CN103685483B - A kind of sensor network data association method matched relative to position based on echo signal - Google Patents

Abstract

The present invention provides a kind of sensor network data association method matched based on echo signal relative to position, compare the relative position between sensor measurement signal by employing and extract the method that the method for relative mode position obtains object matching pair corresponding to different sensors system, and giving the matching algorithm being applicable to the association of sensor target signal and the method for estimation of sensor bias of a kind of improvement.The method sets up sensor bias model, and give the expression formula of relative position between sensor target signal and between different sensors, by find between different sensors position relatively maximum mate to method, the echo signal match point that a pair different sensors is corresponding can be found, and obtain a estimation of deviation the most coarse, by this estimation of deviation, the object matching pair between remaining sensor signal can be found, complete the data correlation of different target signal and obtain the result of a more accurate estimation of deviation.

Description

A kind of sensor network data association method matched relative to position based on echo signal

Technical field

The present invention relates to multiple technical fields of sensor network, signal transacting, Multi-sensor Fusion and data correlation, It is specifically related to a kind of sensor network data association method matched based on echo signal relative to position.

Background technology

The application background of the present invention is:

Multi-sensor data corresponding technology is widely used in multiple-sensor network system, and data association technique is to pass the modern times more A major issue in sensor network system, by utilizing the redundancy of different sensors, multiple-sensor network system phase (document [1] D.L.Hall and is seen than having better performance in traditional Method for Single Sensor System J.Llinas.Handbook of Multisensor Data Fusion Boca Raton,FL:CRC Press,2001.)。 If multi-sensor data association purpose is to determine whether the dry measure signal that different sensors observes derives from same mesh Mark.When different sensors in sensor network observes same echo signal, same target is set up in different sensors Measure signal must have certain similar feature because of its physical resources, but meanwhile, due to clutter interference with And the instability of sensor self performance, the feature measuring signal of sensor may be caused incomplete same (to see document [2] J.Llinas,E.Waltz.Multisensor Data Fusion Boston,MA:Artech House,1990).Many sensings Device data association technique is i.e. the similar features utilizing and measuring signal, judges that the incomplete same measurement signal of these features is No from same target and eliminate the impact for association results of clutter and sensor self performance.

Being analyzed as follows of relevant prior art:

Scheme one

Scenario Name: overall situation arest neighbors data correlation method (GNN) (sees document [3] S.Blackman and R.Popoli.Design and Analysis of Modern Tracking Systems.Boston,MA:Artech House, 1999., and see document [4] P.Konstantinova, A.Udvarev, and T.Semerdjiev.A Study of a Target Tracking Algorithm Using Global Nearest Neighbor Approach.in Proceedings of the International Conference on Computer Systems and Technologies(CompSysTech03),2003.)

Algorithm idea: overall situation arest neighbors data correlation method firstly the need of the deviation estimated between different sensors to disappearing Except deviation is for the impact of association results, then form the incidence matrix of cost function based on object statistics distance, by not Same optimization method, solves the optimal solution of this incidence matrix, thus finds different sensors to measure the corresponding relation of echo signal.

Algorithm shortcomings: overall situation arest neighbors data correlation method needs to estimate the deviation between different sensors, and this is in reality Border is difficult to.Additionally, under intensive echo signal or many clutter environment, its association results error rate is higher.

Scheme two

Scenario Name: the data correlation method (GNP) of overall situation pattern recently (sees document [5] M.Levedahl.An Explicit Pattern Matching Assignment Algorithm.in Proceedings of SPIE, vol.4728,2002.pp.461-469.)

Algorithm idea: the data correlation method of the overall situation recently pattern is by by the deviation of sensor and loss, false alarm The sensor performance parameters such as rate introduce the statistical distance cost function of echo signal, the method meter estimated by maximum likelihood function Calculate the deviation under each possible relevance assumption.After eliminating estimated bias impact, form cost incidence matrix, solve this pass The optimal solution of connection matrix, thus find different sensors to measure the corresponding relation of echo signal.

Algorithm shortcomings: the algorithm complex of this method is the highest, when the quantity of echo signal increases, the complexity of the method Degree can great rising.

Scheme three

Scenario Name: the fuzzy data correlation method with reference to topology based on echo signal (see document [6] Y.Shi, Y.Wang,X.M.Shan.A Novel Fuzzy Pattern Recognition Data Association Method for Biased Sensor Data in Information Fusion,2006.FUSION 06.9th International Conference on.2006, pp.1-5., and see document [7] X.J.Du, Y.Wang, X.M.Shan.Track-to- Track Association using Reference Topology in the Presence of Sensor Bias.In Proc.2010 International Conf.on Signal Processing.pp.2196-2201.)

Algorithm idea: the fuzzy data correlation method with reference to topology based on echo signal is by extracting the fuzzy reference of one The method of topology is as the feature of echo signal, and the cost function defining a kind of parameter including sensor performance comes Form the incidence matrix of echo signal, by solving the optimal solution of this incidence matrix, thus find different sensors to measure target The corresponding relation of signal.

Algorithm shortcomings: the fuzzy data correlation method with reference to topology based on echo signal is relatively vulnerable to sensor missing inspection Affecting, and this method is easily subject to the impact that parameter is arranged, the complexity of this algorithm is higher.

Summary of the invention

The object of the invention is: 1) can eliminate the sensor bias impact for association results.2) relative to conventional method, Promote on this method overall performance.3) arithmetic speed of association algorithm meets requirement of real time.

