CN101907461A - Measuration data correlation method for passive multisensor based on angle cotangent value - Google Patents

Abstract

The invention discloses a rapid data correlation method based on angle cotangent values, which mainly solves the problem of slow correlation speed and low correlation precision rate in the measuration data of the existing passive multisensor. The method of the invention comprises the following steps: building statistic by using the angle cotangent values, and building a candidate correlation set by partitioning pretreatment; simplifying the candidate correlation set by azimuth angle and pitch angle measuring which adopt repeatedly random iterations; and finally picking out correct correlation combine through an indicator function and a cost function. The invention directly adopts the angle information for data correlation, avoids the conversion from angle to distance; the operation efficiency is obviously higher than that of the traditional method; and the invention has excellent engineering application value, can be applied to the fields such as infrared guidance, intelligence fusion war, air traffic control and aerospace, aviation, navigation and the like.

Description

Passive multi-sensor metric data correlating method based on angle cotangent value

Technical field

The invention belongs to technical field of data processing, relate to the data association of target following, specifically a kind of rapid measuring data correlation method of passive multi-sensor, can be widely used in infrared guidance, information fusion operation, air traffic control and space flight, aviation, fields such as navigation.

Background technology

Because passive sensor is outside radiated electromagnetic wave, compare with active sensor that to have an antijamming capability strong, advantages such as good concealment, therefore more and more scholars begins to be devoted to the research of this respect both at home and abroad.But in the passive multi-sensor system, at first need an association that key issue is exactly a metric data solving, determine promptly which measurement source is in same target.Because adopt passive positioning, sensor only can obtain target direction angle and angle of pitch information, when a plurality of targets are carried out cross bearing, different position lines will produce a large amount of false bearing points.In addition,, how fast and effeciently to get rid of false point, and then obtain the correct related emphasis that has become numerous scholar's research because situations such as target omission, false-alarm are difficult to avoid.

Usually, the passive multi-sensor data association can be described as the multidimensional assignment problem, and asking its optimum solution with the method for exhaustion is a NP-hard problem, and computation complexity is exponential increase with the increase of problem dimension.At this problem, people propose various sub-optimal algorithm, as Pattipati K R, Deb S, the Lagrangian Relaxation Algorithm that people such as Bar-Shalom Y propose, Deb S, Yeddana Pud I M, the A Generalized S-D assignment algorithm for multisensor-multitarget state estimation that Pattipati K R proposes etc., but these algorithms all were difficult to obtain satisfactory solution in the given time.Recent Liu Hang, Dou Li-hua, Pan Feng, the Research on data association in three passive sensors network of Dong Ling-xun proposes a kind of incidence matrix analytic approach, adopting indicator function to substitute multidimensional distributes, improved arithmetic speed to a certain extent, but it still is based on the algorithm of line-of-sight distance, and this class algorithm must be converted into angle distance, and comprise a large amount of matrix operations and ask the local derviation computing, limit the further raising of arithmetic speed, influenced the real-time follow-up effect of target.

Summary of the invention

At the problems referred to above, the objective of the invention is to propose a kind of passive multi-sensor metric data correlating method based on angle cotangent value, to be implemented in clutter, metric data is carried out in the omission environment is fast and effeciently related, improve arithmetic speed significantly, guarantee the real-time follow-up effect of target.

The key problem in technology of realizing the object of the invention is: at first adopt angle cotangent value to replace traditional line-of-sight distance to make up statistic, and set up the candidate association collection by partitioning pretreatment, adopt repeatedly the position angle of the iteration detection at random and the angle of pitch to detect then respectively the candidate association collection is carried out abbreviation, pick out correct associative combination by indicator function and cost function at last, effectively improved operation efficiency.Its concrete steps comprise as follows:

1) calculates the cotangent value of all measurements that each sensor obtains

Wherein

Represent the j group metric data position angle and the angle of pitch of i sensor respectively, two primary iteration number of times k are set ₁=0, k ₂=0 and two maximum iteration time N ₁, N ₂

2) be { (S with M sensor group ₁S ₂S ₃), (S ₂S ₃S ₄) ..., (S _M-2S _M-1S _M), (S wherein _I-2S _I-1S _i) one group of sensor combinations of expression, S _iRepresent i sensor, each associative combination metric data of organizing sensor carried out position angle detection and angle of pitch detection respectively, utilize by the associative combination metric data that detects and set up candidate association collection P according to following steps:

A) position angle is detected

A1), calculate the position angle test statistics of three sensor metric data according to the position angle cotangent value in the step 1:

$F({\mathrm{\α}}_i^{l_1},{\mathrm{\α}}_j^{l_2},{\mathrm{\α}}_k^{l_3})=\cot {\mathrm{\α}}_k^{l_3}-\cot {\mathrm{\α}}_j^{l_2}+\frac{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\α}}_j^{l_2}}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{L_{\mathrm{jk}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}$

Wherein,

θ _Ijk∈ { ∠ S _iS _jS _k, (x _i, y _i, z _i) expression sensor S _iPosition coordinates, i, j, k ∈ Ω=1,2 ..., M};

A2) computer azimuth angle test statistics variance:

Wherein,

$R_{\mathrm{ijk}}^1=\left[{(\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{\cot {\mathrm{\α}}_j^{l_2}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}{{(\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}})}^2})}^2{(1+\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{1}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}})}^{2}1\right],$

σ _sBe sensor measurement noise standard deviation;

A3) utilize position angle test statistics variance, set fiducial interval [3 σ _F, 3 σ _F], if test statistics drops in this fiducial interval, then by detecting; Otherwise, deleted;

B) angle of pitch detects

B1), calculate angle of pitch test statistics: e according to the angle of pitch cotangent value in the step 1 _Mn=H _m-H _nWherein, m, n ∈ 1,2,3,4}, m＞n, H ₁, H ₂, H ₃, H ₄Four height that expression sensor sight line is determined, they are respectively:

$H_1=h_{i\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_i}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_k-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)},$ $H_2=h_{k\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_k}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_i-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)},$

$H_3=h_{j\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\β}}_j}\·\frac{1}{{\sin \mathrm{\α}}_j(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)},$ $H_4=h_{k\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\α\β}}_k}\·\frac{1}{{\sin \mathrm{\α}}_k(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)};$

h _{K (ij)}The height of k the sensor position line that expression is determined by sensor i and j, i, j, k ∈ Ω=1,2 ..., M};

B2) calculate angle of pitch test statistics variance:

${\mathrm{\σ}}_{e_{\mathrm{mn}}}^2={(H_m\·(\cot {\mathrm{\β}}_p+\frac{1}{\cot {\mathrm{\β}}_p})\·{\mathrm{\σ}}_s)}^2+{(H_n\·(\cot {\mathrm{\β}}_q+\frac{1}{\cot {\mathrm{\β}}_q})\·{\mathrm{\σ}}_s)}^2$

Wherein, m, n ∈ 1,2,3, and 4}, m＞n, p, q ∈ i, and j, k}, p ≠ q, i, j, k ∈ Ω=1,2 ..., M}, σ _sBe sensor measurement noise standard deviation;

B3) utilize angle of pitch test statistics variance, set fiducial interval If angle of pitch check system

Metering drops in the fiducial interval, then by detecting; Otherwise, deleted;

3) three sensors of picked at random carry out the position angle to the metric data of these three sensors and detect, and can not delete from candidate association collection P by the associative combination that detects;

4) to by all associative combination among the candidate association collection P that detects, set up indicator function ξ (l one by one _s)=NUM (P, l _s), wherein, s=1,2 ..., M, NUM (P, l _s) element l among the expression candidate association collection P _sTotal number, for ξ (l _sAssociative combination { the l of)=1 ₁..., l _s..., l _M, put it among the final correct incidence set Z, and contain { l among the deletion candidate association collection P ₁..., l _s..., l _MThe associative combination of arbitrary element, then at current iteration number of times k ₁On to add 1 be k ₁=l ₁+ 1;

5) further candidate association collection P is screened, if k ₁＜N ₁Then three sensors of picked at random and guarantee this three sensor groups be combined in before the screening in do not choose, utilize the position angle cotangent value in the step 1, these three sensor metric data are carried out the position angle to be detected, can not from candidate association collection P, delete by the associative combination that detects, return step 4; Otherwise, P is put into new candidate association collection Q, enter step 6;

6) three sensors of picked at random carry out the angle of pitch to the metric data of these three sensors and detect, and can not delete from candidate association collection Q by the associative combination that detects;

7) to by all associative combination among the candidate association collection Q that detects, set up indicator function ξ (l one by one _s)=NUM (Q, l _s), wherein, s=1,2 ..., M, NUM (Q, l _s) element l among the expression candidate association collection Q _sTotal number, for ξ (l _sAssociative combination { the l of)=1 ₁..., l _s..., l _M, put it among the final correct incidence set Z, and contain { l among the deletion candidate association collection Q ₁..., l _s..., l _MThe associative combination of arbitrary element, at current iteration number of times k ₂On to add 1 be k ₂=k ₂+ 1;

