CN106468771A - A kind of multi-target detection and tracking method under the high clutter conditions of low Observable - Google Patents

Abstract

Multi-target detection and tracking method under a kind of high clutter conditions of low Observable of this disclosure of the invention, belongs to radar and sonar technique field.The thinking of the present invention is, when processing the related question between target measurement, consider that the multiple measurements reaching receptor by different propagation paths are that possible target measures, and these measurements are correctly associated with known each many diameter measurings function respectively, thus obtaining the accumulation of target information, strengthen target detection capabilities；Then carry out target following by way of sliding window.Present invention utilizes reach the target information of sensor by different approaches, and these measurement informations are correctly associated with known each many diameter measurings function respectively, thus obtaining the accumulation of target information, strengthen target in low Observable, power of test under high clutter environment, can effectively reduce the impact between adjacent target.

Description

A kind of multi-target detection and tracking method under the high clutter conditions of low Observable

Technical field

The invention belongs to radar and sonar technique field, relate generally to maximum likelihood-probability multiple hypotheis tracking (ML-PMHT) Extended method.

Technical background

Target following technology is widely used in each field, particularly radar (sonar) signaling system.And target following skill Art follows the tracks of (TBD) two big class before following the tracks of (TAD) and detection after being divided into detection, and comparatively speaking, TAD algorithm amount of calculation is relatively low, profit In real-time implementation, but because TAD algorithm depends on the detection to target for the front end signal processor, in low signal-to-noise ratio (SNR) situation Lower tracking performance is undesirable.TBD algorithm due to follow the tracks of while add target detection, therefore to target under low signal-to-noise ratio There is stronger ability of tracking, but lead to TBD algorithm to be applied in engineering by the restriction of amount of calculation and much limited.

The basic thought that TBD algorithm realizes target detection is, according to known observation function, can set up and measure and possible The likelihood function that dbjective state parameter is constituted.Come from the observation of target and will obtain bigger likelihood value than clutter, and then In engineer applied, generally required flight path is initialized, to find the initial of target before target tracking algorism is implemented State vector, thus being tracked further, in batch processing TBD algorithm, maximum likelihood-probability multiple hypotheis tracking (ML- PMHT) algorithm is a kind of effective and complete object detecting and tracking algorithm.

The most important basic assumption of ML-PMHT algorithm：In same frame, it is independent mutually, that is, for measuring with target association Multiple can measure one target of association.Based on this it is assumed that ML-PMHT is very easy to expand to multiobject situation, and count Calculation amount and destination number linearly increase.ML-PMHT is carried out based on total log-likelihood ratio (LLR) that multiframe observation data is obtained Maximize, export corresponding state parameter vector obtaining to be based on after LLR table reaches formula after searching algorithm obtains LLR maximum, often Searching algorithm has：Grid data service (MPG), genetic search algorithm (GA) and based on observation space reflection be mapped to parameter space Direct subspace search method (DSS).Existing basic ML-PMHT algorithm carries out LLR using the likelihood function of a fixation Calculate.When there is multipath in environment, observer exists in the frame data receiving and multiple comes from same target and through difference What path reached measures it is clear that respectively coming from measurement all information containing target of same target.However, these measure and target Observation function relation before state is different, and the LLR carrying out calculating gained with the likelihood function of a fixation not only can not Accumulation target information, also can form the dbjective state estimates of parameters of falseness.In addition, existing basic ML-PMHT algorithm pair By the way of Sequence Detection, when adjacent to one another between target, target is searched to be arrived multiple target, and other targets are simultaneously It is not easy to be found.

The target following of ML-PMHT algorithm is to be executed in the way of sliding window, that is, every time can be by searching in sliding window Rope algorithm obtains a state estimation, then the certain frame number of sliding window forward slip, under being obtained by Local Optimization Algorithm again One state estimation.These state point sets can be obtained by the track of target by flight path management program.