Technical solution of the present invention is: a kind of sensor network data affiliated party matched relative to position based on echo signal Method, the method sets up sensor bias model, and give between sensor target signal and between different sensors relative The expression formula of position, by find between different sensors position relatively maximum mate to method, it is possible to find a pair not With the echo signal match point that sensor is corresponding, and obtain a estimation of deviation the most coarse, by this estimation of deviation, energy Enough find the object matching pair between remaining sensor signal, complete the data correlation of different target signal and obtain one more The result of accurate estimation of deviation, idiographic flow is as follows

1, sensor bias model

Assume two different sensing system A and B, whole observation area is observed N number of target, wherein sensor system System A observes m echo signal, and sensing system B observes that n echo signal, each sensing system can exist partially Differ from and affected by clutter noise, then sensing system buggy model is set up as follows:

$A_i=X_i+G\left(P\right)+{\stackrel{\‾}{x}}_A;i=\mathrm{1...}m$

$B_j=X_j+G\left(Q\right)+{\stackrel{\‾}{x}}_B;j=\mathrm{1...}n$

Wherein A_iThe i-th echo signal observed for sensors A, B_jThe jth echo signal observed for sensor B,For the physical location of i-th target, X_jFor the physical location of jth target, G (v) is the noise of sensing system, its average Being 0, covariance matrix is v, and for sensing system A and B, its covariance matrix is respectively P and Q,It is respectively sensing Device system A and the deviation of B, the purpose of data correlation is to find echo signal A that sensing system A and B observes_iAnd B_jIt Between corresponding relation；

2, the relative position of echo signal

Assume that sensing system A observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

${\stackrel{\→}{X}}_{Aj}={\stackrel{\→}{X}}_j+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

WhereinIt is expressed as the i-th dbjective state that sensing system A observes,It is expressed as sensing system A to see The jth dbjective state measured,Represent i-th target and the virtual condition of jth target respectively,Represent sensing The deviation of device system A,Representing the Gauss measurement noise of sensing system A, its average is 0, and covariance matrix is WhereinRepresent noiseVariance；

The i-th dbjective state that then sensing system A observes can be expressed as follows with the relative position of jth dbjective state:

${\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{X}}_{Aj}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_j-{\stackrel{\→}{X}}_i+{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{X}}_{ij}+{\stackrel{\→}{v}}_A^{\′}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noise's With, whereinIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noiseVariance；

In like manner, sensing system B observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\→}{X}}_{Bi}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

${\stackrel{\→}{X}}_{Bj}={\stackrel{\→}{X}}_j+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

WhereinIt is expressed as the i-th dbjective state that sensing system B observes,It is expressed as sensing system B observation The jth dbjective state arrived,Represent i-th target and the virtual condition of jth target respectively,Represent sensor The deviation of system B,Representing the Gauss measurement noise of sensing system B, its average is 0, and covariance matrix isIts InRepresent noiseVariance；

The i-th dbjective state that then sensing system B observes can represent such as with the relative position of jth dbjective state Under:

${\stackrel{\→}{X}}_{Bij}={\stackrel{\→}{X}}_{Bj}-{\stackrel{\→}{X}}_{Bi}={\stackrel{\→}{X}}_j-{\stackrel{\→}{X}}_i+{\stackrel{\→}{v}}_B^{\′}={\stackrel{\→}{X}}_{ij}+{\stackrel{\→}{v}}_B^{\′}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noise's With, whereinIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noiseVariance；

RelativelyWithCan obtain:

${\stackrel{\→}{X}}_{Bij}-{\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{v}}_B^{\′}-{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{v}}^{\′\′}$

Above formula can obtain, and the difference of the relative position of the corresponding target pair between different sensors system is by Gaussian noiseDetermining, its average is 0, and covariance matrix isWhereinRepresent noiseSide Difference；

3, the relative position of different sensors system

Assuming that target i that sensors A observes corresponds to target a that sensor B observes, then its state is represented by:

${\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

${\stackrel{\→}{X}}_{Ba}={\stackrel{\→}{X}}_a+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

WhereinRepresentative sensor A observed object signal i position,Represent target i physical location,Representative sensor A Deviation,Representative sensor A noise,Representative sensor B observed object signal a position,Represent target a physical location,Representative sensor B deviation,Representative sensor B noise.

Then

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{B}}_B-{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_B-{\stackrel{\→}{v}}_A={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

Target i that i.e. sensing system A and B matches and the difference of aRelative deviation for sensing system A and BWith Gaussian noise v " ' determine, sensing system Gaussian noise v " ' average be 0, covariance matrix is WhereinRepresent noise v " ' variance；

4, based on echo signal relative to the pairing algorithm of position

4.1, find twin target signal match point and sensor bias is estimated

Assume that sensing system A observes m echo signal and sensing system B observes n target, from sensor system The echo signal of system A observation is chosen echo signal i, and from the echo signal that sensing system B observes, chooses target letter Number a, calculates remaining m-1 echo signal j of sensing system A surplus with relative position and the sensing system B of echo signal i N-1 remaining echo signal b is with the relative position of echo signal a and compares, when the fiducial value of relative position | | A_ij-B_ab| |≤△₁, wherein A_ijRepresent the relative distance between echo signal i and j, B_abRepresent the relative distance between echo signal a and b, △₁Represent threshold value 1, it is believed that j and b is the echo signal of pairing, and defines new Matrix C ntNum_iaCalculate possibility Echo signal j of pairing and the number of b, by remaining n-1 echo signal a of cycle sensor system B, can obtain Arrive as different corresponding match point i-＞ a, maximum number MaxCntNum of possible pairing echo signal point_ia, definition can The number of pairing is Matchingpair, and quantity Matchingpair of the point owing to matching necessarily is less than or equal to sensor Target number m that system A observes and the minimum of a value of target number n that sensing system B observes, if that finds may join Maximum number MaxCntNum to echo signal point_iaEqual to m-1, it is believed that the most corresponding sensing system A observes Echo signal a that observes of echo signal i and sensing system A be match point, and can mate to the number of point be Matchingpair, then can enter next step 4.2, the number of point that otherwise explanation can be matched is less than m-1；

