighborhood is a set of objects in a circular area with p as the center of circle and σ as the radius, and is recorded as

Nб(p)＝{q|q∈D∩d(p,q)<б}

Wherein D is the metrology data set and D (p, q) is the distance between the object p and the point q;

core object: if at least MinPts objects are contained in the Be neighborhood of the object p, the object p is a core object;

the direct density can reach: for sample set D, if sample point q is within the sigma domain of p, and p is the core object, then object q is directly density reachable from object p;

the density can reach: for a sample set D, a string of sample points p is given ₁ ，p ₂ ….p _n Wherein p = p ₁ ，q＝p _n If the object p _i From p _i-1 The direct density is reachable, then object q is reachable from object p density;

density connection: for a point o in the sample set D, if object o through object p and object q are density reachable, then p and q are density-linked;

density-based clusters: a set of maximum density-connected objects based on density reachability;

1.2 Input measurement data set D), randomly extracting an unprocessed object p from the data set D, counting the number of objects in the sigma neighborhood of p, if the number of the objects in the sigma neighborhood of p reaches MinPts, marking p as a core object, otherwise marking the object p as processed, and extracting the next unprocessed object p from the data set D for counting;

1.3 Traversing the measurement data set D, recording all core objects, finding out density reachable objects of all the core objects, forming a new cluster, and further obtaining a final cluster result through density connection;

1.4 Update the measured data set D, and replace the previous measured data set D with the final cluster result to complete the clustering step.

Further, the prediction update in step 3 specifically includes the following steps:

3.1 Prediction: for target state set X _k Probability hypothesis density D at time k +1 _k+1|k (x) And potential distribution p _k+1|k (n) predicting:

at time k, the known parameters are: density of probability hypotheses D _k (x) Desired n of number of targets _k Potential distribution p _k (x) Then the target state set X survived at time k _k The probability hypothesis density of (a) is:

D _k+1|k (ξ)＝∫p _s (x')·f _k+1 |k(x|x')·D _k|k (x')dx'

wherein: p is a radical of _s (x') is the target survival probability, f _k+1|k (x | x') is the single target markov transfer density; d _k|k (X') is the target state set X at the previous time _k A probability hypothesis density of;

potential distribution p _k+1|k (n) is:

wherein:is the weight of the jth target, N _max Is the maximum possible number of potential distributions, p _k (l) The target survival probability for the previous time instant i.e. time k,is a binomial coefficient;

3.2 Update: for target state set X _k Probability hypothesis density D at time k +1 _k+1 (x) And potential distribution p _k+1 (n) updating:

intensity function upsilon in predicting target state _k+1|k (x) And potential distribution p _k+1|k Known conditionsNext, the update equation of the CPHD filter is obtained as follows:

and (3) potential distribution updating:

updating the intensity function of the target state:

updating the target number:

wherein

Wherein, delta _j (. Is a balancing function, k _k (. Cndot.) is a function of clutter intensity,the number of targets at time k is,predicted value of target number at time k +1, p _D,k+1 For the target detection probability, H is the measurement matrix,in order to target the state covariance matrix,is the mean of the individual gaussian components in the GM-CPHD function,for measurement bias, R is the measurement covariance.

Further, the prediction update in step 3 is specifically as follows:

a) Introduction of a scaling factor

Doppler shift f of moving object in three-dimensional coordinate system _d Expressed as:

wherein V _t And V _a Respectively the moving speeds of the target and the carrier, phi is the deflection angle between the carrier route and the radar, and beta is the course deflection angle between the target and the carrier;

doppler blind area f _d Is less than or equal to delta f, the Doppler blind area is [ -delta f, delta f]The target doppler shift is:

wherein v is _r Is the radial velocity of the target relative to the sensor, f ₀ Is the emission frequency of the target radiation source, c is the propagation speed of the target radiation source signal;the components of the target velocity vector in the x, y, z directions, respectively; the components of the speed vector of the carrier in the directions of x, y and z are respectively;

based on GM-CPHD algorithm framework, combining DBSCAN clustering, providing a DBSCAN-CPHD filtering algorithm, specifically comprising the following steps:

firstly, clustering and dividing a measurement data set of a sensor by adopting a DBSCAN algorithm;

then, adding an n-dimensional square matrix lambda (k) in the gain matrix calculation formula to adjust the gain matrix of the GM-CPHD filter to obtain:

