CN105975772A - Multi-target track-before-detect method based on probability hypothesis density filtering - Google Patents

Abstract

The invention discloses a multi-target track-before-detect method based on probability hypothesis density filtering. The method deeply analyzes the problem of a traditional method and points out the essential reason of the problem of the traditional method that the traditional method considers that one target influences the observation of a whole area and also considers that the number of each frame of false alarm can be approximated into one constant value, i.e. the traditional method does not comply with two pieces of basic hypothesis for realizing PHD (Probability Hypothesis Density) filtering: firstly, one target only can generate one observation, and secondly, the number of each frame of false alarm must submit to Poisson distribution on an aspect of time. In order to solve the problems, the invention puts forward the multi-target track-before-detect method based on the probability hypothesis density filtering, can improve the accuracy of target number estimation, enhances detection and tracking performance, and also achieves an effect on lowering a calculated amount.

Description

Tracking before multi-target detection based on probability hypothesis density filtering

Technical field

The invention belongs to object detecting and tracking technical field, be specifically related to a kind of many based on probability hypothesis density filtering Tracking before target detection.

Background technology

In current research under strong clutter background to dim target detection and tracking, follow the tracks of (TBD) before detection square Method is unanimously thought by Chinese scholars can be with the detection of high degree raising weak target and tracking performance.TBD method main Feature is single frames observation not to be set thresholding, due to it whole primary signal as observation input, so retaining to greatest extent Target information, it is to avoid single frame detection loses, it utilizes many frame informations of accumulation can improve signal to noise ratio simultaneously, therefore can improve The detection of weak target and tracking performance.Probability hypothesis density (PHD) is a kind of filtering based on random set theoretical frame, due to The association process of its observation information with track data without carrying out complexity, it is possible to effectively estimate multiple target number and target-like State, adds that it has and adapts to that target numbers is unknown and the advantage of changeable scene, therefore scholars begin one's study PHD filtering application In TBD field.In recent years, relevant scholars the most successfully prove that PHD-TBD method is feasible, and propose to be somebody's turn to do Method be embodied as step, simultaneously by the effectiveness of relevant emulation explanation the method.

Although above-mentioned tradition PHD-TBD method achieves some achievements, but it yet suffers from numerous deficiency, mainly has two Point: one is that it estimates that the accuracy rate of target numbers is low, frequent missing inspection or false retrieval cause its detection unsatisfactory with tracking effect； Two is the computationally intensive of it, causes its poor real, it is impossible to actual application.Therefore, current PHD-TBD method remains in In theoretical research, want from theoretical research, the method is advanced to actual application, it is necessary to emphasis solves above-mentioned 2 points of the method Not enough.

Summary of the invention

Present invention aims to the problem that tradition PHD-TBD method exists, analyse in depth the essential reason of problem, And by solving these problems, tracking before the multi-target detection based on probability hypothesis density filtering of a kind of improvement is proposed. The present invention can be effectively improved the accuracy rate that target numbers is estimated, strengthens detection and tracking performance, reduces calculating simultaneously The effect of amount.

It is an object of the invention to be achieved through the following technical solutions: a kind of many mesh based on probability hypothesis density filtering Tracking before mark detection, comprises the steps:

(1) state equation of target and the observational equation of sensor are set up；

Target state equation is:

$\begin{array}{cc}{X}_k^l=f_k(X_{k-1}^l,v_k)& l=1,\mathrm{...},N_k\end{array}$

WhereinIt is the state vector of k l target of moment,It it is target x-axis The position in direction and speed,It is position and the speed in target y-axis direction,It is the intensity of echo signal；N_kWhen being k Carve the total number of target；f_k(.) is the state transition function of target；v_kIt it is the process noise of known statistical nature.