8) further candidate association collection Q is screened, if k ₂＜N ₂Then three sensors of picked at random and guarantee that this three sensor groups do not choose in the screening before being combined in utilize the angle of pitch cotangent value of step 1, these three sensor metric data are carried out the angle of pitch detect, can not from candidate association collection Q, delete by the associative combination that detects, return step 7; Otherwise, Q is put into new candidate association collection R, enter step 9;

9) if candidate association collection R is not an empty set,, set up cost function one by one then to associative combination all among the R

Wherein, c is e _MnTotal number, choose and make the combination of overall cost minimum as final association results, put into final correct incidence set Z and output as a result of; Otherwise, directly will final correct incidence set Z output.

The present invention has the following advantages:

1) the present invention substitutes traditional line-of-sight distance with angle cotangent value and makes up statistic, avoid a large amount of matrix operations and asked the local derviation computing, thereby effectively improved operation efficiency, and the candidate association that the position angle is detected and angle of pitch detection screening is fallen is many more, associated speed is also just fast more.

2) the present invention adopts repeatedly iteration position angle detection at random and angle of pitch detection that the candidate association collection is carried out abbreviation, and does not need all possible associative combination is traveled through, thereby has further improved operation efficiency.

When 3) the present invention utilizes position angle and angle of pitch detection that various sensor combinations are carried out pre-service, independently carry out between each combination, be independent of each other, help the parallel processing that the position angle and the angle of pitch detect.

Description of drawings

Fig. 1 is overall flow figure of the present invention;

Fig. 2 is the sub-process figure that the present invention screens candidate association collection P;

Fig. 3 is the present invention when not having the error of measurement, the sight line perspective geometry graph of a relation of three sensors;

Fig. 4 is sensor S _p, S _rHeight of sighting line figure;

Fig. 5 is sensor S _r, S _qHeight of sighting line figure.

Embodiment

One, basic theory introduction

Be provided with 3 sensor S _p, S _q, S _r, when not having error in measurement 3 position lines in the space and the projection in 3 sensors constitute planes all should meet at a bit.Yet when having error in measurement, 3 position lines and corresponding projection line thereof all can't meet at a bit.This deviation can be understood as two kinds of forms, the one, the deviation that the position angle causes, the 2nd, the deviation that the angle of pitch causes.Therefore, adopt the position angle to detect respectively at the deviation of these two kinds of forms below and angle of pitch detection is handled.

1. the position angle is detected

Fig. 3 shows when do not have measuring error the perspective geometry of 3 position lines relation in the plane that 3 sensors constitute.Do you for the sake of simplicity, suppose? S _pS _rS _qQ,

With

Sensing as azimuthal zero degree reference line.At Δ S _pS _rO and Δ S _qS _rUtilize the sine can be among the O in the hope of the length of 3 projection lines

And

Further can obtain 3 position angles the relation that must satisfy:

${\mathrm{ctg\α}}_q-{\mathrm{ctg\α}}_r+\frac{{\mathrm{ctg\α}}_p-\mathrm{ctg}{\mathrm{\α}}_r}{\mathrm{ctg}{\mathrm{\α}}_p-\mathrm{ctg\θ}}\·\frac{L_{\mathrm{qr}}}{L_{\mathrm{pr}}\·\sin \mathrm{\θ}}=0---\left(1\right)$

If there is error in measurement, then formula (1) right-hand member is not 0, and the structure test statistics is as follows:

$F({\mathrm{\α}}_p,{\mathrm{\α}}_q,{\mathrm{\α}}_r)=\mathrm{ctg}{\mathrm{\α}}_q-\mathrm{ctg}{\mathrm{\α}}_r+\frac{\mathrm{ctg}{\mathrm{\α}}_p-\mathrm{ctg}{\mathrm{\α}}_r}{\mathrm{ctg}{\mathrm{\α}}_p-\mathrm{ctg\θ}}\·\frac{L_{\mathrm{qr}}}{L_{\mathrm{pr}}\·\sin \mathrm{\θ}}---\left(2\right)$

The approximate obedience of this statistic average is 0, and variance is

Gaussian distribution,

Provide by formula (3):

${\mathrm{\σ}}_F^2=R_{\mathrm{pqr}}^1\·R_{\mathrm{pqr}}^2\·{\mathrm{\σ}}_s^2---\left(3\right)$

Wherein, σ s is a sensor measurement noise standard deviation,

With

Respectively suc as formula shown in (4) and the formula (5):