S(k+1)＝H(k+1)P(k+1|k)H ^T (k+1)+(λ(k)-I)R ₀ (k+1)+R(k+1)

wherein I is a unit matrix, R ₀ (k + 1) is a diagonal matrix, which takes the value of the diagonal element of R (k + 1), and H is an observation matrix;

wherein, the calculation formula of S (k + 1) is as follows:

xi is the number of sliding windows, e (k + 1) is the measurement error vector;

finally, λ (k) is calculated:

let the gain adjustment matrix be λ ^* (k) The formula is obtained as follows:

in the formula of lambda _ii (k) I row and i column elements of λ (k), i.e. the ith element on the diagonal of λ (k);

b) Design of adaptive threshold

Firstly, setting a threshold gamma:

wherein, P _D For detection probability, β is the new source density;

from the formula, the threshold γ is related to the residual covariance matrix S (k), and S (k) is a variable;

then, the measurement set of the threshold area is expressed as:

finally, since the measurement set is composed of Z _k Is changed intoThe resulting clutter intensity function changes toThen:

wherein the content of the first and second substances,for new measurement zone volumes, M _new And lambda is the number of clutter in the unit volume and the number of targets tracked by N.

Further, the pruning and merging of the gaussian terms of the intensity function of the target, extracting the target state estimation, and performing the performance evaluation in step 4 are specifically as follows:

trimming: filtering out Gaussian components smaller than the weight tau;

merging: when the distance between the Gaussian components is smaller than a threshold value U, combining the Gaussian components;

and (3) state estimation: the extraction weight is greater than tau ₁ The gaussian component of (a);

performance evaluation: and evaluating a target tracking result by using the OSPA distance error as an index.

Compared with the prior art, the invention has the remarkable advantages that: (1) A DBSCAN algorithm is introduced under a Gaussian mixture potential probability hypothesis density filtering framework, the problem that a GM-CPHD filter is difficult to effectively track multiple extended targets is solved, and the target tracking precision under a clutter environment is improved; (2) Due to the introduction of a scale factor and the design of a self-adaptive threshold, the problems of measurement data loss and calculation complexity optimization are solved, the multi-extension target tracking performance is improved, and the engineering application of the GM-CPHD filter becomes possible.

Drawings

Fig. 1 is a general flow diagram of the improved multiple extended target tracking method of the present invention.

FIG. 2 is a schematic diagram of target metrology information in accordance with the present invention.

FIG. 3 is a three-dimensional graph of the filtering results of the present invention and the conventional method.

Fig. 4 is a two-dimensional detail of the filtering result of the present invention.

FIG. 5 is a graph of the number of targets estimated by the present invention and conventional methods.

FIG. 6 is a graph comparing the time taken for the operation of the present invention with the conventional algorithm.

Figure 7 is an OSPA distance map for each algorithm.

FIG. 8 is an enlarged view of the OSPA distance of the algorithm of the present invention.

Detailed Description

With reference to fig. 1, the improved multi-extended target tracking method of the present invention introduces a DBSCAN algorithm to divide measurement sets in a measurement set processing process under a gaussian mixture potential probability hypothesis density (GM-CPHD) filtering framework, thereby achieving a function of tracking extended targets; and then, the gain matrix and the observation volume of the filter are respectively adjusted by utilizing the scale factor and the adaptive threshold, so that the robustness of the filter is improved, and the calculated amount is reduced. The method comprises the following specific steps:

step 1, clustering: and clustering and dividing the measurement data set of the sensor.

And (3) clustering and dividing the measurement data set of the sensor by adopting a DBSCAN algorithm:

first, two parameters of the DBSCAN algorithm are initialized, namely a radius parameter sigma and a neighborhood density threshold MinPts.

Nб(p)＝{q|q∈D∩d(p,q)<б}

the density can reach: for a sample set D, a string of sample points p is given ₁ ，p ₂ ….p _n Wherein p = p ₁ ，q＝p _n If the object p _i From p _i-1 Direct density is reachable, then object q is reachable from object p density;

density connection: for a point o in the sample set D, if object o to object p and object q are both density reachable, then p and q are density linked;

density-based clusters: a set of maximum density connected objects based on density reachability.