Sensor observational equation is:

Rectangle monitor area is observed by sensor every T time, and sensor has n × m sensing unit, each sensing (i, j) corresponding rectangular area fritter Δ x × Δ y, (i, centre coordinate j) is (i Δ x, j Δ y), i=to sensing unit to unit 1 ..., n, j=1 ..., m, then (i, strength observations j) is k moment sensing unit

$h_k^{(i.j)}\left(X_k^l\right)\≈\frac{{\mathrm{\Δx\ΔyI}}_k^l}{2\mathrm{\π}{\Σ}^2}\exp \left\{\frac{{(i\mathrm{\Δ}x-x_k^l)}^2+{(j\mathrm{\Δ}y-y_k^l)}^2}{2{\Σ}^2}\right\}$

WhereinIt is k moment sensing unit (i, observation noise j), it is assumed that its statistical nature is known； For k moment target l to sensing unit (i, signal intensity contribution j)；Σ is the measurement error of sensor；

(2) weight of k moment particle is obtained by sequential Monte Carlo method, including prediction and two stages of renewal；

K-1 moment multiple target posterior probability density D_k-1|k-1(X_k-1|Z_1:k-1) represent with a series of particles with weight, That is:

$D_{k-1|k-1}\left(X_{k-1}\right|Z_{1:k-1})=\underset{p=1}{\overset{L_{k-1}}{\Σ}}{w}_{k-1}^{\left(p\right)}\mathrm{\δ}(X_{k-1}-X_{k-1}^{\left(p\right)})$

Wherein,It is the state of particle,It is the weight of particle, L_k-1It it is the number of k 1 moment particle Mesh,It is the observation set in k moment whole region, Z_1:k={ Z_i: i=1 ..., k} It is from all of observation set of 1 moment to k moment.

Forecast period: the particle state of predictionTwo parts are had to originate, Part ICome Shift from the state of previous moment particle, Part IIFrom the most newborn particle, this two parts grain The weight of son is respectivelyWith

${\left\{w_{k|k-1}^{\left(p\right)}\right\}}_{p=1}^{L_{k-1}}=\frac{e_{k|k-1}\left(X_{k-1}^{\left(p\right)}\right)f_k\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)})+b_{k|k-1}\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)})}{q_k\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)},Z_k)}=w_{k-1}^{\left(p\right)}$

${\left\{w_{k|k-1}^{\left(p\right)}\right\}}_{p=L_{k-1}+1}^{L_{k-1}+J_k}=\frac{{\mathrm{\γ}}_k\left(X_{k|k-1}^{\left(p\right)}\right)}{p_k\left(X_{k|k-1}^{\left(p\right)}\right|Z_k)J_k}$

Therefore the k moment multiple target priori probability density D predicted_k|k-1(X_k|k-1|Z_1:k-1) it is:

$D_{k|k-1}\left(X_{k|k-1}\right|Z_{1:k-1})=\underset{p=1}{\overset{L_{k-1}+J_k}{\Σ}}{w}_{k|k-1}^{\left(p\right)}\mathrm{\δ}(X_{k|k-1}-X_{k|k-1}^{\left(p\right)})$

Wherein J_kIt it is the number of particles of k moment new life；e_k|k-1It is that k 1 moment particle is survived to the probability in k moment；b_k|k-1It is The probability that k moment particle derives from k 1 moment particle；γ_kIt is the PHD of k moment completely newborn particle；q_kAnd p_kIt is that importance is adopted Sample function.

The more new stage: k moment particle weightsMore new formula be:

${\left\{w_k^{\left(p\right)}\right\}}_{p=1}^{L_{k-1}+J_k}=\frac{l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})}{K_k\left(Z\right)+C_k\left(Z_k^{(r,s)}\right)}{w}_{k|k-1}^{\left(p\right)}$

Wherein

$K_k\left(Z\right)=\frac{p^{*}}{\mathrm{\Δ}x\×\mathrm{\Δ}y}$

$C_k\left(Z_k^{(r,s)}\right)=\underset{p\∈P^{r,s}}{\Σ}l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})w_{k|k-1}^{\left(p\right)}$

WhereinBe sensing unit (i, j) in target and total likelihood function of observation noise,Be sensing unit (i, j) in the likelihood function of observation noise, σ is the standard deviation of observation noise；K_k(Z) it is empty Alert density function, p^*It it is threshold probability；p^r,s=p:p ∈ 1 ..., L_k-1+J_kIt is particle assembly, (r s) is target place Sensing unit.

(3) posterior probability density D of k moment target is calculated_k|k(X_k|Z_1:k):

$D_{k|k}\left(X_k\right|Z_{1:k})=\underset{p=1}{\overset{L_k}{\Σ}}{w}_k^{\left(p\right)}\mathrm{\δ}(X_k-X_k^{\left(p\right)})$

(4) particle is carried out resampling: the particle after updating weight is concentrated, and obtains according to the size resampling of particle weights To new particle collection.