Start the cycle in the echo signal of system A observation and choose echo signal i, and repeat above step, it is assumed that when following During echo signal i=c that ring observes to sensors A, if maximum number MaxCntNum of possible pairing echo signal point_iaLittle In m-c, the most now explanation match point number Matchingpair is necessarily less than m-c, then reduce the number of the point that may match, and Continue cycling through；If the number of the point that can match is equal to m-c, then number Matchingpair of the point that explanation can be matched is Find and equal to m-c, then store match point i-＞ a now, enter next step 4.2；

4.2, remaining echo signal match point is found

By 4.1 steps, have found the first point to pairing, then can be the thickest to match point calculating one by this Estimation of deviation slightly, the echo signal now observed by sensing system A is by adding acquired estimation of deviation, Ke Yiying It is mapped in the observation area of sensing system B, if the some map (A being mapped in B_j) the target letter that observes with sensing system B Number B_bMeet | | map (A_j)-B_b||≤△₂, wherein map (A_j) represent echo signal A_jIt is mapped to the corresponding points in sensor B region, B_bThe echo signal that representative sensor B observes, △₂Represent threshold value 2, and now B_bUniquely, then it is believed that j-＞ b now For match point, by finding these match point j-＞ b meeting uniqueness, an estimation of deviation the most accurate can be calculated Value, the echo signal observed for remaining sensors A, by adding this more accurate estimation of deviation value by sensor system The echo signal of system A observation is mapped in the observation area of sensing system B, searches out the target letter of the nearest B of same mapping point Number, the pairing of left point can be completed, thus complete whole association process；

5, the determination of thresholding

In above-mentioned steps, need to use threshold value △₁,△₂Find match point, it is therefore necessary to calculate suitable door Limit value realizes whole association process；

During above-mentioned steps 4, need by threshold value △₁Compare relative distance A_ijAnd B_ij, by step 2 Analyze:

${\stackrel{\→}{X}}_{Bij}-{\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{v}}_B^{\′}-{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{v}}^{\′\′}$

WhereinRepresent sensor B observed object i and j Relative position vector,Represent sensors A observed object I and j Relative position vector,Represent the noise that B with A sensor is comprised relative to position.The i.e. mesh of sensors A observation The difference of the relative position that the relative position of mark signal leads to the echo signal of sensor B observation is one and meets making an uproar of Gaussian Profile Sound, its average is 0, and covariance matrix isWhereinRepresent noiseVariance, Then utilize the 3-σ principle of Gaussian Profile, select threshold value △₁For

During above-mentioned steps 4, need by threshold value △₂Compare the observed object signal simultaneous interpretation of sensors A The mapping corresponding relation of sensor B observed object signal, by the analysis of step 3:

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{B}}_B-{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_B-{\stackrel{\→}{v}}_A={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

WhereinRepresent the deviation between sensors A and sensor B, whereinRepresentative sensor A observed object signal i Position,Representative sensor A deviation,Representative sensor A noise,Representative sensor B observed object signal a position, Representative sensor B deviation,One is differed between the echo signal that representative sensor B noise, i.e. sensors A and sensor B observe Individual deviationWith remaining noiseWherein remaining noiseMeeting Gaussian Profile and its average is 0, covariance matrix isWhereinRepresent noiseVariance, then utilize the 3-σ principle of Gaussian Profile, select door Limit value △₂For

6, relative deviation is estimated

After searching out a match point, estimate to determine that remaining coupling is right by relative deviation, dividing by step 2 Analysis, it can be seen that the measured deviation of a match point i-＞ a can be expressed as follows:

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

WhereinRepresent the relative deviation between sensors A and sensor B observation signal,Represent sensor B to see Survey the position of echo signal a,Represent the position of sensors A observed object signal i,Between sensing system A and B Relative deviation,For noise.

Assume have n coupling right, then measured deviation is:

${\stackrel{\→}{X}}_{AB}=H\×{\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}_{(2n\×1)}$

WhereinIllustrate n coupling right Between relative distance vector,For observed differential matrix,Represent noise vector,Illustrate Need the relative deviation between the different sensors estimated；

Least-squares estimation is to minimize:

WhereinRepresent error sum of squares,Representing the estimation to relative deviation, T represents the transposition of matrix.

By taking differential and to make it be 0, can obtain:

WhereinRepresent the value of the relative deviation of least-squares estimation.

Then sensor relative deviationEstimate is:

${\hat{R}}_{bls}={\left(H^{T}H\right)}^{-1}{H}^T{\stackrel{\→}{X}}_{AB}.$

The advantage of technical solution of the present invention and good effect be:

1), the sensor bias of shadow to(for) association results is decreased based on target relative to the correlating method of position by employing Ring, by using based on target relative to the correlating method of position, utilize the echo signal intrinsic characteristic relative to position, effectively subtract The little sensor bias impact for association results, compared to conventional method, has had bigger lifting from performance.