Content of the invention

It is an object of the invention to the deficiency that the traditional ML-PMHT algorithm of extension is applied in multi-path environment, a kind of profit is proposed With dim multitarget detection and the tracking system of multipath observation, can correctly estimate the faint multiple target kinematic parameter in multi-path environment The method is referred to as joint maximum likelihood-multipath-probability multiple hypotheis tracking (JML-MP-PMHT) algorithm.Meanwhile, a kind of many mesh are proposed Mark joint initial method, carries out target detection and state initialization with multiple target formula, can effectively reduce between adjacent target Impact.

The thinking of the present invention is, when processing the related question between target-measurement it is considered to be arrived by different propagation paths The multiple measurements reaching receptor are that possible target measures, and correct with known each many diameter measurings function respectively for these measurements Association, thus obtaining the accumulation of target information, strengthens target detection capabilities.Then carried out by way of sliding window target with Track.

The technical scheme is that the multi-target detection and tracking method under a kind of high clutter conditions of low Observable, the party Method includes:

Step 1：Initialization；

1a. initialization observing environment parameters include：Slant range variance, orientation variance, Doppler variance, false-alarm is general Rate, detection probability, clutter density λ, in the sampling interval, verify thresholding, monitoring space V；

1b. imports observation information：Including total T frame data, in each sliding window, there is N_wFrame data, measure in this sliding window Data acquisition systemI-th frame amount surveys data acquisition system Z (i), and the i-th frame amount surveys collective number m_iReach receptor with L kind propagation path Measurement model；

(2) construct the LLR computing formula of JML-MP-PMHT：

The most important basic assumption of 2a. is any measurement z_jI () ∈ Z (i) at most passes through a kind of propagation road by a target Footpath produces, and a target can produce any amount of measurement by a kind of propagation path；

2b. suppose there is K target x^K=[x₁,x₂,...,x_K], then define prior probability represent a measurement source in The probability of certain propagation path of certain target, its computing formula is usually：

WhereinFor target x_kThe detection probability measuring is produced by path l；

The computing formula of 2c.LLR value is：

Wherein p_l(z_j(i)|x_k) represent target x_kProduced by path l and measure z_jThe likelihood function of (i)：

Wherein x^tFor transmitter state, x^rFor receiver state, h^l() is the measurement model corresponding to l kind path, R^l I () is the covariance matrix of measurement model corresponding to l kind path；

(3) N in initialization sliding window_wFrame data and metric data setKnown with the presence of K target；Work as K=0 When, direct execution step (8)；Otherwise execute next step；

(4) to already present K targeted packets；Purpose is will to gather one piece apart near target, by apart from remote mesh Mark separates；Its rule of classification is χ²Inspection：

(x_m-x_n)^T(C_m+C_n)^-1(x_m-x_n)≤γ

Wherein C_m、C_nRepresent target x respectively_m、x_nState covariance, γ be predefined thresholding；

(5) the multiple target state in each packet carries out local optimum with JML-MP-PMHT LLR formula；

(6) existence verification is carried out to each target：

6a. initializing variable k=K

6b. selected target x_k, other goal sets are x^K-1=[x₁,...,x_k-1,x_k+1,...,x_K]

6c. has individual other of K-1 to there is dbjective state, has complete metric data set in sliding windowDefine frame sequence Number variable i=1；

6d., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path l

Thus can get three-dimensional probability matrix [L, K-1, a m_i]；

6e. takes the greatest member value in probability matrixA given probability threshold if more than, then will In three-dimensional matrice, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^*All elements be one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until not having Probit is more than probability threshold；

6f. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether set up, if set up, Execution next step；Otherwise i=i+1, returns execution step 6d；

The remaining measurement of 6g. forms new measurement setThen calculate and only have target x_kJML-MP-PMHT LLR Formula；If this LLR value is more than verification thresholding, target x_kExist；Otherwise target x_kDo not exist, delete this target, and K=K- 1；

If 6h. is k=1, execute next step；Otherwise k=k-1, returns execution step 6b；

(7) suppose there is K^*Individual target has passed through existence verification, makes K=K^*, that is, there is K target；

(8) search for fresh target；

Make K^*=K+1, solves the LLR formula of JML-MP-PMHT using multipath-direct subspace search (MD-DDS) method Overall maximal solution, its state parameter corresponding to overall maximal solution be estimate fresh target init state；