(5) circulation performs step 1-4, until reaching the observation time T set_O, finally give T_OThe target posteriority in individual moment Probability density, thus follow the tracks of before realizing multi-target detection.

Further, in described step 2, threshold probability p^*Meet:

$p(Z_k^{(i,j)}\≥\mathrm{\θ})={\∫}_{\mathrm{\θ}}^{\mathrm{\∞}}{p}_n\left(Z_k^{(i,j)}\right){\mathrm{dZ}}_k^{(i,j)}\≥p^{*}$

Whereinθ is the observation threshold value set, and θ value must assure that p^*≈1。

Further, in described step 4, updating the particle collection after weight isResampling obtains New particle collection isWherein n_kThe target numbers estimated for the k moment, $n_k=\underset{p=1}{\overset{L_{k-1}+J_k}{\Σ}}{w}_k^{\left(p\right)}.$

The present invention is by analysing in depth the problem that traditional method exists, it is indicated that its essential reason is it considers that a target pair The observation in whole region all has an impact, and thinks that every frame false-alarm number can be approximated to a definite value simultaneously, i.e. traditional method does not has Observe two basic assumptions realizing PHD filtering: first, a target can only produce an observation；Secondly, the number of every frame false-alarm Mesh must obey Poisson distribution in time.The present invention, by solving these problems, proposes assuming based on probability of a kind of improvement Tracking before the multi-target detection of density filtering, can improve the accuracy rate that target numbers is estimated, strengthens detection and tracing property Can, reduce the effect of amount of calculation simultaneously.Compared with traditional method, the present invention has the advantage that

1. point out the in-problem essential reason of traditional method, and solve traditional method and do not meet PHD and filter basic assumption Problem so that the inventive method the most more can be based oneself upon；

2. traditional method thinks that the observation in whole region is all had an impact by a target, and the present invention is by changing sensor Observation model a so that target can only affect the observation of its place sensing unit a, it is achieved target can only produce a sight Survey.By changing the observation model of sensor, the present invention can reduce numerous unnecessary observation data, reduce amount of calculation Effect, thus be advantageously implemented and online process in real time；

3. traditional method thinks that every frame false-alarm number can be approximated to a definite value, and due in the present invention, false-alarm is to see Survey what noise caused, so the present invention is by introducing threshold probability p^*, observation noise is screened, the most each observation noise Being to obey binomial distribution by threshold value, again according to poisson's theorem, when observation noise data are a lot, its binomial distribution can be near Seemingly for Poisson distribution, therefore realize every frame false-alarm number and obey Poisson distribution in time.

4. the present invention obeys Poisson distribution according to new sensor observation model and false-alarm number, the particle power made new advances of deriving Weight more new formula.The accuracy rate that target numbers is estimated can be improved by the particle weights more new formula that simulating, verifying is new, thus Strengthen object detecting and tracking performance.

Accompanying drawing explanation

Fig. 1 is the simulation process design sketch of traditional method；

Fig. 2 is the simulation process design sketch of the inventive method；

Fig. 3 is the estimation target numbers design sketch of traditional method；

Fig. 4 is the estimation target numbers design sketch of the inventive method.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

The present invention is tracking before a kind of multi-target detection based on probability hypothesis density filtering, comprises the steps:

(1) state equation of target and the observational equation of sensor are set up；

Target state equation is:

$\begin{array}{cc}{X}_k^l=f_k(X_{k-1}^l,v_k)& l=1,...,N_k\end{array}$

Being explained as follows of each parameter:

WhereinIt is the state vector of k l target of moment,It it is target x-axis The position in direction and speed,It is position and the speed in target y-axis direction,It is the intensity of echo signal；N_kWhen being k Carve the total number of target；f_k(.) is the state transition function of target；v_kIt it is the process noise of known statistical nature.