2), it is applicable to the pairing algorithm of echo signal of multi-sensor data association, at the mesh of multi-sensor data association In the pairing algorithm of mark signaling point, first pass through and circulate maximum between corresponding echo signal point searching different sensors system Can match the logarithm of echo signal, thus search out a pair reliable echo signal point, by this pair echo signal, can estimate Count out the relative deviation between sensing system, utilize this deviation estimated can obtain remaining match point, and calculate Obtain the relative deviation between a more accurate different sensors system.

3), give the method for estimation of more accurate sensor relative deviation, in the present invention, first pass through searching the A pair reliable match point, can obtain a sensor relative deviation the most coarse, recycle this sensor the most inclined After difference, remaining target pairing signal can be obtained, finally, a more essence can be obtained by the method for least-squares estimation True sensor relative deviation.

Accompanying drawing explanation

Fig. 1 is a kind of sensor network data association method flow process matched relative to position based on echo signal of the present invention Figure.

Detailed description of the invention

Below in conjunction with the accompanying drawings and detailed description of the invention further illustrates the present invention.

The present invention proposes a kind of relative position comparing between sensor measurement signal by employing and extracts phase contraposition Put the method for pattern to the method obtaining object matching pair corresponding to different sensors system, and give being suitable for of a kind of improvement Matching algorithm and the method for estimation of sensor bias in the association of sensor target signal.The method sets up sensor bias mould Type, and give the expression formula of relative position between sensor target signal and between different sensors, by finding difference Between sensor relative to position maximum coupling to method, the echo signal pairing that a pair different sensors is corresponding can be found Point, and obtain a estimation of deviation the most coarse, by this estimation of deviation, can find between remaining sensor signal Object matching pair, completes the data correlation of different target signal and obtains the result of a more accurate estimation of deviation.Specifically Flow process is as follows:

1, sensor bias model

Assume two different sensing system A and B, whole observation area is observed N number of target, wherein sensor system System A observes m echo signal, and sensing system B observes that n echo signal, each sensing system can exist partially Differ from and affected by clutter noise, then sensing system buggy model is set up as follows:

$A_i=X_i+G\left(P\right)+{\stackrel{\‾}{x}}_A;i=\mathrm{1...}m$

$B_j=X_j+G\left(Q\right)+{\stackrel{\‾}{x}}_B;j=\mathrm{1...}n$

Wherein A_iThe i-th echo signal observed for sensors A, B_jThe jth echo signal observed for sensor B,For the physical location of i-th target, X_jFor the physical location of jth target, G (v) is the noise of sensing system, its average Being 0, covariance matrix is v, and for sensing system A and B, its covariance matrix is respectively P and Q,It is respectively sensing Device system A and the deviation of B.The purpose of data correlation is to find echo signal A that sensing system A and B observes_iAnd B_jIt Between corresponding relation.

2, the relative position of echo signal

Assume that sensing system A observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

${\stackrel{\→}{X}}_{Aj}={\stackrel{\→}{X}}_j+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

WhereinIt is expressed as the i-th dbjective state that sensing system A observes,It is expressed as sensing system A to see The jth dbjective state measured,Represent i-th target and the virtual condition of jth target respectively,Represent sensing The deviation of device system A,Representing the Gauss measurement noise of sensing system A, its average is 0, and covariance matrix is WhereinRepresent noiseVariance；

The i-th dbjective state that then sensing system A observes can represent such as with the relative position of jth dbjective state Under:

${\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{X}}_{Aj}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_j-{\stackrel{\→}{X}}_i+{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{X}}_{ij}+{\stackrel{\→}{v}}_A^{\′}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noise's With, whereinIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noiseVariance；

In like manner, sensing system B observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\→}{X}}_{Bi}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

${\stackrel{\→}{X}}_{Bj}={\stackrel{\→}{X}}_j+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

WhereinIt is expressed as the i-th dbjective state that sensing system B observes,It is expressed as sensing system B to see The jth dbjective state measured,Represent i-th target and the virtual condition of jth target respectively,Represent sensing The deviation of device system B,Representing the Gauss measurement noise of sensing system B, its average is 0, and covariance matrix is WhereinRepresent noiseVariance；

The i-th dbjective state that then sensing system B observes can represent such as with the relative position of jth dbjective state Under:

${\stackrel{\→}{X}}_{Bij}={\stackrel{\→}{X}}_{Bj}-{\stackrel{\→}{X}}_{Bi}={\stackrel{\→}{X}}_j-{\stackrel{\→}{X}}_i+{\stackrel{\→}{v}}_B^{\′}={\stackrel{\→}{X}}_{ij}+{\stackrel{\→}{v}}_B^{\′}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noise's With, whereinIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noiseVariance；

RelativelyWithCan obtain:

${\stackrel{\→}{X}}_{Bij}-{\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{v}}_B^{\′}-{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{v}}^{\′\′}$

Above formula can obtain, and the difference of the relative position of the corresponding target pair between different sensors system is by Gaussian noiseDetermining, its average is 0, and covariance matrix isWhereinRepresent noiseSide Difference；.

3, the relative position of different sensors system

Assuming that target i that sensors A observes corresponds to target a that sensor B observes, then its state is represented by:

${\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{X}}_i+{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_A$

${\stackrel{\→}{X}}_{Ba}={\stackrel{\→}{X}}_a+{\stackrel{\→}{B}}_B+{\stackrel{\→}{v}}_B$

WhereinRepresentative sensor A observed object signal i position,Represent target i physical location,Representative sensor A Deviation,Representative sensor A noise,Representative sensor B observed object signal a position,Represent target a physical location,Representative sensor B deviation,Representative sensor B noise.