(9) thresholding verification is carried out to fresh target, verify its whether necessary being：

9a. has K to there is dbjective state, has complete metric data set in sliding windowDefine frame number variable I=1；

9b., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path lObtain three-dimensional probability matrix [L, K, a m_i]；

9c. takes the greatest member value in probability matrixA given probability threshold if more than, then will In three-dimensional matrice, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^* All elements be one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until not general Rate value is more than probability threshold；

9d. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether set up, if set up, Execution next step；Otherwise i=i+1, returns execution step 9b；

The remaining measurement of 9e. forms new measurement setThen calculate the JML-MP-PMHT LLR only having fresh target Formula.If this LLR value is more than verification thresholding, fresh target exists, and makes K=K^*, return to step (8) continues to search for fresh target； Otherwise fresh target checking does not exist, and executes next step；

(10) judge whether sliding window comprises the last N of data set_wFrame data, if it did not, sliding window forward slip is certain In the sampling interval, form N in new window_wFrame data and metric data setReturn execution step (3)；Otherwise method terminates.

Further, the concrete grammar of described step 8 is：

8a. arranges free parameter grid；

State parameter spaceIn, [ρ (i) b (i)] represent geographical coordinates under radial distance and Angle,Represent radial distance rate of change and angle variable rate；And measure space [Rg Rr Az] and represent sight respectively Measurement：Slant range, Doppler, angle of inclination；Can only determine to parameter space from measuring space reflectionThree Individual parameter, so claimFor free parameter；In parameter space, free parameter is divided into grid, each mesh point corresponds to OneParameter；Define frame number variable i=1 simultaneously；

Each of i-th frame data is measured z by 8b._jI () all changes to parameter space by L kind observation model inversion；

State parameter is by h by l kind measurement model to the conversion measuring^l() measurement equation, then measure inversion Changing to state parameter needs to be inversely transformed into h to l kind measurement equation^l(·)^-1；Due to there being m_iIndividual metric data and L kind measure mould Type, then the number that parameter space is changed in measurement inversion is m_iL value；

8c. is based on range information, by this m_iL location point is clustered, and chooses the cluster of most location points；If maximum Only one of which element in cluster, then skip direct execution step 8e of this step, because this frame data is likely to be produced by clutter , there is no target information, therefore ignore and can reduce amount of calculation；Otherwise seek the average of maximum cluster

8d. is by mean location pointThe free parameter of joint step 8a settingMesh point, has formed Whole state parameter mesh pointIn conjunction with K dbjective state having been found that, substituting into prediction has K^* LLR value is calculated in the JML-MP-PMHT LLR formula of individual target；

8e. judges i=N_wWhether setting up, if set up, executing next step；Otherwise i=i+1, returns execution step 8b；

8f. takes the maximum in all LLR value, by its corresponding state parameter pass to local optimization process carry out excellent Change, obtain solution.

The present invention has the following advantages：

First, present invention utilizes reach the target information of sensor by different approaches, and these measurement informations are divided Correctly not associating with known each many diameter measurings function, thus obtaining the accumulation of target information, strengthening target in low Observable, high Power of test under clutter environment,

Second, present invention achieves a kind of multiple target joint initial method, with multiple target formula carry out target detection and State initialization, can effectively reduce the impact between adjacent target.

3rd, the present invention carries out Target state estimator by the batch processing mode of sliding window, carries out flight path by these point sets Management, it is achieved thereby that multiple target tracking.

Brief description

Fig. 1 is under over-the-horizon radar, the position of target and sensor and measurement model geometric graph.

Fig. 2 is that under two kinds of ionosphere E and F, signal is from transmitter sensor to target again to the propagation of receiver sensor Pathway figure.It is respectively this 4 kinds of propagation paths of EE, EF, FE and FF, corresponding 4 kinds of measurement models.

The slant range of lower 35 sampling instants of respectively 5 target environment of Fig. 3-5, Doppler, angle of inclination observation. In figure：Clutter asterisk represents, is represented by the measurement square that 4 kinds of propagation paths produce by target 1, in the same manner, derives from The measurement rhombus of target 2 represents, the measurement five-pointed star from target 3 represents, from the measurement triangle of target 4 Represent, the measurement circle from target 5 represents.