Then, inputting a measurement data set D, randomly extracting an unprocessed object p from the data set D, counting the number of objects in sigma neighborhood of p, if the number of objects in sigma neighborhood of p reaches MinPts, marking p as a core object, otherwise marking the object p as processed, and extracting a next unprocessed object p from D for counting.

And finally, traversing the measurement data set D, recording all the core objects, finding out all the density reachable objects of the core objects, forming a new cluster, and further obtaining a final cluster result through density connection. And finally, updating the measurement data set D, and replacing the previous measurement data set D with the obtained final clustering result to finish the clustering step.

Aiming at the phenomenon of white gaussian noise of multiple extended targets, in the DBSCAN algorithm, the final cluster does not contain noise data by setting a reasonable radius parameter sigma and a neighborhood density threshold MinPts, so that the denoising effect is achieved.

Step 2, initialization: probability hypothesis density D of initialization target ₀ (x) And potential distribution P ₀ (n) in the formula (I). Initial probability hypothesis density D ₀ (x) Fitting Gaussian distribution, and being represented by normal distribution probability sum of each target; potential distribution P ₀ (n) is the probability distribution of the target number n.

Step 3, prediction updating:

3.1 Prediction: for target state set X _k Probability hypothesis density D at time k +1 _k+1|k (x) And potential distribution p _k+1|k (n) performing a prediction. At time k, the known parameters are: probability hypothesis density D _k (x) Desired n of target number _k Potential distribution p _k (x) Then the target state set X survived at time k _k The probability hypothesis density of (a) is:

D _k+1|k (ξ)＝∫p _s (x')·f _k+1 |k(x|x')·D _k|k (x')dx'

wherein: p is a radical of _s (x') is the target survival probability, f _k+1|k (x | x') is the single target markov transfer density; d _k|k (X') is the target state set X at the previous time _k The probability of (c) assumes a density.

Potential distribution p _k+1|k (n) is:

wherein:is the weight of the jth target, N _max Is the maximum possible number of potential distributions, p _k (l) The target survival probability for the previous time instant i.e. time k,are binomial coefficients.

3.2 Update: for target state set X _k Probability hypothesis density D at time k +1 _k+1 (x) And potential distribution p _k+1 (n) updating. Intensity function upsilon in predicted target state _k+1|k (x) And potential distribution p _k+1|k The update equation for the CPHD filter can be obtained, given the known case, as follows:

and (3) potential distribution updating:

updating the intensity function of the target state:

updating the target number:

wherein

Wherein, delta _j (. Cndot.) is an equalization function, κ _k (. Cndot.) is a function of clutter intensity,the number of targets at time k is,predicted value of target number at time k +1, p _D，k+1 For the target detection probability, H is the measurement matrix,in order to target the state covariance matrix,is the mean of the individual gaussian components in the GM-CPHD function,for measurement bias, R is the measurement covariance.

a) Introduction of a scaling factor

In the actual radar measurement information, particularly in extended target tracking, a doppler blind area inevitably exists and causes loss of part of target measurement information, thereby affecting the filtering accuracy. Therefore, the filtering precision of the target measurement data needs to be maintained under the condition of loss (radar blind area), and the influence of the algorithm on the filtering precision when the target data is lost can be reduced by introducing a scale factor to adjust a gain matrix of the filtering algorithm.

In a three-dimensional coordinate system, the doppler shift of a target in motion can be expressed as:

wherein V _t And V _a The moving speeds of the target and the carrier are respectively, phi is a deflection angle between a carrier route and the radar, and beta is a course deflection angle between the target and the carrier.

Doppler blind area | f _d Is less than or equal to delta f, and the Doppler blind zone is [ -delta f, delta f]The target doppler shift is:

wherein v is _r Is the radial velocity of the target relative to the sensor, f ₀ Is the emission frequency of the target radiation source, c is the propagation speed of the target radiation source signal,the components of the target velocity vector in the x, y, z directions, the components of the carrier velocity vector in the x, y, z directions, respectively.

Based on the above, the invention provides a robust DBSCAN-CPHD filtering algorithm based on a GM-CPHD algorithm framework and combined with DBSCAN clustering, which comprises the following specific steps:

firstly, clustering and dividing a measurement data set of the sensor by adopting a DBSCAN algorithm.