Sensor observational equation is:

Rectangle monitor area is observed by sensor every T time, and sensor has n × m sensing unit, each sensing (i, j) corresponding rectangular area fritter Δ x × Δ y, (i, centre coordinate j) may be considered (i Δ x, j Δ to sensing unit to unit Y), i=1 ..., n, j=1 ..., m, then (i, strength observations j) is k moment sensing unit

Wherein

Being explained as follows of each parameter:

It is k moment sensing unit (i, observation noise j), it is assumed that its statistical nature is known；

For k moment target l, to sensing unit, (Σ is that the measurement of sensor misses for i, signal intensity contribution j) Difference；

(2) obtain the weight of k moment particle by sequential Monte Carlo method, prediction can be divided into and update two stages；

K-1 moment multiple target posterior probability density D_k-1|k-1(X_k-1|Z_1:k-1) can be with a series of particle tables with weight Show,It is the state of particle,It is the weight of particle, L_k-1It is the number of k 1 moment particle,It is the observation set in k moment whole region, Z_1:k={ Z_i: i=1 ..., k} is From all of observation set of 1 moment to k moment, it may be assumed that

$D_{k-1|k-1}\left(X_{k-1}\right|Z_{1:k-1})=\underset{p=1}{\overset{L_{k-1}}{\Σ}}{w}_{k-1}^{\left(p\right)}\mathrm{\δ}(X_{k-1}-X_{k-1}^{\left(p\right)})$

Forecast period: the particle state of predictionTwo parts are had to originate, Part ICome Shift from the state of previous moment particle, Part IIFrom the most newborn particle, this two parts grain The weight of son is respectivelyWith

${\left\{w_{k|k-1}^{\left(p\right)}\right\}}_{p=1}^{L_{k-1}}=\frac{e_{k|k-1}\left(X_{k-1}^{\left(p\right)}\right)f_k\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)})+b_{k|k-1}\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)})}{q_k\left(X_{k|k-1}^{\left(p\right)}\right|X_{k-1}^{\left(p\right)},Z_k)}=w_{k-1}^{\left(p\right)}$

${\left\{w_{k|k-1}^{\left(p\right)}\right\}}_{p=L_{k-1}+1}^{L_{k-1}+J_k}=\frac{{\mathrm{\γ}}_k\left(X_{k|k-1}^{\left(p\right)}\right)}{p_k\left(X_{k|k-1}^{\left(p\right)}\right|Z_k)J_k}$

Therefore the k moment multiple target priori probability density D predicted_k|k-1(X_k|k-1|Z_1:k-1) it is:

$D_{k|k-1}\left(X_{k|k-1}\right|Z_{1:k-1})=\underset{p=1}{\overset{L_{k-1}+J_k}{\Σ}}{w}_{k|k-1}^{\left(p\right)}\mathrm{\δ}(X_{k|k-1}-X_{k|k-1}^{\left(p\right)})$

Being explained as follows of each parameter:

J_kIt it is the number of particles of k moment new life；e_k|k-1It is that k 1 moment particle is survived to the probability in k moment；b_k|k-1When being k Carve the probability that particle derives from k 1 moment particle；γ_kIt is the PHD of k moment completely newborn particle；q_kAnd p_kIt it is importance sampling letter Number, q_kIt is typically chosen in f_k(.)。

The more new stage: k moment particle weightsMore new formula be:

${\left\{w_k^{\left(p\right)}\right\}}_{p=1}^{L_{k-1}+J_k}=\frac{l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})}{K_k\left(Z\right)+C_k\left(Z_k^{(r,s)}\right)}{w}_{k|k-1}^{\left(p\right)}$

Wherein

$K_k\left(Z\right)=\frac{p^{*}}{\mathrm{\Δ}x\×\mathrm{\Δ}y}$

$C_k\left(Z_k^{(r,s)}\right)=\underset{p\∈P^{r,s}}{\Σ}l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})w_{k|k-1}^{\left(p\right)}$

Being explained as follows of each parameter:

Be sensing unit (i, j) in target and total likelihood function of observation noise, observation noise take It is the normal distribution of σ from zero-mean, standard deviation,It is that (i, j) middle observation is made an uproar at sensing unit The likelihood function of sound；K_k(Z) it is false-alarm density function, p^*It is threshold probability, and θ is the observation threshold value set for ensureing false-alarm number to obey Poisson distribution, and simultaneously in order to meet TBD thought, θ value must be very Little, it is ensured that p^*≈1；p^r,s=p:p ∈ 1 ..., L_k-1+J_kIt is particle assembly, (r s) is the sensing unit at target place.