$R_{\mathrm{pqr}}^1=\left[{{(\frac{L_{\mathrm{rq}}}{L_{\mathrm{pq}}\·{\sin \mathrm{\θ}}_{\mathrm{pqr}}}\·\frac{\cot {\mathrm{\α}}_q-c\cot {\mathrm{\θ}}_{\mathrm{pqr}}}{{(\cot {\mathrm{\α}}_p-\cot {\mathrm{\θ}}_{\mathrm{pqr}})}^2})}^2(1+\frac{L_{\mathrm{rq}}}{L_{\mathrm{pq}}\·{\sin \mathrm{\θ}}_{\mathrm{pqr}}}\·\frac{1}{\cot {\mathrm{\α}}_p-\cot {\mathrm{\θ}}_{\mathrm{pqr}}})}^{2}1\right]---\left(4\right)$

$R_{\mathrm{pqr}}^2={\left[{(1+\cot {{\mathrm{\α}}_p}^2)}^2{(1+\cot {{\mathrm{\α}}_q}^2)}^2{(1+\cot {{\mathrm{\α}}_r}^2)}^2\right]}^T---\left(5\right)$

If test statistics drops in the fiducial interval, think that then this candidate association may belong to same target, is kept; Otherwise,, deleted for the mistake combination.

2. the angle of pitch detects

Because the existence of error in measurement makes position line not wait perpendicular to the height on the direction of projecting plane, can pick out possible associative combination by the difference that detects each position line height.Fig. 4 and Fig. 5 have shown the space geometry relation of position line height, utilize triangle relation to be easy to obtain following 4 height

$H_1=h_{p\left(\mathrm{pr}\right)}=\frac{L_{\mathrm{pr}}}{\cot {\mathrm{\β}}_p}\·\frac{\sin \mathrm{\θ}({\mathrm{ctg\α}}_r-\mathrm{ctg\θ})}{{\sin \mathrm{\α}}_p(\cot {\mathrm{\α}}_p-\cot {\mathrm{\α}}_r)}---\left(6\right)$

$H_2=h_{r\left(\mathrm{pr}\right)}=\frac{L_{\mathrm{pr}}}{\mathrm{ctg}{\mathrm{\β}}_r}\·\frac{\sin \mathrm{\θ}({\mathrm{ctg\α}}_p-\mathrm{ctg\θ})}{{\sin \mathrm{\α}}_p(\mathrm{ctg}{\mathrm{\α}}_p-\mathrm{ctg}{\mathrm{\α}}_r)}---\left(7\right)$

$H_3=h_{q\left(\mathrm{qr}\right)}=\frac{L_{\mathrm{qr}}}{\mathrm{ctg}{\mathrm{\β}}_q}\·\frac{1}{{\sin \mathrm{\α}}_q(\mathrm{ctg}{\mathrm{\α}}_r-\mathrm{ctg}{\mathrm{\α}}_q)}---\left(8\right)$

$H_4=h_{r\left(\mathrm{qr}\right)}=\frac{L_{\mathrm{qr}}}{\mathrm{ctg}{\mathrm{\β}}_r}\·\frac{1}{{\sin \mathrm{\α}}_r(\mathrm{ctg}{\mathrm{\α}}_r-\mathrm{ctg}{\mathrm{\α}}_q)}---\left(9\right)$

Wherein, h _{K (ij)}The height of k the sensor position line that expression is determined by sensor i and j.

Get any two difference in above 4 height as test statistics:

e _ij＝H _i-H _j (10)

The approximate Gaussian distribution of obeying zero-mean of this statistic, its variance is provided by formula (11)

${\mathrm{\σ}}_{e_{\mathrm{ij}}}^2={(H_i\·(\mathrm{ctg}{\mathrm{\β}}_m+\frac{1}{\mathrm{ctg}{\mathrm{\β}}_m})\·{\mathrm{\σ}}_s)}^2+{(H_j\·(\mathrm{ctg}{\mathrm{\β}}_n+\frac{1}{\mathrm{ctg}{\mathrm{\β}}_n})\·{\mathrm{\σ}}_s)}^2---\left(11\right)$

Wherein, i, j=1,2,3,4, i＞j, m, n ∈ { p, q, r}, m ≠ n, σ _sBe sensor measurement noise standard deviation.

Equally, if test statistics drops in the fiducial interval, think that then this candidate association may belong to same target, is kept; Otherwise,, deleted for the mistake combination.

