CN104597439A - Target-echo-emission source ternary data associated digital broadcasting passive positioning method - Google Patents

Abstract

The invention discloses a target-echo-emission source ternary data associated digital broadcasting passive positioning method which is used for solving the technical problem of poor practicability of the existing digital broadcasting passive positioning method. The technical scheme is that in the track starting stage, infeasible branches are cut by aid of station distribution geometrical information; in the track maintaining stage, a wave gate is generated by aid of the existing track information and the scale of a distribution tree is reduced; a feasible measurement sequence meeting wave gate constraint is gathered for cost evaluation; finally, the multi-dimension assignment problem is continuously relaxed to a sequence two-dimensional distribution problem by aid of the lagrangian relaxation algorithm, and solution is acquired through the improved auction algorithm. The target-echo-emission source ternary data associated digital broadcasting passive positioning method achieves passive target tracing under target-echo-emission source ternary data association, increases the track starting speed, improves the target tracing accuracy, effectively improves the passive target tracing performance in the clutter environment, and has significance in practical application of the passive target tracing projects.

Description

The digital broadcasting passive location method of target-echo-emissive source trinary data association

Technical field

The present invention relates to a kind of digital broadcasting passive location method, particularly relate to the digital broadcasting passive location method of a kind of target-echo-emissive source trinary data association.

Background technology

Document " Tracking in multi-static passive radar systems using DAB/DVB-T illumination; Signal Processing; Vol92 (6); 2012; p1365 – 1386 " discloses a kind of Multi-Station passive location system keeps track method based on digital broadcasting, the method takes three stage tracking strategy: first tracking phase, in target component space (comprising dual station distance, dual station distance velocity), takes multiple hypotheis tracking method (MHT); Second stage mainly deletes false target based on likelihood ratio (LR) and integer programming (IP); Three phases completes the target following of cartesian space, takes single goal multiple hypotheis tracking and multiple goal multiple hypotheis tracking two schemes respectively according to the method that subordinate phase is taked.It is low that method described in document is not suitable for detection probability (Pd), the scene that clutter is intensive.When detection probability is lower, follow the tracks of due to loss of learning to target component space simple component, imperfect, effect is generally poor; When clutter number is more, the uncertainty of this problem will be more serious, the information of effective integration multisensor can not carry out co-located and tracking, the literature method particularly crucially first stage in addition, under complex background, the very possible error result that produces causes subsequent tracking phase nonsensical, reduces tracker quality.

Summary of the invention

In order to overcome the deficiency of existing digital broadcast passive location method poor practicability, the invention provides the digital broadcasting passive location method of a kind of target-echo-emissive source trinary data association.The method, in the track initiation stage, utilizes cloth station geological information to delete infeasible branch; In the flight path maintenance stage, first utilize the information of existing flight path to generate ripple door, reduce the scale of allocation tree; Then cost evaluation is carried out to the feasible measurement sequence set meeting the constraint of ripple door; Finally, use Lagrangian Relaxation Algorithm to be relaxed continuously by multi-dimension assignment as sequence two dimension assignment problem and use improvement auction algorithm to solve.The method can realize target-echo-emissive source trinary data association under passive target tracking, promote track initiation speed, improve target tracking accuracy, under acquisition clutter environment, effective lifting of passive target tracking performance, has very important significance for passive target tracking practical implementation.

The technical solution adopted for the present invention to solve the technical problems is: the digital broadcasting passive location method of a kind of target-echo-emissive source trinary data association, is characterized in adopting following steps:

Step one, before the foundation of allotment, first according to the flight path information of target t before kth time scanning, k moment target t is corresponded to the measurement of transmitter s predict, according to measurement covariance set up ripple door, for N number of target, S transmitter, has N × S to confirm ripple door, confirms that ripple door is defined as follows:

$v_{\mathrm{ts}}^k=\{z;{(z-{\hat{z}}_{\mathrm{ts}})}^T{\left(S_t^k\right)}^{-1}(z-{\hat{z}}_{\mathrm{ts}})\≤\mathrm{\τ}\}---\left(1\right)$

Wherein: t=1 ... N; S=1 ... S; τ is ripple door size setting value;

${\hat{z}}_{\mathrm{ts}}=h_s\left({\hat{X}}_t^{k|k-1}\right)---\left(2\right)$

$S_t^k={\tilde{h}}_s^T{P_t}^{k|k-1}{\tilde{h}}_s+R_s---\left(3\right)$

${\tilde{h}}_s=\frac{\∂h_s\left(X\right)}{\∂X}{|}_{X={\hat{X}}_t^{\mathrm{k\; k}-1}}---\left(4\right)$

In formula, h _s() is measurement equation, R _sfor measurement noise covariance, for newly ceasing covariance.