Fig. 6 is JML-MP-PMHT algorithm multiple target tracking result figure under 5 target environment.

Specific embodiment

In order that the object, technical solutions and advantages of the present invention are clearer, below by the specific embodiment party to the present invention Formula is described in further detail.

(1) initial background parameter.

In over-the-horizon radar application scenarios, receiver sensor is fixed on [0km, 0km] and collects by ionospheric reflection 1a. The signal returned, transmitter sensor is fixed on [100km, 0km].Suppose there is two preferable ionosphere E and F as shown in figure 1, They should have the height h of two fixations relatively_E=100km and h_F=220km, then signal from transmitter sensor to target again There are EE, EF, FE and FF totally 4 kinds of propagation paths to receiver sensor.35 sampling instants, JML- has been observed altogether in this scene The sliding window of MP-PMHT algorithm comprises 10 sampling instants, i.e. 10 frame data, execution sliding window forward slip 1 frame data every time. Wherein in sampling process, there are 5 targets to be divided into the motion vector of original state to be：

x₁=[1100km 0.15km/s 0.10472rad 8.72665e-5rad/s],

x₂=[1130km 0.15km/s 0.10472rad 8.72665e-5rad/s],

x₃=[1260km -0.15km/s 0.10472rad 8.72665e-5rad/s],

x₄=[1200km -0.15km/s 0.10472rad 8.72665e-5rad/s],

x₅=[1220km 0.15km/s 0.10472rad 8.72665e-5rad/s],

Do linear uniform motion, and the current moment that goes out of this 5 targets be respectively [1,1,1,10,1], the moment that disappears be [35, 35,35,35,20].The track of target and sensor is as shown in Figure 2.

It is assumed that the echo amplitude that sensor receives is in rayleigh distributed, then corresponding detection probability P_dWith false-alarm probability P_FA's Computing formula is as follows：

In formula, d is the signal to noise ratio of monitoring of environmental, and Th is the detection threshold to echo for the sensor.

Sensor parameters in its Scene, slant range resolution cell size C_Rg, Doppler's resolution cell size C_RrWith incline Rake angle resolution cell size C_AzIt is respectively 17.3205km, 0.0035km/s and 0.0104rad.By different propagation path EE, The SNR value of EF, FE and FF is respectively [5dB, 4dB, 4dB, 5dB], Th=2.70, then P_FA=0.026, corresponding each path detection Probability [0.42,0.35,0.35,0.42].

It is then assumed that clutter is uniformly distributed in unit, then measuring standard difference is respectively：

The observation data that 1b. sensor receives is as in Figure 3-5.After JML-MP-PMHT algorithm environment parameter determination, also Observation model to be determined.From state of ground parameter coordinateTo sensor observation coordinate [Rg Rr Az] Mapping be that observation model can be obtained by the geometric model of Fig. 2：

η=ρ-dsin (b)

Rg=r₁+r₂

Az=sin^-1{ρsin(b)/(2r₁)}

Wherein h_rAnd h_tIt is substituted for the height of ionosphere E and F, as 4 kinds different observation models respectively.Accordingly, from sight Survey coordinate to state parameter coordinate inverse mapping be：

r₂=Rg-r₁

(2) construct JML-MP-PMHT LLR computing formula：

(3) N in initialization sliding window_w=10 frame data and metric data setKnown with the presence of K target.When During K=0, direct execution step (8)；Otherwise execute next step；

(4) to already present K targeted packets.Purpose is will to gather one piece apart near target, by apart from remote mesh Mark separates.Its rule of classification is χ²Inspection：

(x_m-x_n)^T(C_m+C_n)^-1(x_m-x_n)≤γ

Wherein C_m、C_nRepresent target x respectively_m、x_nState covariance, γ be predefined thresholding；

(5) the multiple target state in each packet carries out local optimum with JML-MP-PMHT LLR formula；

(6) existence verification is carried out to each target：

6a. initializing variable k=K

6b. selected target x_k, other goal sets are x^K-1=[x₁,...,x_k-1,x_k+1,...,x_K]