3. indicator function

If { l ₁, l ₂..., l _MRepresent a kind of candidate association combination, and all possible array configuration is put into candidate association collection R, promptly

$R=\underset{k=1}{\overset{C}{U}}\left\{(l_{1_k},...,l_{M_k})\right\}$

Wherein, C represents the candidate association sum.

The definition indicator function

ξ(l _s)＝NUM(R，l _s)

Wherein, s=1,2 ..., M, element l among NUM () the expression candidate association collection R _sNumber.

If ξ is (l _s) equal 1, l then is described _sBe unique translocation that is associated with this target, then this candidate association directly can be taken out, simultaneously all are comprised l as correct associative combination _sAssociative combination from R, delete;

If ξ is (l _s) equal 0, the l of s sensor then is described _sIndividual measurement is not carried out related with any measurement of other sensors;

If ξ is (l _s) greater than 1, the l of s sensor is described then _sIndividual measurement can be related with a plurality of measurements of other M-1 sensor, at this moment, need utilize a plurality of detection limits structure cost functions of the angle of pitch in detecting, and the combination of choosing overall cost minimum is as final association results.

Two. based on the passive multi-sensor metric data association of angle cotangent value

With reference to Fig. 1, specific implementation process of the present invention may further comprise the steps:

Step 1. initialization

(θ ∈ [π, π]) is written into the internal memory from external memory storage with predefined angle cotangent value relation table, obtains the measurement angle of each sensor, obtains the cotangent value of their correspondences by the mode of searching

Wherein

The position angle and the angle of pitch of representing the j group measurement of i sensor respectively; Two primary iteration number of times k are set ₁=0, k ₂=0 and two maximum iteration time N ₁, N ₂

Step 2. is set up candidate association collection P

2.1) be { (S with M sensor group ₁S ₂S ₃), (S ₂S ₃S ₄) ..., (S _M-2S _M-1S _M), (S wherein _I-2S _I-1S _i) one group of sensor combinations of expression, S _iRepresent i sensor,, can organize data to each and carry out following parallel processing owing to independently carry out between each sensor combinations;

2.2) the position angle detection

2.2.1) according to the position angle cotangent value in the step 1, calculate the position angle test statistics of these three sensor metric data:

$F({\mathrm{\α}}_i^{l_1},{\mathrm{\α}}_j^{l_2},{\mathrm{\α}}_k^{l_3})=\cot {\mathrm{\α}}_k^{l_3}-\cot {\mathrm{\α}}_j^{l_2}+\frac{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\α}}_j^{l_2}}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{L_{\mathrm{jk}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}$

Wherein,

θ _Ijk∈ { ∠ S _iS _jS _k, (x _i, y _i, z _i) table

Show sensor S _iPosition coordinates, i, j, k ∈ Ω=1,2 ..., M};

2.2.2) computer azimuth angle detection statistic variance:

Wherein,

$R_{\mathrm{ijk}}^1=\left[{(\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{\cot {\mathrm{\α}}_j^{l_2}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}{{(\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}})}^2})}^2{(1+\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{1}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}})}^{2}1\right],$

i，j，k∈Ω＝{1，2，...，M}，

σ _sBe sensor measurement noise standard deviation;

2.2.3) setting fiducial interval [3 σ _F, 3 σ _F], because the approximate average of obeying of this position angle statistic is zero, variance is

Gaussian distribution, thereby set fiducial interval [3 σ _F, 3 σ _F], thereby guarantee that its degree of confidence is not less than 0.997, if test statistics drops in this fiducial interval, think that then this candidate association may belong to same target, by detecting; Otherwise,, deleted for the mistake combination;

2.3) angle of pitch detection

2.3.1) according to the angle of pitch cotangent value in the step 1, the difference in height of utilizing the sensor sight line to determine is calculated angle of pitch test statistics: e _Mn=H _m-H _n

Wherein, m, n=1,2,3,4, m＞n, H ₁, H ₂, H ₃, H ₄Four height that expression sensor sight line is determined, they are respectively:

$H_1=h_{i\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_i}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_k-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)},$ $H_2=h_{k\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_k}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_i-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)}$

$H_3=h_{j\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\β}}_j}\·\frac{1}{{\sin \mathrm{\α}}_j(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)},$ $H_4=h_{k\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\α\β}}_k}\·\frac{1}{{\sin \mathrm{\α}}_k(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)};$

Wherein, h _{K (ij)}The height of k the sensor position line that expression is determined by sensor i and j, i, j, k ∈ Ω=1,2 ..., M};

2.3.2) calculating angle of pitch test statistics variance:

${\mathrm{\σ}}_{e_{\mathrm{mn}}}^2={(H_m\·(\cot {\mathrm{\β}}_p+\frac{1}{\cot {\mathrm{\β}}_p})\·{\mathrm{\σ}}_s)}^2+{(H_n\·(\cot {\mathrm{\β}}_q+\frac{1}{\cot {\mathrm{\β}}_q})\·{\mathrm{\σ}}_s)}^2$

Wherein, p, q=i, j, k, p ≠ q, i, j, k ∈ Ω=1,2 ..., M};

2.3.3) the setting fiducial interval Because the approximate average of obeying of this angle of pitch statistic is zero, variance is

Gaussian distribution, thereby by setting fiducial interval

Guarantee that its degree of confidence is not less than 0.997,, think that then this candidate association may belong to same target, by detecting if test statistics drops in this fiducial interval; Otherwise,, deleted for the mistake combination;

2.4) utilize by the associative combination that detects and set up candidate association collection P

At first, establish I=1,2 ..., K represents a certain associative combination by detecting in i the sensor groups, K represents the number of sensor groups;

Then, choose two adjacent sensor groups L arbitrarily _I-1And L _i, guarantee

The expression empty set, identical sensor has identical measurement in the promptly adjacent sensor groups;

At last, will meet each sensor measurement of above-mentioned condition

Be combined into the candidate association collection

Wherein,

Represent a kind of possible associative combination, C represents the candidate association sum,

Three sensors of step 3. picked at random carry out the position angle identical with step 2 to the metric data of these three sensors and detect, and can not delete from candidate association collection P by the associative combination that detects.

Step 4. indicator function

To by all associative combination among the candidate association collection P of orientation detection, set up indicator function ξ (l one by one _s)=NUM (P, l _s), wherein, s=1,2 ..., M, NUM (P, l _s) element l among the expression candidate association collection P _sTotal number.

If ξ is (l _s) equal 0, the l of s sensor then is described _sIndividual measurement is not carried out related with the measurement of other sensors of M-1; If ξ is (l _s) equal 1, the l of s sensor then is described _sIndividual measurement can only be related with certain M-1 measurement of other M-1 sensors; If ξ is (l _s) greater than 1, the l of s sensor is described then _sIndividual measurement can be related with a plurality of measurements of other M-1 sensor;

For ξ (l _sAssociative combination { the l of)=1 ₁..., l _s..., l _M, put it among the final correct incidence set Z, and contain { l among the deletion candidate association collection P ₁..., l _s..., l _MThe associative combination of arbitrary element, at current iteration number of times k ₁On to add 1 be k ₁=k ₁+ 1.

Step 5. is further screened candidate association collection P, if k ₁＜N ₁Then three sensors of picked at random and guarantee this three sensor groups be combined in before the screening in do not choose, utilize the position angle cotangent value in the step 1, these three sensor metric data are carried out the position angle to be detected, can not from candidate association collection P, delete by the associative combination that detects, return step 4; Otherwise, P is put into new candidate association collection Q, enter step 6.

Three sensors of step 6. picked at random carry out the angle of pitch identical with step 2 to the metric data of these three sensors and detect, and can not delete from candidate association collection Q by the associative combination that detects.

All associative combination among the candidate association collection Q that step 7. pair detects by the angle of pitch are set up indicator function ξ (l one by one _s)=NUM (Q, l _s), wherein, s=1,2 ..., M, NUM (Q, l _s) element l among the expression candidate association collection Q _sTotal number.

If ξ is (l _s) equal 0, the l of s sensor then is described _sIndividual measurement is not carried out related with the measurement of other sensors of M-1; If ξ is (l _s) equal 1, the l of s sensor then is described _sIndividual measurement can only be related with certain M-1 measurement of other M-1 sensors; If ξ is (l _s) greater than 1, the l of s sensor is described then _sIndividual measurement can be related with a plurality of measurements of other M-1 sensor.

For ξ (l _sAssociative combination { the l of)=1 ₁..., l _s..., l _M, put it among the final correct incidence set Z, and contain l among the deletion candidate association collection Q ₁..., l _s..., l _MThe associative combination of arbitrary element, at current iteration number of times k ₂On to add 1 be k ₂=k ₂+ 1.

Step 8. is further screened candidate association collection Q, if k ₂＜N ₂Then three sensors of picked at random and guarantee that this three sensor groups do not choose in the screening before being combined in utilize the angle of pitch cotangent value of step 1, these three sensor metric data are carried out the angle of pitch detect, can not from candidate association collection Q, delete by the associative combination that detects, return step 7; Otherwise, Q is put into new candidate association collection R, enter step 9.