Step 2, suppose there is S portion transmitter, kth time is scanned the measurement obtained to form a line and be then corresponding in turn to each transmitter and line up S row, add target column like this, just define the distribution Solve problems of a S+1-D dimension. by setting up cost function, realize combining the cost function minimization under constraint, thus complete assignment problem and solve.

In order to represent that assignment problem is convenient, define a binary indieating variable

The object of assignment problem is exactly find optimum one group minimization global association cost:

$\mathrm{Cost}=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}{c}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}---\left(6\right)$

following restriction set must be met:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=0,\mathrm{if}{i}_o=i_p;o\≠p;o,p\∈\{1,...S\}---\left(7\right)$

$\underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}I({\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s},i)=1,i=\mathrm{1,2},...m---\left(8\right)$

$\left\{\begin{array}{c}\underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_1=\mathrm{1,2},...m\\ \underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_2=\mathrm{1,2},...m\\ \·\\ \·\\ \·\\ \underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_{s-1}=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_s=\mathrm{1,2},...m\end{array}\right.---\left(9\right)$

Wherein

Different from the S-D assignment problem of standard, except man-to-man association restraint-type (9), also need increase by two restriction set: restriction diversity (7) shows that same measurement should from different transmitters; Restriction diversity (8) shows that same measurement should from different targets;

Now define S measurement the cost distributing to targetpath t is:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=-\ln \frac{p\left(Z_{i_1{i}_2\·\·\·i_s}\right|X_t)}{p\left(Z_{i_1{i}_2\·\·\·i_s}\right|t=\mathrm{\Φ})}---\left(11\right)$

Wherein $p\left(Z_{i_1{i}_2\·\·\·i_s}\right|t=\mathrm{\Φ})=\underset{s=1}{\overset{S}{\mathrm{\Π}}}{\left[\frac{1}{{\mathrm{\Ψ}}_s}\right]}^{u\left(i_s\right)}$ Represent and measure come from the probability of false-alarm.

$p\left(Z_{i_1{i}_2\·\·\·i_s}\right|X_t)=p\left(z\right|{\hat{X}}_t)\underset{s=1}{\overset{S}{\mathrm{\Π}}}{(1-P_{D_s})}^{1-u\left(i_s\right)}{P_{D_s}}^{u\left(i_s\right)}---\left(12\right)$

Wherein:

$p\left(z\right|{\hat{X}}_t)=\frac{1}{\sqrt{\left|2\mathrm{\π}{S}_t^k\right|}}\exp \left[{(z-\stackrel{\‾}{z})}^T{\left(S_t^k\right)}^{-1}(z-\stackrel{\‾}{z})\right]---\left(13\right)$

$\stackrel{\‾}{z}=h\left({\hat{X}}_t\right);S_t^k=H_X{P_t}^{k|k-1}{H}_X^T+R---\left(14\right)$

it is the detection probability of sensor s; U (i _s) be binary variable; Represent the echo signal whether detected from transmitter s:

$u\left(i_s\right)=\left\{\begin{array}{cc}0& i_s=0;\\ 1& \mathrm{otherwise};\end{array}\right.---\left(15\right)$

Therefore individual measurement sequence distribute to the cost of targetpath t:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=-\ln p\left(z\right|{\hat{X}}_t)+\underset{s=1}{\overset{S}{\mathrm{\Σ}}}\{(u\left(i_s\right)-1)\ln (1-P_{D_s})-u\left(i_s\right)\ln \left(P_{D_s}{\mathrm{\Ψ}}_s\right)\}---\left(16\right)$

Step 3, multi-dimension assignment is changed into a series of 2-D problem solving.

Step 4, to solve based on improving the 2-D assignment problem of auction algorithm.

Two dimension distributes mathematical model:

$\max \underset{n=0}{\overset{N}{\mathrm{\Σ}}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}{a}_{\mathrm{nm}}{\mathrm{\χ}}_{\mathrm{nm}}---\left(17\right)$

St.