Then

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{B}}_B-{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_B-{\stackrel{\→}{v}}_A={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

Target i that i.e. sensing system A and B matches and the difference of aRelative deviation for sensing system A and BWith Gaussian noise v " ' determine, sensing system Gaussian noise v " ' average be 0, covariance matrix is WhereinRepresent noiseVariance；

4, based on echo signal relative to the pairing algorithm of position

4.1, find twin target signal match point and sensor bias is estimated

Assume that sensing system A observes m echo signal and sensing system B observes n target.From sensor system The echo signal of system A observation is chosen echo signal i, and from the echo signal that sensing system B observes, chooses target letter Number a, calculates remaining m-1 echo signal j of sensing system A surplus with relative position and the sensing system B of echo signal i N-1 remaining echo signal b is with the relative position of echo signal a and compares, when the fiducial value of relative position | | A_ij-B_ab| |≤△₁(wherein A_ijRepresent the relative distance between echo signal i and j, B_abRepresent the relative distance between echo signal a and b, △₁Represent threshold value 1), it is believed that j and b is the echo signal of pairing, and defines new Matrix C ntNum_iaCalculating can Echo signal j that can match and the number of b.By remaining n-1 echo signal a of cycle sensor system B, permissible Obtain as different corresponding match point i-＞ a, maximum number MaxCntNum of possible pairing echo signal point_ia.Definition can Mate to number be Matchingpair, due to may pairing point quantity Matchingpair necessarily less than or equal to sensing Target number m that device system A observes and the minimum of a value of target number n that sensing system B observes, if the possibility found Maximum number MaxCntNum of pairing echo signal point_iaEqual to m-1, it is believed that the most corresponding sensing system A observation To echo signal a that observes of echo signal i and sensing system A be match point, and can mate to the number of point be Matchingpair, then can enter next step 4.2, the number of point that otherwise explanation can be matched is less than m-1.

Start the cycle in the echo signal of system A observation and choose echo signal i, and repeat above step, it is assumed that when following During echo signal i=c that ring observes to sensors A, if maximum number MaxCntNum of possible pairing echo signal point_iaLittle In m-c, the most now explanation match point number Matchingpair is necessarily less than m-c, then reduce the number of the point that may match, and Continue cycling through；If the number of the point that can match is equal to m-c, then number Matchingpair of the point that explanation can be matched is Find and equal to m-c, then store match point i-＞ a now, enter next step 4.2.

4.2, remaining echo signal match point is found

By 4.1 steps, have found the first point to pairing, then can be the thickest to match point calculating one by this Estimation of deviation slightly, the echo signal now observed by sensing system A is by adding acquired estimation of deviation, Ke Yiying It is mapped in the observation area of sensing system B, if the some map (A being mapped in B_j) the target letter that observes with sensing system B Number B_bMeet | | map (A_j)-B_b||≤△₂(wherein map (A_j) represent echo signal A_jIt is mapped to the corresponding points in sensor B region, B_bThe echo signal that representative sensor B observes, △₂Represent threshold value 2), and now B_bUniquely, then it is believed that j-＞ b now For match point.By finding these match point j-＞ b meeting uniqueness, an estimation of deviation the most accurate can be calculated Value.The echo signal observed for remaining sensors A, by adding this more accurate estimation of deviation value by sensor system The echo signal of system A observation is mapped in the observation area of sensing system B, searches out the target letter of the nearest B of same mapping point Number, the pairing of left point can be completed, thus complete whole association process.

5, the determination of thresholding

In above-mentioned steps, need to use threshold value △₁,△₂Find match point, it is therefore necessary to calculate suitable door Limit value realizes whole association process.

During above-mentioned steps 4, need by threshold value △₁Compare relative distance A_ijAnd B_ij, by step 2 Analyze:

${\stackrel{\→}{X}}_{Bij}-{\stackrel{\→}{X}}_{Aij}={\stackrel{\→}{v}}_B^{\′}-{\stackrel{\→}{v}}_A^{\′}={\stackrel{\→}{v}}^{\′\′}$

WhereinRepresent sensor B observed object i and j Relative position vector,Represent sensors A observed object I and j Relative position vector,Represent the noise that B with A sensor is comprised relative to position.The i.e. mesh of sensors A observation The difference of the relative position that the relative position of mark signal leads to the echo signal of sensor B observation is one and meets making an uproar of Gaussian Profile Sound, its average is 0, and covariance matrix isWhereinRepresent noiseVariance. Then utilize the 3-σ principle of Gaussian Profile, select threshold value △₁For

During above-mentioned steps 4, need by threshold value △₂Compare the observed object signal simultaneous interpretation of sensors A The mapping corresponding relation of sensor B observed object signal, by the analysis of step 3:

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{B}}_B-{\stackrel{\→}{B}}_A+{\stackrel{\→}{v}}_B-{\stackrel{\→}{v}}_A={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

WhereinRepresent the deviation between sensors A and sensor B, whereinRepresentative sensor A observed object signal i Position,Represent target i physical location,Representative sensor A deviation,Representative sensor A noise,Representative sensor B sees Survey echo signal a position,Represent target a physical location,Representative sensor B deviation,Representative sensor B noise, i.e. passes A deviation is differed between the echo signal that sensor A and sensor B observesWith remaining noiseWherein remaining noiseMeet Gaussian Profile and its average are 0, and covariance matrix isWhereinRepresent noiseSide Difference.Then utilize the 3-σ principle of Gaussian Profile, select threshold value △₂For

6, relative deviation is estimated

It is a fundamental problem during whole data correlation that relative deviation is estimated.When searching out a match point After, estimate to determine that remaining coupling is right by relative deviation.By the analysis of step 2, it can be seen that a match point i-＞ a Measured deviation can be expressed as follows:

${\stackrel{\→}{X}}_{ia}={\stackrel{\→}{X}}_{Ba}-{\stackrel{\→}{X}}_{Ai}={\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}^{\′\′\′}$

WhereinRepresent the relative deviation between sensors A and sensor B observation signal,Represent sensor B to see Survey the position of echo signal a,Represent the position of sensors A observed object signal i,Between sensing system A and B Relative deviation,For noise.