6c. has individual other of K-1 to there is dbjective state, has complete metric data set in sliding windowDefine frame Sequence number variable i=1；

6d., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path l

Thus can get three-dimensional probability matrix [L, K-1, a m_i]；

6e. takes the greatest member value in probability matrixA given probability threshold if more than, then will In three-dimensional matrice, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^*All elements be one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until not having Probit is more than probability threshold；

6f. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether set up, if set up, Execution next step；Otherwise i=i+1, returns execution step 6d；

The remaining measurement of 6g. forms new measurement setThen calculate and only have target x_kJML-MP-PMHT LLR Formula.If this LLR value is more than verification thresholding, target x_kExist；Otherwise target x_kDo not exist, delete this target, and K=K- 1；

If 6h. is k=1, execute next step；Otherwise k=k-1, returns execution step 6b.

(7) suppose there is K^*Individual target has passed through existence verification, makes K=K^*, that is, there is K target；

(8) search for fresh target.Make K^*=K+1, solves JML- using multipath-direct subspace search (MD-DDS) method The overall maximal solution of MP-PMHT LLR formula, it is initial that its state parameter corresponding to overall maximal solution is the fresh target estimated Change state

8a. arranges free parameter grid.In parameter space, free parameter is drawnIt is divided into grid.Define frame sequence simultaneously Number variable i=1；

Each of i-th frame data is measured z by 8b._jI () all changes to parameter space by L=4 kind observation model inversion.Shape State parameter is by h by l kind measurement model to the conversion measuring^l() measurement equation, then measure inversion and change to state ginseng Number needs to be inversely transformed into h to l kind measurement equation^l(·)^-1, i.e. inverse mapping in step 1b.Due to there being m_iIndividual metric data and L Plant measurement model, then the number that parameter space is changed in measurement inversion is m_iL value；

8c. is based on range information, by this m_iL location point is clustered, and chooses the cluster of most location points.If maximum Only one of which element in cluster, then skip direct execution step 8e of this step, because this frame data is likely to be produced by clutter , there is no target information, therefore ignore and can reduce amount of calculation；Otherwise seek the average of maximum cluster

8d. is by mean location pointThe free parameter of joint step 8a settingMesh point, has formed Whole state parameter mesh pointIn conjunction with K dbjective state having been found that, substituting into prediction has K^* LLR value is calculated in the JML-MP-PMHT LLR formula of individual target；

8e. judges i=N_wWhether setting up, if set up, executing next step；Otherwise i=i+1, returns execution step 8b；

8f. takes the maximum in all LLR value, by its corresponding state parameter pass to local optimization process carry out excellent Change, obtain solution；

(9) thresholding verification is carried out to fresh target, verify its whether necessary being：

9a. has K to there is dbjective state, has complete metric data set in sliding windowDefine frame number variable I=1；

9b., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path lObtain three-dimensional probability matrix [L, K, a m_i]；

9c. takes the greatest member value in probability matrixA given probability threshold if more than, then will In three-dimensional matrice, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^*All elements be one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until not having Probit is more than probability threshold；

9d. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether set up, if set up, Execution next step；Otherwise i=i+1, returns execution step 9b；

The remaining measurement of 9e. forms new measurement setThen calculate the JML-MP-PMHT LLR only having fresh target Formula.If this LLR value is more than verification thresholding, fresh target exists, and makes K=K^*, return to step (8) continues to search for fresh target； Otherwise fresh target checking does not exist, and executes next step；

(10) judge whether sliding window comprises the last N of data set_wFrame data, if it did not, sliding window forward slip 1 frame number According to interval, form N in new window_wFrame data and metric data setReturn execution step (3)；Otherwise method terminates.

In this example is implemented, in Fig. 6, solid line is the track result to multiple target tracking 200 times.Result shows, follows the tracks of Flight path and the true flight path of target closely, are effective with the multiple target tracking that ML-MP-PMHT is carried out under multi-path environment.

Finally illustrate, above implement only in order to technical scheme to be described and unrestricted, all according to Shen of the present invention Please the impartial change done of the scope of the claims and modification, all should belong to the covering scope of the present invention.