$\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\χ}}_{\mathrm{nm}}=1\∀m=\mathrm{1,2},...M---\left(18\right)$

$\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\χ}}_{\mathrm{nm}}=1\∀n=\mathrm{1,2},...N---\left(19\right)$

χ _nm=1 represents that m measurement is assigned with gives the n-th target; χ _nm=0 expression does not associate, and explains this problem: a from the angle of auction _nmrepresent and measure the Attraction Degree of m for target n; μ _mrepresent the cost measuring m; The pure profit of target n is defined as λ _n=a _nm-μ _m;

Provide the concrete steps that auction algorithm solves below:

A) bid the stage: the target i that each is not assigned with.

1. calculate each and measure the profit of j for target i:

v _ij＝a _ij-μ _j(20)

2. optimum measurement j is found ^*:

$j*=\underset{j}{\max }{v}_{\mathrm{ij}}---\left(21\right)$

3. the suboptimum profit for target i is calculated:

$w=\underset{j,j\≠j^{*}}{\max }{v}_{\mathrm{ij}}---\left(22\right)$

4. target i is calculated to measuring bidding of j:

$b_{{\mathrm{ij}}^{*}}=a_{{\mathrm{ij}}^{*}}-w+\mathrm{\ϵ}---\left(23\right)$

In formula, ε characterizes microvariations.

B) allocated phase:

J is measured for each, if there is target i to bid to it, bids and be greater than himself value μ _j, then μ is upgraded _j=b _ij; To the target record that measurement j bids simultaneously before cancelling, make it again seek other and measure.

C) if still had, target is unallocated must be measured, and enters steps A), otherwise stop.

Step 5, the S-D track initiation deleted based on the cloth station infeasible branch of geological information.

Consider four cell sites, a receiver, Mei Liangge cell site can make a perpendicular bisector, so just whole plane can be divided into different regions, defines 18 regions under this scene altogether.Assuming that existing measurement collection initial for new flight path.

Concrete steps are as follows:

A) feasible, infeasible branch list is set up according to cloth station information:

Collect the geographical location information at all digital broadcast transmitting stations in monitor area, use PC Tools to make perpendicular bisector to every two transmitters, region is divided into different regions, a kind of feasible measurement sequence combination of each Regional Representative.

B) carry out cost calculating for the branch meeting feasible constraint condition, the branch for discontented constraint directly deletes;

C) carry out the distribution of S-D multidimensional for the branch's set meeting constraint condition to solve, concrete method for solving is identical with classical S-D method for solving;

For the optimal set selected as new interim flight path, enter flight path management.

The invention has the beneficial effects as follows: the method, in the track initiation stage, utilizes cloth station geological information to delete infeasible branch; In the flight path maintenance stage, first utilize the information of existing flight path to generate ripple door, reduce the scale of allocation tree; Then cost evaluation is carried out to the feasible measurement sequence set meeting the constraint of ripple door; Finally, use Lagrangian Relaxation Algorithm to be relaxed continuously by multi-dimension assignment as sequence two dimension assignment problem and use improvement auction algorithm to solve.The method can realize target-echo-emissive source trinary data association under passive target tracking, promote track initiation speed, improve target tracking accuracy, under acquisition clutter environment, effective lifting of passive target tracking performance, has very important significance for passive target tracking practical implementation.

Due to the target-echo-emissive source trinary data related question based on digital broadcasting passive location is modeled as a multi-dimension assignment, in the track initiation stage, according to cloth station geological information, delete infeasible branch hypothesis; In the flight path maintenance stage, first utilization is stable associates ripple door with the echo ensembles generation of interim flight path to current time, reduces the scale of allocation tree; Then cost evaluation is carried out to the feasible measurement sequence set meeting the constraint of ripple door; The auction algorithm of Lagrange relaxation and improvement is finally utilized to solve assignment problem.For under SFN digital broadcasting, trinary data association uncertain problem in passive target tracking system, the present invention uses for reference the thought that multidimensional is distributed, flexible use multidimensional distributes the framework of Solve problems, not only solve the trinary data association difficult problem under SFN digital broadcasting in target following, and the calculated amount in track initiation stage is greatly reduced by introducing cloth station geological information, shorten the time of track initiation.