(3) posterior probability density D of k moment target is calculated_k|k(X_k|Z_1:k):

$D_{k|k}\left(X_k\right|Z_{1:k})=\underset{p=1}{\overset{L_k}{\Σ}}{w}_k^{\left(p\right)}\mathrm{\δ}(X_k-X_k^{\left(p\right)})$

(4) particle is carried out resampling, specific as follows:

Target numbers n that the k moment is estimated_kFor:

$n_k=\underset{p=1}{\overset{L_{k-1}+J_k}{\Σ}}{w}_k^{\left(p\right)}$

In order to prevent the degeneration of particle, need the particle collection after updating weightMiddle according to particle The size resampling of weight obtains new particle collectionPrepare for subsequent time filtering.

(5) circulation performs step 1-4, until reaching the observation time T set_O, finally give T_OThe target posteriority in individual moment Probability density, thus follow the tracks of before realizing multi-target detection.

Embodiment

Moving equation is linear uniform motion x_k+1=Fx_k+v_k；v_kIt is the white Gaussian noise of zero-mean, its covariance Matrix is Q.Sensor Continuous Observation T_OThe data in=30 moment, it has n × m=35 × 35 sensing unit, sensing unit The length of fritter and wide Δ x=Δ y=1, time interval T=1, standard deviation sigma=1 of noise, measurement error Σ of sensor= 0.7.Target 1 occurred the 2nd moment, disappeared the 18th moment；Target 2 occurred the 12nd moment, the 27th moment Disappear.Each target represents with 2048 particles, per moment new life number of particles J=1024.The survival probability of target is 0.95, Derivative probability is 0, and newborn probability is 0.2.Threshold probability p set^*=0.98.

$\begin{array}{ccc}F=\left[\begin{array}{ccccc}1& T& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 1& T& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 1\end{array}\right]& Q=\left[\begin{array}{ccccc}\frac{q_1}{3}{T}^3& \frac{q_1}{2}{T}^2& 0& 0& 0\\ \frac{q_1}{2}{T}^2& q_{1}T& 0& 0& 0\\ 0& 0& \frac{q_1}{3}{T}^3& \frac{q_1}{2}{T}^2& 0\\ 0& 0& \frac{q_1}{2}{T}^2& q_{1}T& 0\\ 0& 0& 0& 0& q_{2}T\end{array}\right]& (q_1=0.001,q_2=0.01)\end{array}$

Fig. 1 and Fig. 2 is the target trajectory treatment effect figure of traditional method and the inventive method respectively, and contrast can be seen that this Inventive method can preferably follow the tracks of target trajectory, and its detection is substantially better than traditional method with tracking performance.Fig. 3 and Fig. 4 is respectively Being traditional method and the target numbers situation of the inventive method per moment estimation, contrast can be seen that the inventive method only has 2 Moment estimates that target numbers is forbidden, and traditional method has 8 moment estimation target numbers to be forbidden, and therefore the present invention can substantially carry High target numbers estimates accuracy rate.In the present embodiment, the operation time of traditional method is 1229 seconds, and if the inventive method 59 seconds, the checking present invention can reduce amount of calculation, it is easy to processes in real time.

Claims (4)

1. tracking before a multi-target detection based on probability hypothesis density filtering, it is characterised in that comprise the steps:

(1) state equation of target and the observational equation of sensor are set up；

Described sensor observational equation is: rectangle monitor area is observed by sensor every T time, and sensor has n × m Sensing unit, (i, j) corresponding rectangular area fritter Δ x × Δ y, (i, centre coordinate j) is sensing unit each sensing unit (i Δ x, j Δ y), i=1 ..., n, j=1 ..., m, then (i, strength observations j) is k moment sensing unit

$h_k^{\left(i.j\right)}\left(X_k^l\right)\≈\frac{{\mathrm{\Δx\ΔyI}}_k^l}{2{\mathrm{\π\Σ}}^2}\exp \{-\frac{{(i\mathrm{\Δ}x-x_k^l)}^2+{(j\mathrm{\Δ}y-y_k^l)}^2}{2{\mathrm{\Σ}}^2}\}$