Claims (2)

1. the multi-target detection and tracking method under a kind of high clutter conditions of low Observable, the method includes:

Step 1：Initialization；

1a. initialization observing environment parameters include：Slant range variance, orientation variance, Doppler variance, false-alarm probability, Detection probability, clutter density λ, in the sampling interval, verify thresholding, monitoring space V；

1b. imports observation information：Including total T frame data, in each sliding window, there is N_wFrame data, metric data in this sliding window SetI-th frame amount surveys data acquisition system Z (i), and the i-th frame amount surveys collective number m_iReach the amount of receptor with L kind propagation path Survey model；

(2) construct the LLR computing formula of JML-MP-PMHT：

The most important basic assumption of 2a. is any measurement z_jI () ∈ Z (i) is at most produced by a kind of propagation path by a target Raw, and a target can produce any amount of measurement by a kind of propagation path；

2b. suppose there is K target x^K=[x₁,x₂,...,x_K], then define prior probability and represent a measurement source in certain mesh The probability of certain propagation path of target, its computing formula is usually：

${\mathrm{\π}}_{00}=\frac{\mathrm{\λ}V}{\mathrm{\λ}V+\underset{k=1}{\overset{K}{\Σ}}\underset{l=1}{\overset{L}{\Σ}}{P}_d^l\left(x_k\right)},{\mathrm{\π}}_{kl}=\frac{P_d^l\left(x_k\right)}{\mathrm{\λ}V+\underset{k=1}{\overset{K}{\Σ}}\underset{l=1}{\overset{L}{\Σ}}{P}_d^l\left(x_k\right)}$

WhereinFor target x_kThe detection probability measuring is produced by path l；

The computing formula of 2c.LLR value is：

$\mathrm{\φ}\left(Z^{N_w}\right|x^K)=\underset{i=1}{\overset{N_w}{\Σ}}\underset{j=1}{\overset{m_i}{\Σ}}ln\[{\mathrm{\π}}_{00}+V\underset{k=1}{\overset{K}{\Σ}}\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\π}}_{kl}{p}_l\left(z_j\right(i\left)\right|x_k)\]$

Wherein p_l(z_j(i)|x_k) represent target x_kProduced by path l and measure z_jThe likelihood function of (i)：

Wherein x^tFor transmitter state, x^rFor receiver state, h^l() is the measurement model corresponding to l kind path, R^lI () is The covariance matrix of measurement model corresponding to l kind path；

(3) N in initialization sliding window_wFrame data and metric data setKnown with the presence of K target；As K=0, directly Connect execution step (8)；Otherwise execute next step；

(4) to already present K targeted packets；Purpose is will to gather one piece apart near target, will divide apart from remote target Every；Its rule of classification is χ²Inspection：

(x_m-x_n)^T(C_m+C_n)^-1(x_m-x_n)≤γ

Wherein C_m、C_nRepresent target x respectively_m、x_nState covariance, γ be predefined thresholding；

(5) the multiple target state in each packet carries out local optimum with JML-MP-PMHT LLR formula；

(6) existence verification is carried out to each target：

6a. initializing variable k=K

6b. selected target x_k, other goal sets are x^K-1=[x₁,...,x_k-1,x_k+1,...,x_K]

6c. has individual other of K-1 to there is dbjective state, has complete metric data set in sliding windowDefine frame number to become Amount i=1；

6d., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path l

${\mathrm{\ω}}_{jk}^l\left(i\right)=\frac{{\mathrm{\π}}_{kl}{p}_l\left(z_j\right(i\left)\right|x_k)}{{\mathrm{\π}}_{00}+V\underset{k=1}{\overset{K-1}{\Σ}}\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\π}}_{kl}{p}_l\left(z_j\right(i\left)\right|x_k)}$

Thus can get three-dimensional probability matrix [L, K-1, a m_i]；

6e. takes the greatest member value in probability matrixA given probability threshold if more than, then by three-dimensional In matrix, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^*'s All elements are one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until there is no probability Value is more than probability threshold；

6f. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether setting up, if set up, executing Next step；Otherwise i=i+1, returns execution step 6d；