Below in conjunction with the drawings and specific embodiments, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the framework flow graph of the inventive method;

Fig. 2 is the inventive method data correlation stage S+1-D dynamic multidimensional used distribution frame schematic diagram;

Fig. 3 is that the Lagrangian Relaxation Algorithm that the inventive method relates to resolves process flow diagram;

The S-D multidimensional distribution frame schematic diagram that Fig. 4 taked for the inventive method track initiation stage;

Fig. 5 is that the inventive method cloth station geometric space divides schematic diagram;

Fig. 6 a is the inventive method simulating scenes, Fig. 6 b is target 1 location estimation root-mean-square error (RMSE), the y direction velocity estimation RMSE of Fig. 6 c to be the x direction velocity estimation RMSE of target 1, Fig. 6 d be target 1, Fig. 6 e be intersect, the tracking results of parallel four targets;

Fig. 7 is that in the inventive method, the change of number along with cell site's number is deleted by infeasible branch.

Embodiment

With reference to Fig. 1-7.The digital broadcasting passive location method concrete steps of target-echo of the present invention-emissive source trinary data association are as follows:

1, the definition of ripple door is confirmed.

In multidimensional is distributed, the foundation of allocation tree approximately occupies the CPU computing time of 90%, and in order to reduce operand, before the foundation of allotment, before first scanning according to kth time, the flight path information of target t corresponds to the measurement of transmitter s to k moment target t predict, according to measurement covariance set up ripple door, so for N number of target, S transmitter, just has N × S to confirm ripple door, confirms that ripple door is defined as follows:

$v_{\mathrm{ts}}^k=\{z;{(z-{\hat{z}}_{\mathrm{ts}})}^T{\left(S_t^k\right)}^{-1}(z-{\hat{z}}_{\mathrm{ts}})\≤\mathrm{\τ}\}---\left(1\right)$

Wherein: t=1 ... N; S=1 ... S; τ is ripple door size setting value;

${\hat{z}}_{\mathrm{ts}}=h_s\left({\hat{X}}_t^{k|k-1}\right)---\left(2\right)$

$S_t^k={\tilde{h}}_s^T{P_t}^{k|k-1}{\tilde{h}}_s+R_s---\left(3\right)$

${\tilde{h}}_s=\frac{\∂h_s\left(X\right)}{\∂X}{|}_{X={\hat{X}}_t^{\mathrm{k\; k}-1}}---\left(4\right)$

In formula, h _s() is measurement equation, R _sfor measurement noise covariance, for newly ceasing covariance.

2, S+1-D multidimensional apportion model.

Kth time is scanned the measurement obtained to form a line and be then corresponding in turn to each transmitter (supposing there is S portion transmitter) and line up S row, add target column like this, just define the distribution Solve problems of a S+1-D dimension. by setting up cost function, realize combining the cost function minimization under constraint, thus complete assignment problem and solve.

In order to represent that assignment problem is convenient, define a binary indieating variable

The object of assignment problem is exactly find optimum one group minimization global association cost:

$\mathrm{Cost}=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}{c}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}---\left(6\right)$

following restriction set must be met:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=0,\mathrm{if}{i}_o=i_p;o\≠p;o,p\∈\{1,...S\}---\left(7\right)$

$\underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}I({\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s},i)=1,i=\mathrm{1,2},...m---\left(8\right)$

$\left\{\begin{array}{c}\underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_1=\mathrm{1,2},...m\\ \underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_3=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_s=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_2=\mathrm{1,2},...m\\ \·\\ \·\\ \·\\ \underset{t=0}{\overset{T}{\mathrm{\Σ}}}\underset{i_1=0}{\overset{m}{\mathrm{\Σ}}}\underset{i_2=0}{\overset{m}{\mathrm{\Σ}}}\·\·\·\underset{i_{s-1}=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=1,i_s=\mathrm{1,2},...m\end{array}\right.---\left(9\right)$

Wherein

Slightly different from the S-D assignment problem of standard, except man-to-man association restraint-type (9), also need increase by two restriction set: restriction diversity (7) shows that same measurement should from different transmitters; Restriction diversity (8) shows that same measurement should from different targets;

Now define S measurement the cost distributing to targetpath t is:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=-\ln \frac{p\left(Z_{i_1{i}_2\·\·\·i_s}\right|X_t)}{p\left(Z_{i_1{i}_2\·\·\·i_s}\right|t=\mathrm{\Φ})}---\left(11\right)$

Wherein $p\left(Z_{i_1{i}_2\·\·\·i_s}\right|t=\mathrm{\Φ})=\underset{s=1}{\overset{S}{\mathrm{\Π}}}{\left[\frac{1}{{\mathrm{\Ψ}}_s}\right]}^{u\left(i_s\right)}$ Represent and measure come from the probability of false-alarm.