The realization flow of above-mentioned steps 3～step 8 as shown in Figure 2.

Step 9. candidate association set analysis

If candidate association collection R is not an empty set,, set up cost function one by one then to associative combination all among the R Wherein, c is difference in height e _MnTotal number, this cost function has reflected average height difference, cost is more for a short time to show that to measure the possibility that comes from same target big more, the cost value that compares various associative combination among the candidate association collection R, choose the correct associative combination of one group of conduct of overall cost minimum, put into final correct incidence matrix Z and also as a result of export; Otherwise, directly will final correct incidence set Z output.

Effect of the present invention can further specify by following experiment simulation:

1. simulated conditions and content

Emulation experiment adopts 35 targets that sensors observe is aerial, measures to comprise the position angle and the angle of pitch.The position of 3 sensors is respectively: S ₁(0,10,0), S ₂(10,0,0), S ₃(0,0,0), the measurement noise standard deviation of the position angle and the angle of pitch is σ _sTarget divides level to form into columns and two kinds of situations of cross formation, and target distance is d.Horizontal formation target position: target 1 (5,5,1), target 2 (5+d, 5,1), target 3 (5-d, 5,1), target 4 (5+2d, 5,1), target 5 (5-2d, 5,1); Cross formation target position: target 1 (5,5,1), target 2 (5+d, 5,1), target 3 (5-d, 5,1), and target 4 (5,5+d, 1), target 5 (5,5-d, 1), unit is km, emulation experiment is analyzed incidence matrix analytic approach and the Lagrangian Relaxation Algorithm among correlating method of the present invention and the document Research on data association in three passive sensors network, carries out 100 Monte Carlo emulation respectively, and the result is respectively as table 1, table 2, shown in table 3 and the table 4, wherein t represents the working time of an emulation, and p represents related accuracy.

2. analysis of simulation result

Table 1 and table 2 are the situation of no clutter environment, detection probability P _d=1.When target distance during greater than 1km, the incidence matrix analytic approach is approaching with related accuracy of the present invention and Lagrangian Relaxation Algorithm, but shortens greatly working time as can be seen, and the present invention has also improved nearly 7 times than incidence matrix analytic approach algorithm on speed.Because the target distribution situation is fairly simple, accuracy is generally higher in the table 1.When target distance was 0.5km, accuracy of the present invention slightly was worse than Lagrangian Relaxation Algorithm in the table 2, but still was higher than incidence matrix analytic approach algorithm.

Table 3 and table 4 are the situation of clutter environment.Detection probability P _d=0.95, false alarm rate P _f=0.05, the size that clutter produces the zone is 0.1rad * 0.1rad.From table 3 and table 4, as can be seen, be subjected to the influence of omission and false-alarm, compare with no clutter environment, related accuracy all descends to some extent, and along with reducing of target distance, the related accuracy trend that tapers off, but performance of the present invention still is higher than incidence matrix analytic approach institute extracting method.

Level is formed into columns under the no clutter environment of table 1

Cross is formed into columns under the no clutter environment of table 2

Level is formed into columns under table 3 clutter environment

Cross is formed into columns under table 4 clutter environment

Claims (2)

1. the passive multi-sensor metric data correlating method based on angle cotangent value comprises the steps:

1) calculates the cotangent value of all measurements that each sensor obtains

Wherein

Represent the j group metric data position angle and the angle of pitch of i sensor respectively, two primary iteration number of times k are set ₁=0, k ₂=0 and two maximum iteration time N ₁, N ₂

2) be { (S with M sensor group ₁S ₂S ₃), (S ₂S ₃S ₄) ..., (S _M-2S _M-1S _M), (S wherein _I-2S _I-1S _i) one group of sensor combinations of expression, S _iRepresent i sensor, each associative combination metric data of organizing sensor carried out position angle detection and angle of pitch detection respectively, utilize by the associative combination metric data that detects and set up candidate association collection P according to following steps:

A) position angle is detected

A1), calculate the position angle test statistics of three sensor metric data according to the position angle cotangent value in the step 1:

$F({\mathrm{\α}}_i^{l_1},{\mathrm{\α}}_j^{l_2},{\mathrm{\α}}_k^{l_3})=\cot {\mathrm{\α}}_k^{l_3}-\cot {\mathrm{\α}}_j^{l_2}+\frac{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\α}}_j^{l_2}}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{L_{\mathrm{jk}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}$

Wherein,

θ _Ijk∈ { ∠ S _iS _jS _k, (x _i, y _i, z _i) expression sensor S _iPosition coordinates, i, j, k ∈ Ω=1,2 ..., M};