Assume have n coupling right, then measured deviation is:

${\stackrel{\→}{X}}_{AB}=H\×{\stackrel{\→}{R}}_b+{\stackrel{\→}{v}}_{(2n\×1)}$

WhereinIllustrate n coupling right Between relative distance vector,For observed differential matrix,Represent noise vector,Illustrate Need the relative deviation between the different sensors estimated.

Least-squares estimation (sees document [8] Kay, S.M.Fundamentals of Statistical Signal Processing:Estimation Theory.Upper Saddle River, NJ:Prentice-Hall, 1998.) it is Littleization:

WhereinRepresent error sum of squares,Representing the estimation to relative deviation, T represents the transposition of matrix.

By taking differential and to make it be 0, can obtain:

WhereinRepresent the value of the relative deviation of least-squares estimation.

Then sensor relative deviationEstimate is:

${\hat{R}}_{bls}={\left(H^{T}H\right)}^{-1}{H}^T{\stackrel{\→}{X}}_{AB}$

7, the algorithm flow of the present invention

The algorithm flow of the present invention is as follows:

STEP1): obtain and storage sensor A and B observed object signal condition；

STEP2): choose echo signal Ai from sensors A, echo signal Ba is chosen from sensor B；

STEP3): by traversal sensor B echo signal Ba, calculate relative position and by comparing different sensors system Relative position find corresponding match point, calculating may the maximum pairing number MaxCntNum of pairing_ia；

STEP4): if possible maximum pairing number MaxCntNum_ia< m-i then needs to return Step2), and choose new sensing Device system A echo signal Ai repeats Step3) step, otherwise find match point i-> a, enter Step5) step；

STEP5): find match point i-> a, sensor relative deviation is calculated；

STEP6): find remaining match point by mapping；

STEP7): find all match points, calculate sensor relative deviation, complete data correlation process.

Claims (1)

1. the sensor network data association method matched relative to position based on echo signal, it is characterised in that the method Set up sensor bias model, and give the expression of relative position between sensor target signal and between different sensors Formula, by find between different sensors position relatively maximum mate to method, it is possible to find a pair different sensors pair The echo signal match point answered, and obtain a estimation of deviation the most coarse, by this estimation of deviation, it is possible to find residue Sensor signal between object matching pair, complete the data correlation of different target signal and obtain a more accurate deviation The result estimated, idiographic flow is as follows:

(1), sensor bias model

Assume two different sensing system A and B, whole observation area is observed N number of target, wherein sensing system A Observe m echo signal, and sensing system B observe n echo signal, each sensing system can exist deviation with And affected by clutter noise, then sensing system buggy model is set up as follows:

$A_i=X_i+G\left(P\right)+{\stackrel{\&OverBar;}{x}}_A;i=1...m$

$B_j=X_j+G\left(Q\right)+{\stackrel{\&OverBar;}{x}}_B;j=1...n$

Wherein A_iThe i-th echo signal observed for sensing system A, B_jThe jth target observed for sensing system B Signal, X_iFor the physical location of i-th target, X_jFor the physical location of jth target, G (v) is the noise of sensing system, its Average is 0, and covariance matrix is v, and for sensing system A and B, its covariance matrix is respectively P and Q,It is respectively The deviation of sensing system A and B, the purpose of data correlation is to find echo signal A that sensing system A and B observes_iWith B_jBetween corresponding relation；

(2), the relative position of echo signal

Assume that sensing system A observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{X}}_i+{\stackrel{\&RightArrow;}{B}}_A+{\stackrel{\&RightArrow;}{v}}_A$

${\stackrel{\&RightArrow;}{X}}_{Aj}={\stackrel{\&RightArrow;}{X}}_j+{\stackrel{\&RightArrow;}{B}}_A+{\stackrel{\&RightArrow;}{v}}_A$

WhereinIt is expressed as the i-th dbjective state that sensing system A observes,It is expressed as what sensing system A observed Jth dbjective state,Represent i-th target and the virtual condition of jth target respectively,Represent sensing system A Deviation,Representing the Gauss measurement noise of sensing system A, its average is 0, and covariance matrix isWherein Represent noiseVariance；

The i-th dbjective state that then sensing system A observes can be expressed as follows with the relative position of jth dbjective state:

${\stackrel{\&RightArrow;}{X}}_{Aij}={\stackrel{\&RightArrow;}{X}}_{Aj}-{\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{X}}_j-{\stackrel{\&RightArrow;}{X}}_i+{\stackrel{\&RightArrow;}{v}}_A^{\&prime;}={\stackrel{\&RightArrow;}{X}}_{ij}+{\stackrel{\&RightArrow;}{v}}_A^{\&prime;}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noiseSum, its InIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noise's Variance；

In like manner, sensing system B observes echo signal i and j, then their state can be expressed as follows:

${\stackrel{\&RightArrow;}{X}}_{Bi}={\stackrel{\&RightArrow;}{X}}_i+{\stackrel{\&RightArrow;}{B}}_B+{\stackrel{\&RightArrow;}{v}}_B$

${\stackrel{\&RightArrow;}{X}}_{Bj}={\stackrel{\&RightArrow;}{X}}_j+{\stackrel{\&RightArrow;}{B}}_B+{\stackrel{\&RightArrow;}{v}}_B$

WhereinIt is expressed as the i-th dbjective state that sensing system B observes,It is expressed as what sensing system B observed Jth dbjective state,Represent i-th target and the virtual condition of jth target respectively,Represent sensing system B Deviation,Representing the Gauss measurement noise of sensing system B, its average is 0, and covariance matrix isWherein Represent noiseVariance；

The i-th dbjective state that then sensing system B observes can be expressed as follows with the relative position of jth dbjective state:

${\stackrel{\&RightArrow;}{X}}_{Bij}={\stackrel{\&RightArrow;}{X}}_{Bj}-{\stackrel{\&RightArrow;}{X}}_{Bi}={\stackrel{\&RightArrow;}{X}}_j-{\stackrel{\&RightArrow;}{X}}_i+{\stackrel{\&RightArrow;}{v}}_B^{\&prime;}={\stackrel{\&RightArrow;}{X}}_{ij}+{\stackrel{\&RightArrow;}{v}}_B^{\&prime;}$

I.e. relative to positionIt is represented by the relative position that i-th target is actual with jth targetWith noiseSum, its InIts average of Gauss measurement noise represented is 0, and covariance matrix isWhereinRepresent noise's Variance；

RelativelyWithCan obtain:

${\stackrel{\&RightArrow;}{X}}_{Bij}-{\stackrel{\&RightArrow;}{X}}_{Aij}={\stackrel{\&RightArrow;}{v}}_B^{\&prime;}-{\stackrel{\&RightArrow;}{v}}_A^{\&prime;}={\stackrel{\&RightArrow;}{v}}^{\&prime;\&prime;}$

Above formula can obtain, and the difference of the relative position of the corresponding target pair between different sensors system is by Gaussian noiseCertainly Fixed, its average is 0, and covariance matrix isWhereinRepresent noiseVariance；

(3), the relative position of different sensors system

Assuming that target i that sensing system A observes corresponds to target a that sensing system B observes, then its state can represent For:

${\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{X}}_i+{\stackrel{\&RightArrow;}{B}}_A+{\stackrel{\&RightArrow;}{v}}_A$

${\stackrel{\&RightArrow;}{X}}_{Ba}={\stackrel{\&RightArrow;}{X}}_a+{\stackrel{\&RightArrow;}{B}}_B+{\stackrel{\&RightArrow;}{v}}_B$

WhereinRepresentative sensor system A observed object signal i position,Represent target i physical location,Representative sensor system System A deviation,Representative sensor system A noise,Representative sensor system B observed object signal a position,Represent target A physical location,Representative sensor system B deviation,Representative sensor system B noise；

Then

${\stackrel{\&RightArrow;}{X}}_{ia}={\stackrel{\&RightArrow;}{X}}_{Ba}-{\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{B}}_B-{\stackrel{\&RightArrow;}{B}}_A+{\stackrel{\&RightArrow;}{v}}_B-{\stackrel{\&RightArrow;}{v}}_A={\stackrel{\&RightArrow;}{R}}_b+v^{\&prime;\&prime;\&prime;}$

Target i that i.e. sensing system A and B matches and the difference of aRelative deviation for sensing system A and BAnd Gauss The average of noise v " ' decision, sensing system Gaussian noise v " ' is 0, and covariance matrix isWhereinRepresent noise v " ' variance；

(4), based on echo signal relative to the pairing algorithm of position

4.1, find twin target signal match point and sensor bias is estimated

Assume that sensing system A observes m echo signal and sensing system B observes n target, from sensing system A The echo signal of observation chooses echo signal i, and chooses echo signal a from the echo signal that sensing system B observes, Calculate remaining m-1 echo signal j of sensing system A remaining with relative position and the sensing system B of echo signal i N-1 echo signal b is with the relative position of echo signal a and compares, when the fiducial value of relative position | | A_ij-B_ab||≤ Δ₁, wherein A_ijRepresent the relative distance between echo signal i and j, B_abRepresent the relative distance between echo signal a and b, Δ₁ Represent threshold value 1, it is believed that j and b is the echo signal of pairing, and defines new Matrix C ntNum_iaCalculate and may join To echo signal j and the number of b, by remaining n-1 echo signal a of cycle sensor system B, can obtain As different corresponding match point i-> a, maximum number MaxCntNum of possible pairing echo signal point_ia, definition can be mated To number be Matchingpair, due to may quantity Matchingpair of point of pairing necessarily less than or equal to sensor system The minimum of a value of target number n that system target number m that observes of A and sensing system B observe, if that finds may pairing Maximum number MaxCntNum of echo signal point_iaEqual to m-1, it is believed that the most corresponding sensing system A observes Echo signal a that echo signal i and sensing system B observe is match point, and can mate to the number of point be Matchingpair, then can enter next step 4.2, the number of point that otherwise explanation can be matched is less than m-1；