$p\left(Z_{i_1{i}_2\·\·\·i_s}\right|X_t)=p\left(z\right|{\hat{X}}_t)\underset{s=1}{\overset{S}{\mathrm{\Π}}}{(1-P_{D_s})}^{1-u\left(i_s\right)}{P_{D_s}}^{u\left(i_s\right)}---\left(12\right)$

Wherein:

$p\left(z\right|{\hat{X}}_t)=\frac{1}{\sqrt{\left|2\mathrm{\π}{S}_t^k\right|}}\exp \left[{(z-\stackrel{\‾}{z})}^T{\left(S_t^k\right)}^{-1}(z-\stackrel{\‾}{z})\right]---\left(13\right)$

$\stackrel{\‾}{z}=h\left({\hat{X}}_t\right);S_t^k=H_X{P_t}^{k|k-1}{H}_X^T+R---\left(14\right)$

it is the detection probability of sensor s; U (i _s) be binary variable; Represent the echo signal whether detected from transmitter s:

$u\left(i_s\right)=\left\{\begin{array}{cc}0& i_s=0;\\ 1& \mathrm{otherwise};\end{array}\right.---\left(15\right)$

Therefore individual measurement sequence distribute to the cost of targetpath t:

$c_{{\mathrm{ti}}_1{i}_2\·\·\·i_s}=-\ln p\left(z\right|{\hat{X}}_t)+\underset{s=1}{\overset{S}{\mathrm{\Σ}}}\{(u\left(i_s\right)-1)\ln (1-P_{D_s})-u\left(i_s\right)\ln \left(P_{D_s}{\mathrm{\Ψ}}_s\right)\}---\left(16\right)$

An obvious advantage of dynamic assignment utilizes upper one trace information clapped to predict, by traditional S-D/2-D Double Step algorithm, (first step: carry out measuring-measure association, obtains combination and measure collection; Second step: combination is measured collection and distributes to the flight path existed .) become a step, and utilize information of forecasting to eliminate more ML estimation stages consuming time in traditional S-D/2-D, reduce further computing time.

3, the multidimensional distribution based on Lagrangian Relaxation Algorithm solves.

It is two-dimensional problems that multi-dimension assignment can utilize Lagrange relaxation method by continuous print restriction relaxing techniques, multidimensional problem one step to be relaxed, and 2-D assignment problem can well solve in polynomial time with auction algorithm or network flow algorithm, increase restrictive condition successively more afterwards, each step is all 2-D assignment problem, so just multi-dimension assignment is changed into a series of 2-D problem solving.

The committed step of Lagrangian Relaxation Algorithm is the renewal of its multiplier, more classical algorithm is as Subgradient Algorithm etc., but because this algorithm all will carry out minimum operation when solving subproblem at every turn, efficiency is lower, someone proposes agency and revises Subgradient Algorithm for this reason, solve a Subgradient Algorithm insurmountable Z curve difficult problem, greatly shorten working time.

4, solve based on the 2-D assignment problem improving auction algorithm.

Two dimension distributes mathematical model:

$\max \underset{n=0}{\overset{N}{\mathrm{\Σ}}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}{a}_{\mathrm{nm}}{\mathrm{\χ}}_{\mathrm{nm}}---\left(17\right)$

St.

$\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\χ}}_{\mathrm{nm}}=1\∀m=\mathrm{1,2},...M---\left(18\right)$

$\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\χ}}_{\mathrm{nm}}=1\∀n=\mathrm{1,2},...N---\left(19\right)$

χ _nm=1 represents that m measurement is assigned with gives the n-th target; χ _nm=0 expression does not associate, and explains this problem: a from the angle of auction _nmrepresent and measure the Attraction Degree (by likelihood ratio determined) of m for target n; μ _mrepresent the cost (price) measuring m; The pure profit of target n is defined as λ _n=a _nm-μ _m;

Provide the concrete steps that auction algorithm solves below:

D) bid the stage: the target i that each is not assigned with.

1. calculate each and measure the profit of j for target i:

v _ij＝a _ij-μ _j(20)

2. optimum measurement j is found ^*:

$j*=\underset{j}{\max }{v}_{\mathrm{ij}}---\left(21\right)$

3. the suboptimum profit for target i is calculated:

$w=\underset{j,j\≠j^{*}}{\max }{v}_{\mathrm{ij}}---\left(22\right)$

4. target i is calculated to measuring bidding of j:

$b_{{\mathrm{ij}}^{*}}=a_{{\mathrm{ij}}^{*}}-w+\mathrm{\ϵ}---\left(23\right)$

In formula, ε characterizes microvariations.