The remaining measurement of 6g. forms new measurement setThen calculate and only have target x_kJML-MP-PMHT LLR public Formula；If this LLR value is more than verification thresholding, target x_kExist；Otherwise target x_kDo not exist, delete this target, and K=K-1；

If 6h. is k=1, execute next step；Otherwise k=k-1, returns execution step 6b；

(7) suppose there is K^*Individual target has passed through existence verification, makes K=K^*, that is, there is K target；

(8) search for fresh target；

Make K^*=K+1, using multipath-directly the LLR formula of subspace search (MD-DDS) method solution JML-MP-PMHT is complete Office's maximal solution, its state parameter corresponding to overall maximal solution is the fresh target init state estimated；

(9) thresholding verification is carried out to fresh target, verify its whether necessary being：

9a. has K to there is dbjective state, has complete metric data set in sliding windowDefinition frame number variable i= 1；

9b., in the i-th frame metric data, calculates and measures z_jI () derives from target x_kPosteriority association probability with path l? To three-dimensional probability matrix [L, K, a m_i]；

9c. takes the greatest member value in probability matrixA given probability threshold if more than, then by three-dimensional In matrix, the third dimension is equal toAll elements be two-dimensional matrixIt is equal to l with the first dimension^*And second dimension be equal to k^*'s All elements are one-dimensional matrix [l^*,k^*,:] it is set to 0, record this measurement sequence numberRepeatedly execute this step, until there is no probability Value is more than probability threshold；

9d. rejects these more than the metric data corresponding to probability threshold, judges i=N_wWhether setting up, if set up, executing Next step；Otherwise i=i+1, returns execution step 9b；

The remaining measurement of 9e. forms new measurement setThen calculate the JML-MP-PMHT LLR formula only having fresh target. If this LLR value is more than verification thresholding, fresh target exists, and makes K=K^*, return to step (8) continues to search for fresh target；Otherwise new Target verification does not exist, and executes next step；

(10) judge whether sliding window comprises the last N of data set_wFrame data, if it did not, between the certain sampling of sliding window forward slip Every N in the new window of formation_wFrame data and metric data setReturn execution step (3)；Otherwise method terminates.

2. the multi-target detection and tracking method under the high clutter conditions of a kind of low Observable as claimed in claim, its feature exists Concrete grammar in described step 8 is：

8a. arranges free parameter grid；

State parameter spaceIn, [ρ (i) b (i)] represents radial distance and angle under geographical coordinates,Represent radial distance rate of change and angle variable rate；And measure space [Rg Rr Az] and represent observed quantity respectively： Slant range, Doppler, angle of inclination；Can only determine to parameter space from measuring space reflectionThree ginsengs Number, so claimFor free parameter；In parameter space, free parameter is divided into grid, corresponding one of each mesh pointParameter；Define frame number variable i=1 simultaneously；

Each of i-th frame data is measured z by 8b._jI () all changes to parameter space by L kind observation model inversion；

State parameter is by h by l kind measurement model to the conversion measuring^l() measurement equation, then measure inversion and change to shape State parameter needs to be inversely transformed into h to l kind measurement equation^l(·)^-1；Due to there being m_iIndividual metric data and L kind measurement model, then measure The number that parameter space is changed in survey inversion is m_iL value；

8c. is based on range information, by this m_iL location point is clustered, and chooses the cluster of most location points；If maximum cluster Middle only one of which element, then skip direct execution step 8e of this step, because what this frame data was likely to be produced by clutter, do not have There is target information, therefore ignore and can reduce amount of calculation；Otherwise seek the average of maximum cluster

8d. is by mean location pointThe free parameter of joint step 8a settingMesh point, forms complete State parameter mesh pointIn conjunction with K dbjective state having been found that, substituting into prediction has K^*Individual mesh LLR value is calculated in target JML-MP-PMHT LLR formula；

8e. judges i=N_wWhether setting up, if set up, executing next step；Otherwise i=i+1, returns execution step 8b；

8f. takes the maximum in all LLR value, its corresponding state parameter is passed to local optimization process and is optimized, obtain Solution.