Start the cycle in the echo signal of sensing system A observation and choose echo signal i, and repeat above step, it is assumed that when When being recycled to echo signal i=c that sensing system A observes, if the maximum number of possible pairing echo signal point MaxCntNum_iaLess than m-c, the most now explanation match point number Matchingpair is necessarily less than m-c, then reducing may pairing The number of point, and continue cycling through；If the number of the point that can match is equal to m-c, the then number of the point that explanation can be matched Matchingpair has found and equal to m-c, then store match point i-> a now, enter next step 4.2；

4.2, remaining echo signal match point is found

By 4.1 steps, have found the first point to pairing, then can be the most rough to match point calculating one by this Estimation of deviation, the echo signal now observed by sensing system A, by adding acquired estimation of deviation, may map to In the observation area of sensing system B, if the some map (A being mapped in the observation area of sensing system B_j) with sensor system Echo signal B that system B observes_bMeet | | map (A_j)-B_b||≤Δ₂, wherein map (A_j) represent echo signal A_jIt is mapped to biography The corresponding points of the observation area of sensor system B, B_bThe echo signal that representative sensor system B observes, Δ₂Represent threshold value 2, And now B_bUniquely, then it is believed that j-> b now is match point, by finding these match point j-> b meeting uniqueness, can To calculate an estimation of deviation value the most accurate, for the echo signal of remaining sensing system A observation, by adding this The echo signal that sensing system A observes is mapped to the observation area of sensing system B by individual more accurate estimation of deviation value In, search out the echo signal of the nearest sensing system B of same mapping point, the pairing of left point can be completed, thus complete whole Individual association process；

(5), the determination of thresholding

In above-mentioned steps, need to use threshold value Δ₁,Δ₂Find match point, it is therefore necessary to calculate suitable threshold value Realize whole association process；

During above-mentioned steps (4), need by threshold value Δ₁Compare relative distance A_ijAnd B_ij, by step (2) Analyze:

${\stackrel{\&RightArrow;}{X}}_{Bij}-{\stackrel{\&RightArrow;}{X}}_{Aij}={\stackrel{\&RightArrow;}{v}}_B^{\&prime;}-{\stackrel{\&RightArrow;}{v}}_A^{\&prime;}={\stackrel{\&RightArrow;}{v}}^{\&prime;\&prime;}$

WhereinRepresent sensing system B observed object i and j Relative position vector,Represent sensors A observed object I and j Relative position vector,Represent the noise that sensing system B is comprised relative to position with sensing system A, i.e. The relative position of the echo signal of sensing system A observation leads to the difference of the relative position of the echo signal of sensing system B observation It it is a noise meeting Gaussian ProfileIts average is 0, and covariance matrix isWhereinRepresent noiseVariance, then utilize the 3-σ principle of Gaussian Profile, select threshold value Δ₁For

During above-mentioned steps 4, need by threshold value Δ₂Compare the observed object signal of sensors A with sensor system The mapping corresponding relation of system B observed object signal, by the analysis of step (3):

${\stackrel{\&RightArrow;}{X}}_{ia}={\stackrel{\&RightArrow;}{X}}_{Ba}-{\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{B}}_B-{\stackrel{\&RightArrow;}{B}}_A+{\stackrel{\&RightArrow;}{v}}_B-{\stackrel{\&RightArrow;}{v}}_A={\stackrel{\&RightArrow;}{R}}_b+v^{\&prime;\&prime;\&prime;}$

WhereinRepresent the deviation between sensing system A and sensing system B, whereinRepresentative sensor system A observation mesh Mark signal i position,Representative sensor system A deviation,Representative sensor system A noise,Representative sensor system B is seen Survey echo signal a position,Representative sensor system B deviation,Representative sensor system B noise, i.e. sensing system A and biography A deviation is differed between the echo signal that sensor system B observesWith remaining noiseWherein remaining noiseMeet Gauss Distribution and its average are 0, and covariance matrix isWhereinRepresent noiseVariance, then Utilize the 3-σ principle of Gaussian Profile, select threshold value Δ₂For

(6), relative deviation is estimated

After searching out a match point, estimate to determine that remaining coupling is right by relative deviation, by the analysis of step 3, It can be seen that the measured deviation of a match point i-> a can be expressed as follows:

${\stackrel{\&RightArrow;}{X}}_{ia}={\stackrel{\&RightArrow;}{X}}_{Ba}-{\stackrel{\&RightArrow;}{X}}_{Ai}={\stackrel{\&RightArrow;}{R}}_b+{\stackrel{\&RightArrow;}{v}}^{\&prime;\&prime;\&prime;}$

WhereinRepresent the relative deviation between sensing system A and sensing system B observation signal,Represent sensor The position of system B observed object signal a,Represent the position of sensing system A observed object signal i,For sensor system Relative deviation between system A and B,For noise；

Assume have n coupling right, then measured deviation is:

${\stackrel{\&RightArrow;}{X}}_{AB}=H\&times;{\stackrel{\&RightArrow;}{R}}_b+{\stackrel{\&RightArrow;}{v}}_{(2n\&times;1)}$

WhereinIllustrate n coupling between Relative distance vector,For observed differential matrix,Represent noise vector,Illustrate needs Relative deviation between the different sensors estimated；

Least-squares estimation is to minimize:

WhereinRepresent error sum of squares,Representing the estimation to relative deviation, T represents the transposition of matrix；By taking Differential to make it be 0, can obtain:

WhereinRepresent the value of the relative deviation of least-squares estimation；

Then sensor relative deviationEstimate is:

${\hat{R}}_{bls}={\left(H^{T}H\right)}^{-1}{H}^T{\stackrel{\&RightArrow;}{X}}_{AB}.$