Then, an n-dimensional square matrix λ (k) is added to the gain matrix calculation formula to adjust the gain matrix of the GM-CPHD filter, so as to obtain:

S(k+1)＝H(k+1)P(k+1|k)H ^T (k+1)+(λ(k)-I)R ₀ (k+1)+R(k+1)

wherein I is a unit matrix, R ₀ (k + 1) is a diagonal matrix, which takes the value of the diagonal element of R (k + 1), and H is an observation matrix.

Wherein, the calculation formula of S (k + 1) is as follows:

ξ is the number of sliding windows and e (k + 1) is the measurement error vector.

Finally, λ (k) is calculated:

let the gain adjustment matrix be λ ^* (k) The formula is obtained as follows:

in the formula, λ _ii (k) Is the i row and i column element of λ (k), i.e. the i-th element on the diagonal of λ (k).

Adding a scale factor lambda into a GM-CPHD framework ^* (k) When the error between the predicted data and the measured data is large, the scale factor lambda is ^* (k) The gain matrix is adjusted through the previous target data information, the influence of data loss caused by a blind area on a filtering estimated value and covariance is reduced, and the robustness of the algorithm is improved.

b) Design of adaptive threshold

As a classic multi-target tracking algorithm, the CPHD algorithm is improved in tracking precision and simultaneously is accompanied with the improvement of computational complexity, and the computational complexity of the CPHD and PHD filters is O (NM) ³ ) And O (NM). Therefore, for a CPHD filter, reducing the number of measurements (M) in the data set can more effectively reduce the computational complexity, while the adaptive threshold can reduce the value of M. The method comprises the following specific steps:

firstly, setting a threshold gamma:

wherein, P _D For detection probability, β is the new source density; as can be seen from the formula, the threshold γ is related to the residual covariance matrix S (k), which is a variable.

The measurement set of threshold regions is then expressed as:

finally, since the measurement set is composed of Z _k Is changed intoThe resulting clutter intensity function varies asThen:

wherein, the first and the second end of the pipe are connected with each other,for new measurement zone volumes, M _new And lambda is the number of clutter in a unit volume and the number of targets tracked by N for the new measurement number.

Reducing the measurement set Z by designing an adaptive threshold _k Thereby affecting the clutter intensity function κ _k (z) further reducing the volume V of the measurement region _k The measurement number M is reduced, and the purpose of reducing the calculation complexity of the filter is achieved.

Step 4, pruning and combining: and pruning and merging the Gaussian terms of the intensity function of the target, extracting target state estimation and carrying out performance evaluation.

Firstly, trimming: gaussian components smaller than the weight τ are filtered out.

Then merging: some gaussian components are merged when the distance between them is less than a threshold U.

And finally, state estimation: the state estimation of the target is to extract the weight value larger than tau ₁ The gaussian component of (2).

Performance evaluation: and evaluating the performance of the multi-target tracking algorithm by using the OSPA distance error as an index. The OSPA distance is defined as follows:

wherein, the first and the second end of the pipe are connected with each other,

Example 1

The effect of the invention can be further illustrated by the following simulation experiment:

1. simulation conditions

Setting target stateWhere the position unit is m and the velocity unit is m/s. The simulation has four targets, the target motion model comprises a turning (CT) model and a Jerk model, and the initial states of the four targets are as follows:

X _t1 ＝[3000,3000,2400,-30,-30,-10,-0,-0,0.4,0,0,-0.01] ^T ；

X _t2 ＝[2000,1000,1600,30,30,15,-1,-1,0,0,0,-0] ^T ；

X _t3 ＝[2000,1000,1600,30,30,15,-1,-1,0,0.01,0,-0.01] ^T ；

X _t4 ＝[4000,2000,2100,-20,-30,-10,1,1,0,0,0,0.01] ^T ；

for different motion models, the motion equations of the object are respectively:

jerk model:

and (3) CT model:

in the formula: p1= (2-2 x alpha T + alpha ^2-2 x exp (-alpha x T))/(2 x alpha ^ 3);

q1＝(exp(-alpha*T)-1+alpha*T)/alpha^2；

r1＝(1-exp(-alpha*T))/alpha；

s1= exp (-alpha x T); alpha is the maneuvering frequency and ω is the angular velocity, in this case 0.1 and 0.5, respectively.