WhereinIt is k moment sensing unit (i, observation noise j), it is assumed that its statistical nature is known；During for k Carve target l to sensing unit (i, signal intensity contribution j)；Σ is the measurement error of sensor； It is the state vector of k l target of moment,It is position and the speed in target x-axis direction,It it is target y-axis The position in direction and speed,It is the intensity of echo signal；N_kIt it is the total number of k moment target；

(2) weight of k moment particle is obtained by sequential Monte Carlo method, including prediction and two stages of renewal；

K-1 moment multiple target posterior probability density D_k-1|k-1(X_k-1|Z_1:k-1) represent with a series of particles with weight, it may be assumed that

$D_{k-1|k-1}\left(X_{k-1}\right|Z_{1:k-1})=\underset{p=1}{\overset{L_{k-1}}{\mathrm{\Σ}}}{w}_{k-1}^{\left(p\right)}\mathrm{\δ}(X_{k-1}-X_{k-1}^{\left(p\right)})$

WhereinIt is the state of particle,It is the weight of particle, L_k-1It is the number of k 1 moment particle,It is the observation set in k moment whole region, Z_1:k={ Z_i: i=1 ..., k} is From all of observation set of 1 moment to k moment.

Forecast period: the particle of prediction has two parts to originate, Part IState from previous moment particle Transfer, Part IIFrom the most newborn particle, the weight of this two parts particle is respectivelyWith

The more new stage: k moment particle weightsMore new formula be:

${\left\{w_k^{\left(p\right)}\right\}}_{p=1}^{L_{k-1}+J_k}=\frac{l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})}{K_k\left(Z\right)+C_k\left(Z_k^{(r,s)}\right)}{w}_{k|k-1}^{\left(p\right)}$

Wherein

$C_k\left(Z_k^{(r,s)}\right)=\underset{p\∈P^{r,s}}{\Σ}l\left(Z_k^{(i,j)}\right|X_{k|k-1}^{\left(p\right)})w_{k|k-1}^{\left(p\right)}$

WhereinBe sensing unit (i, j) in target and total likelihood function of observation noise,Be sensing unit (i, j) in the likelihood function of observation noise, σ is the standard deviation of observation noise；K_k(Z) it is empty Alert density function, p^*It it is threshold probability；p^r,s=p:p ∈ 1 ..., L_k-1+J_kIt is particle assembly, (r s) is target place Sensing unit.

(3) multiple target posterior probability density D in k moment is calculated_k|k(X_k|Z_1:k)。

(4) particle is carried out resampling: the particle after updating weight is concentrated, and obtains newly according to the size resampling of particle weights Particle collection.

(5) circulation performs step 1-4, until reaching the observation time T set_O, finally give T_OThe target posterior probability in individual moment Density, thus follow the tracks of before realizing multi-target detection.

Tracking before a kind of multi-target detection based on probability hypothesis density filtering the most according to claim 1, it is special Levying and be, in described step 1, sensor observational equation is calculating k moment sensing unit (i, observed strength j)Time, only Can calculate be positioned at sensing unit (i, j) in target produce observed strength, i.e. target can only affect its place sensing unit Observation, does not produce observation impact to sensing unit about, it is ensured that a target produces an observation.

Tracking before a kind of multi-target detection based on probability hypothesis density filtering the most according to claim 1, it is special Levying and be, in described step 2, false-alarm is that observation noise causes, by introducing threshold probability p^*, observation noise is sieved Choosing, it is ensured that false-alarm number obeys Poisson distribution in time.Threshold probability p^*Meet:

$p(Z_k^{(i,j)}\≥\mathrm{\θ})={\∫}_{\mathrm{\θ}}^{\mathrm{\∞}}{p}_n\left(Z_k^{(i,j)}\right){\mathrm{dZ}}_k^{(i,j)}\≥p^{*}$

Whereinθ is the observation threshold value set, and θ value must assure that p^*≈1。

Tracking before a kind of multi-target detection based on probability hypothesis density filtering the most according to claim 1, it is special Levy and be, in described step 2, calculate k moment particle weights in the more new stageTime, molecule item With in denominator termOnly calculate be positioned at sensing unit (i, j) in the observed strength that produces of particle, in denominator term False-alarm density function