E) allocated phase:

J is measured for each, if there is target i to bid to it, bids and be greater than himself value μ _j, then μ is upgraded _j=b _ij; To the target record (if existence) that measurement j bids simultaneously before cancelling, make it again seek other and measure.

F) if still had, target is unallocated must be measured, and enters steps A), otherwise algorithm stops.

5, based on the S-D track initiation that the cloth station infeasible branch of geological information deletes.

In the track initiation stage owing to there is not the flight path information of priori, above-mentioned S+1-D dynamic multidimensional allocative decision can not be adopted, but still ternary association uncertain problem need be solved, for this reason, this programme is still based on multidimensional allocative decision, and the S-D multidimensional proposed based on cloth station geological information distributes track initiation scheme.The advantage of this programme has taken into full account cloth station geological information, by infeasible for physics hypothesis branch tree deletion, thus distributes the scale solved in reduction track initiation, shorten the time of new track initiation.

The object in this stage is exactly how from the unchecked measurement set of association phase, to find out those echoes most possibly coming from real goal, initial as new flight path.The present invention fully excavates cloth station geological information, proposes the S-D track initiation scheme based on cloth station geological information.

Consider four cell sites, a receiver, Mei Liangge cell site can make a perpendicular bisector, so just whole plane can be divided into different regions, defines 18 regions under this scene altogether.Assuming that existing measurement collection { z _i} ⁱ _i ⁼ ₌₁ ^minitial for new flight path.As the S-D distribution of classics, for a certain possible measurement sequence

Table 1 measurement sequence

If multidimensional allocative decision traditionally, combination is measured for every four, need that possible situation is planted to 4 unequal to 24 (>18) and carry out cost calculating, in fact, this wherein has some to be physically infeasible combinations, namely can not belong to above-mentioned arbitrary region, be here six kinds of infeasible branch situations.

Concrete steps are as follows:

D) feasible, infeasible branch list is set up according to cloth station information:

The geographical location information collecting all digital broadcast transmitting stations in monitor area (considers that the difference in height of cell site is negligible relative to the distance between cell site, this programme only considers two-dimensional case), PC Tools is used to make perpendicular bisector to every two transmitters, region is divided into different regions, each Regional Representative a kind of feasible measurement sequence combination, and following table is feasible and infeasible branch table.Citing 1 _(4,2,1,3)if represent a target and belong to and represent region 1, so measurement sequence should meet such constraint: z ₄<z ₂<z ₁<z ₃, magnitude relationship here utilizes the definition of the distance component in measuring.

Feasible, the infeasible measurement sequence of table 2

E) carry out cost calculating for the branch meeting feasible constraint condition, the branch for discontented constraint directly deletes,

F) carry out the distribution of S-D multidimensional for the branch's set meeting constraint condition to solve, concrete method for solving is identical with classical S-D method for solving;

G) for the optimal set selected as new interim flight path, enter flight path management.

Embodiment.

Scene setting: transmitter site coordinate is respectively: (10,0), (60,70), (50,170), (100,50); A receiver, its coordinate is: (50 ,-50) unit km; There are four targets, do respectively and intersect and parallel linear uniform motion, initial state be respectively (165,130,200,20), (20,87,200,200), (200,0,200,100), (200,10,200,200); Unit is respectively km and m/s, and test the speed deviation 2m/s, range finding deviation 1km.

Simulation result is as Fig. 6 a-6e, and wherein Fig. 6 a-6d has carried out 50 Monte Carlo analysis to the tracking accuracy of target 1, and visible the inventive method reaches theoretical optimum boundary substantially; Fig. 6 e follows the tracks of total result figure, no matter be that cross-goal and parallel object can form tenacious tracking flight path as seen.

(note: location estimation deviation definition is the distance of estimated position and physical location on two dimensional surface).

Following table contrasts the performance of data association algorithm under various clutter and noise situations, wherein correctly association rate equal k clap measure in the proportion shared by measurement that correctly associates with target, that is:

Correct association rate under table 1 many kinds of clutters contrasts ( σ ^d=100m)

Correct association rate contrast (clutter number=100) under table 2 many kinds of noises

Carried out compliance test result to the technology of deleting based on cloth station geological information, be not difficult to find from Fig. 7, when transmitter increased number, the effect that the technology of deleting produces can be more obvious.