The simulation experiment assumes that the existing time of each target is t ₁ ＝1-60s，t ₂ ＝14-100s，t ₃ =30-80s, and t ₄ =39-100s. The motion model of each target in each time period is target ₁ In the range of 1 to 26s&40-60 s are CT models, and 26-40 are Jerk models; target ₂ The CT model is obtained in 14-100 s; target ₃ In the range of 30 to 50s&CT model in 65-80 s and Jerk model in 50-65 s; target ₄ The Jerk models are all in 39-100s. Let radar sampling period T =1s, detection probability P _D =0.99, target survival probability P _S =0.9, state estimation threshold τ ₁ =0.5, maximum number of gausses J _max ＝100。

2. Simulation content and result analysis

The generated target measurement information is shown in fig. 2, and the measurement information includes target information and clutter information.

The ratio of the estimated target position of each algorithm to the removed measured value and the actual value is shown in fig. 3. In the figure, CPHD represents a multi-extended target tracking method based on DBSCAN provided by the invention, CPHD2 represents UCM-AG-CPHD under the condition of adding blind areas, CPHD3 represents improved R-UCM-AG-CPHD (a multi-target tracking method under the condition of measuring data loss) (patent application number 201610816184.8)), and PHD represents a traditional Gaussian mixture probability hypothesis density filter algorithm (GM-PHD). As can be seen from the figure, in the four algorithms, the PHD algorithm tracking has larger deviation, the effect is not ideal enough, and the other three algorithms based on the CPHD framework can effectively track each target.

The two-dimensional tracks of each target are shown in fig. 4, the black dots represent the filtering effect of the algorithm (CPHD) of the invention, and it can be seen from the figure that the algorithm has very good tracking accuracy on the first three targets, and the Jerk model effect on the target 4 is reduced, because the motion characteristics of the target 4 are changed, and when 65s,75s,83s and 93s, the acceleration and maneuvering frequency of the target 4 are changed, so that the tracking accuracy is influenced.

The result of the number of targets estimated at each moment of the algorithm is shown in fig. 5, and it can be seen from the figure that the estimation accuracy of the algorithm (CPHD) of the present invention to the number of targets reaches 98%, while the estimation accuracy of the other three algorithms is less than 80%.

The time consumption of the algorithm and the traditional GM-CPHD algorithm obtained through a Monte Carlo experiment is shown in figure 6, the self-adaptive threshold of the algorithm DBSCAN-RAG-CPHD reduces 9.6% of the calculation complexity of the original algorithm, and compared with other algorithms, the algorithm has better engineering application prospect.

It can be seen from the OSPA distance result fig. 7 that the OSPA distance error of the algorithm (CPHD) of the present invention is the smallest, and the tracking precision is the highest (the amplification is shown in fig. 8), which reflects that the clustering DBSCAN algorithm improves the tracking precision of the extended target; an improved post-blind area R-UCM-AG-CPHD (a multi-target tracking method under the condition of loss of measured data) (patent application number 201610816184.8)) represented by CPHD3 has the following tracking precision; the GM-PHD algorithm represented by PHD has the lowest tracking accuracy, and the OSPA distance error is increasing and diverging. When 16-18s, 26-28s, 31-33 s and 36-38 s target data are lost, the OSPA distance errors of the algorithm (CPHD) and the CPHD3 are not obviously changed, which shows that the scale factor plays a good role in improving the tracking precision, the OSPA distance errors of the backsight CPHD2 and PHD algorithms in a data loss section are obviously increased, and the simulation shows that the improved algorithm has a good effect on a blind zone generated by target maneuvering, and can achieve higher tracking precision for expanding a target.

In conclusion, the improved multi-extended target tracking method provided by the invention overcomes the problem that a GM-CPHD filter is difficult to effectively track multi-extended targets, improves the target tracking precision in a clutter environment, reduces the precision loss caused by a radar blind area, reduces the calculated amount of the filter, and is beneficial to the engineering application of the GM-CPHD filter.

Claims

1. An improved multi-extension target tracking method is characterized by comprising the following steps:

Step 3, prediction updating: for target state set X _k Predicting and updating the probability hypothesis density and the potential distribution at the moment of k +1 to obtain the probability hypothesis density D at the moment _k+1 (x) And potential distribution p _k+1 (n), wherein k is not less than 1;

step 4, pruning and combining: pruning and merging Gaussian terms of the strength function of the target, extracting target state estimation, and performing performance evaluation;

2. The improved multi-extension target tracking method as claimed in claim 1, wherein the clustering partitioning is performed on the measured data sets of the sensors in step 1, and the specific steps are as follows:

1.1 Two parameters of the DBSCAN algorithm are initialized: radius parameter 6 and neighborhood density threshold MinPts;

6 neighborhoods of object p: for the data space, i.e. any data object p in the measured dataset, the 6 neighborhoods are the set of objects in the circular area with p as the center and 6 as the radius, and are marked as

N6(p)＝{q|q∈D∩d(p,q)<6}

the core object is: if the 6 neighborhoods of the object p at least comprise MinPts objects, the object p is a core object;

the direct density can reach: for sample set D, if sample point q is within 6 fields of p and p is the core object, then object q is directly density reachable from object p;

the density can reach: for a sample set D, a string of sample points p is given ₁ ，p ₂ ….p _n Wherein p = p ₁ ，q＝p _n If the object p _i From p to p _i-1 Direct density is reachable, then object q is reachable from object p density;

1.2 Input a measured data set D, randomly extract an unprocessed object p from the data set D, count the number of objects in the 6 neighborhoods of p, if the number of the objects in the 6 neighborhoods of p reaches MinPts, mark p as a core object, otherwise mark the object p as processed, extract the next unprocessed object p from the data set D for counting;

3. The improved multi-extension target tracking method according to claim 1, wherein the prediction update in step 3 specifically comprises the following steps:

at time k, the known parameters are: probability hypothesis density D _k (x) Desired n of target number _k Potential distribution p _k (x) Then the target state set X survived at time k _k The probability hypothesis density of (a) is:

D _k+1|k (ξ)＝∫p _s (x')·f _k+1|k (x|x')·D _k|k (x')dx'

wherein: p is a radical of formula _s (x') is the target survival probability, f _k+1|k (x | x') is the single target markov transfer density; d _k|k (X') is the previous time target state set X _k A probability hypothesis density of (c);

potential distribution p _k+1|k (n) is:

intensity function upsilon in predicting target state _k+1|k (x) And potential distribution p _k+1|k In the known case, the update equation for obtaining the CPHD filter is as follows:

and (3) potential distribution updating:

updating the intensity function of the target state:

updating the target number:

wherein

4. The improved multi-extension target tracking method according to claim 3, wherein the prediction update in step 3 is specifically as follows:

a) Introduction of a scaling factor

wherein V _t And V _a Respectively the moving speeds of the target and the carrier, phi is the deflection angle between the carrier flight path and the radar, and beta is the course deflection angle between the target and the carrier;

doppler blind area f _d Is less than or equal to delta f, the Doppler dead zone is [ -delta f, delta f]The target doppler shift is:

based on a GM-CPHD algorithm framework and combined with DBSCAN clustering, a DBSCAN-CPHD filtering algorithm is provided, and the method specifically comprises the following steps:

then, adding an n-dimensional square matrix lambda (k) in the gain matrix solving formula to adjust the gain matrix of the GM-CPHD filter to obtain:

S(k+1)＝H(k+1)P(k+1|k)H ^T (k+1)+(λ(k)-I)R ₀ (k+1)+R(k+1)

wherein, the calculation formula of S (k + 1) is as follows:

xi is the number of sliding windows, e (k + 1) is the measurement error vector;

finally, λ (k) is calculated:

let the gain adjustment matrix be λ ^* (k) The formula is obtained as follows:

in the formula, λ _ii (k) I rows and i columns of elements which are λ (k), i.e. the ith element on the diagonal of λ (k);

b) Design of adaptive threshold

Firstly, setting a threshold gamma:

wherein, P _D For detection probability, β is the new source density;

as can be seen from the formula, the threshold γ is related to the residual covariance matrix S (k), and S (k) is a variable;

then, the measurement set of the threshold area is expressed as:

5. The improved multi-extension target tracking method according to claim 1, wherein the gaussian term of the intensity function of the target is pruned and combined in step 4, the target state estimation is extracted, and the performance evaluation is performed, specifically as follows:

trimming: filtering out Gaussian components smaller than the weight tau;