From above simulation result, infeasible branch based on cloth station geological information proposed by the invention deletes technology and can realize having stablizing under clutter scene effectively to follow the tracks of to multiple goal based on the ternary uncertain data association scheme that S+1-D dynamic multidimensional distributes, and simulation parameter conforms to actual scene, there is actual directive significance.

Claims (1)

1. a digital broadcasting passive location method for target-echo-emissive source trinary data association, is characterized in that comprising the following steps:

Step one, before the foundation of allotment, first according to the flight path information of target t before kth time scanning, k moment target t is corresponded to the measurement of transmitter s predict, according to measurement covariance set up ripple door, for N number of target, S transmitter, has N × S to confirm ripple door, confirms that ripple door is defined as follows:

$v_{\mathrm{ts}}^k=\{z;{(z-{\hat{z}}_{\mathrm{ts}})}^T{\left(S_t^k\right)}^{-1}(z-{\hat{z}}_{\mathrm{ts}})\&le;\mathrm{\&tau;}\}---\left(1\right)$

Wherein: t=1 ... N; S=1 ... S; τ is ripple door size setting value;

${\hat{z}}_{\mathrm{ts}}=h_s\left({\hat{X}}_t^{k|k-1}\right)---\left(2\right)$

$S_t^k={\tilde{h}}_s^T{P}_t^{k|k-1}{\tilde{h}}_s+R_s---\left(3\right)$

${\tilde{h}}_s={\frac{\&PartialD;h_s\left(X\right)}{\&PartialD;X}|}_{X={\hat{X}}_t^{\mathrm{kk}-1}}---\left(4\right)$

In formula, h _s() is measurement equation, R _sfor measurement noise covariance, for newly ceasing covariance;

Step 2, suppose there is S portion transmitter, kth time is scanned the measurement obtained to form a line and be then corresponding in turn to each transmitter and line up S row, add target column like this, just define the distribution Solve problems of a S+1-D dimension. by setting up cost function, realize combining the cost function minimization under constraint, thus complete assignment problem and solve;

In order to represent that assignment problem is convenient, define a binary indieating variable

The object of assignment problem is exactly find optimum one group minimization global association cost:

$\mathrm{Cost}=\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i_1=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_2=0}{\overset{m}{\mathrm{\&Sigma;}}}\&CenterDot;\&CenterDot;\&CenterDot;\underset{i_s=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}{c}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}---\left(6\right)$

following restriction set must be met:

$c_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=0,\mathrm{if}{i}_o=i_p;o\&NotEqual;p;o,p\&Element;\{1,...S\}---\left(7\right)$

$\underset{t=0}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i_1=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_2=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_3=0}{\overset{m}{\mathrm{\&Sigma;}}}\&CenterDot;\&CenterDot;\&CenterDot;\underset{i_s=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}I({\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s},i)=1,i=\mathrm{1,2},...m---\left(8\right)$

$\left\{\begin{array}{c}\underset{t=0}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i_2=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_3=0}{\overset{m}{\mathrm{\&Sigma;}}}\&CenterDot;\&CenterDot;\&CenterDot;\underset{i_s=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=1,i_1=\mathrm{1,2},...m\\ \underset{t=0}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i_1=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_3=0}{\overset{m}{\mathrm{\&Sigma;}}}\&CenterDot;\&CenterDot;\&CenterDot;\underset{i_s=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=1,i_2=\mathrm{1,2},...m\\ .\\ .\\ .\\ \underset{t=0}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i_1=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i_2=0}{\overset{m}{\mathrm{\&Sigma;}}}\&CenterDot;\&CenterDot;\&CenterDot;\underset{i_{s-1}=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=1,i_s=\mathrm{1,2},...m\end{array}\right.---\left(9\right)$

Wherein

Different from the S-D assignment problem of standard, except man-to-man association restraint-type (9), also need increase by two restriction set: restriction diversity (7) shows that same measurement should from different transmitters; Restriction diversity (8) shows that same measurement should from different targets;

Now define S measurement the cost distributing to targetpath t is:

$c_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=-\ln \frac{p\left(Z_{i_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}\right|X_t)}{p\left(Z_{i_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}\right|t=\mathrm{\&Phi;})}---\left(11\right)$

Wherein represent and measure come from the probability of false-alarm.

$p\left(Z_{i_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}\right|X_t)=p\left(z\right|{\hat{X}}_t)\underset{s=1}{\overset{S}{\mathrm{\&Pi;}}}{(1-P_{D_s})}^{1-\left(i_s\right)}{P_{D_s}}^{u\left(i_s\right)}---\left(12\right)$

Wherein:

$p\left(z\right|{\hat{X}}_t)=\frac{1}{\sqrt{\left|2\mathrm{\&pi;}{S}_t^k\right|}}\exp \left[{(z-\stackrel{\&OverBar;}{z})}^T{\left(S_t^k\right)}^{-1}(z-\stackrel{\&OverBar;}{z})\right]---\left(13\right)$

$\stackrel{\&OverBar;}{z}=h\left({\hat{X}}_t\right);S_t^k=H_X{P}_t^{k|k-1}{H}_X^T+R---\left(14\right)$

it is the detection probability of sensor s; U (i _s) be binary variable; Represent the echo signal whether detected from transmitter s:

$u\left(i_s\right)=\left\{\begin{array}{cc}0& i_s=0;\\ 1& \mathrm{otherwise};\end{array}\right.---\left(15\right)$

Therefore individual measurement sequence distribute to the cost of targetpath t:

$c_{t{i}_1{i}_2\&CenterDot;\&CenterDot;\&CenterDot;i_s}=-\ln p\left(z\right|{\hat{X}}_t)+\underset{s=1}{\overset{S}{\mathrm{\&Sigma;}}}\{(u\left(i_s\right)-1)\ln (1-P_{D_s})-u\left(i_s\right)\ln \left(P_{D_s}{\mathrm{\&Psi;}}_s\right)\}---\left(16\right)$

Step 3, multi-dimension assignment is changed into a series of 2-D problem solving;

Step 4, to solve based on improving the 2-D assignment problem of auction algorithm;

Two dimension distributes mathematical model:

$\max \underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}\underset{m=0}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{\mathrm{nm}}{\mathrm{\&chi;}}_{\mathrm{nm}}---\left(17\right)$

St.

$\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&chi;}}_{\mathrm{nm}}=1\&ForAll;m=\mathrm{1,2},...M---\left(18\right)$

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&chi;}}_{\mathrm{nm}}=1\&ForAll;n=\mathrm{1,2},...N---\left(19\right)$

χ _nm=1 represents that m measurement is assigned with gives the n-th target; χ _nm=0 expression does not associate, and explains this problem: a from the angle of auction _nmrepresent and measure the Attraction Degree of m for target n; μ _mrepresent the cost measuring m; The pure profit of target n is defined as λ _n=a _nm-μ _m;

Provide the concrete steps that auction algorithm solves below:

A) bid the stage: the target i that each is not assigned with;

1. calculate each and measure the profit of j for target i:

v _ij＝a _ij-μ _j(20)

2. optimum measurement j is found ^*:

$j^{*}=\underset{j}{\max }{v}_{\mathrm{ij}}---\left(21\right)$

3. the suboptimum profit for target i is calculated:

$w=\underset{j,j\&NotEqual;j^{*}}{\max }{v}_{\mathrm{ij}}---\left(22\right)$

4. target i is calculated to measuring bidding of j:

$b_{{\mathrm{ij}}^{*}}=a_{{\mathrm{ij}}^{*}}-w+\mathrm{\&epsiv;}---\left(23\right)$

In formula, ε characterizes microvariations;

B) allocated phase:

J is measured for each, if there is target i to bid to it, bids and be greater than himself value μ _j, then μ is upgraded _j=b _ij; To the target record that measurement j bids simultaneously before cancelling, make it again seek other and measure;

C) if still had, target is unallocated must be measured, and enters steps A), otherwise stop;

Step 5, the S-D track initiation deleted based on the cloth station infeasible branch of geological information;

Consider four cell sites, a receiver, Mei Liangge cell site can make a perpendicular bisector, so just whole plane can be divided into different regions, defines 18 regions under this scene altogether; Assuming that existing measurement collection initial for new flight path;

Concrete steps are as follows:

A) feasible, infeasible branch list is set up according to cloth station information:

Collect the geographical location information at all digital broadcast transmitting stations in monitor area, use PC Tools to make perpendicular bisector to every two transmitters, region is divided into different regions, a kind of feasible measurement sequence combination of each Regional Representative;

B) carry out cost calculating for the branch meeting feasible constraint condition, the branch for discontented constraint directly deletes;

C) carry out the distribution of S-D multidimensional for the branch's set meeting constraint condition to solve, concrete method for solving is identical with classical S-D method for solving;

For the optimal set selected as new interim flight path, enter flight path management.