A2) computer azimuth angle test statistics variance:

Wherein,

$R_{\mathrm{ijk}}^1=\left[{(\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{\cot {\mathrm{\α}}_j^{l_2}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}}{{(\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}})}^2})}^2{(1+\frac{L_{\mathrm{kj}}}{L_{\mathrm{ij}}\·\sin {\mathrm{\θ}}_{\mathrm{ijk}}}\·\frac{1}{\cot {\mathrm{\α}}_i^{l_1}-\cot {\mathrm{\θ}}_{\mathrm{ijk}}})}^{2}1\right],$

σ _sBe sensor measurement noise standard deviation;

A3) utilize position angle test statistics variance, set fiducial interval [3 σ _F, 3 σ _F], if test statistics drops in this fiducial interval, then by detecting; Otherwise, deleted;

B) angle of pitch detects

B1), calculate angle of pitch test statistics: e according to the angle of pitch cotangent value in the step 1 _Mn=H _m-H _n

Wherein, m, n ∈ 1,2,3,4}, m＞n, H ₁, H ₂, H ₃, H ₄Four height that expression sensor sight line is determined, they are respectively:

$H_1=h_{i\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_i}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_k-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)},$ $H_2=h_{k\left(\mathrm{ik}\right)}=\frac{L_{\mathrm{ik}}}{\cot {\mathrm{\β}}_k}\·\frac{\sin {\mathrm{\θ}}_{\mathrm{ijk}}({\cot \mathrm{\α}}_i-{\cot \mathrm{\θ}}_{\mathrm{ijk}})}{{\sin \mathrm{\α}}_i(\cot {\mathrm{\α}}_i-\cot {\mathrm{\α}}_k)},$

$H_3=h_{j\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\β}}_j}\·\frac{1}{{\sin \mathrm{\α}}_j(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)},$ $H_4=h_{k\left(\mathrm{jk}\right)}=\frac{L_{\mathrm{jk}}}{\cot {\mathrm{\α\β}}_k}\·\frac{1}{{\sin \mathrm{\α}}_k(\cot {\mathrm{\α}}_k-\cot {\mathrm{\α}}_j)};$

h _{K (ij)}The height of k the sensor position line that expression is determined by sensor i and j, i, j, k ∈ Ω=1,2 ..., M};

B2) calculate angle of pitch test statistics variance:

${\mathrm{\σ}}_{e_{\mathrm{mn}}}^2={(H_m\·(\cot {\mathrm{\β}}_p+\frac{1}{\cot {\mathrm{\β}}_p})\·{\mathrm{\σ}}_s)}^2+{(H_n\·(\cot {\mathrm{\β}}_q+\frac{1}{\cot {\mathrm{\β}}_q})\·{\mathrm{\σ}}_s)}^2$

Wherein, m, n ∈ 1,2,3, and 4}, m＞n, p, q ∈ i, and j, k}, p ≠ q, i, j, k ∈ Ω=1,2 ..., M}, σ _sBe sensor measurement noise standard deviation;

B3) utilize angle of pitch test statistics variance, set fiducial interval

If angle of pitch test statistics drops in the fiducial interval, then by detecting; Otherwise, deleted;

3) three sensors of picked at random carry out the position angle to the metric data of these three sensors and detect, and can not delete from candidate association collection P by the associative combination that detects;

4) to by all associative combination among the candidate association collection P that detects, set up indicator function ξ (l one by one _s)=NUM (P, l _s), wherein, s=1,2 ..., M, NUM (P, l _s) element l among the expression candidate association collection P _sTotal number, for ξ (l _sAssociative combination { the l of)=1 ₂..., l _s..., l _M, put it among the final correct incidence set Z, and contain { l among the deletion candidate association collection P ₁..., l _s..., l _MThe associative combination of arbitrary element, then at current iteration number of times k ₁On to add 1 be k ₁=k ₁+ 1;

5) further candidate association collection P is screened, if k ₁＜N ₁Then three sensors of picked at random and guarantee this three sensor groups be combined in before the screening in do not choose, utilize the position angle cotangent value in the step 1, these three sensor metric data are carried out the position angle to be detected, can not from candidate association collection P, delete by the associative combination that detects, return step 4; Otherwise, P is put into new candidate association collection Q, enter step 6;

6) three sensors of picked at random carry out the angle of pitch to the metric data of these three sensors and detect, and can not delete from candidate association collection Q by the associative combination that detects;

7) to by all associative combination among the candidate association collection Q that detects, set up indicator function ξ (l one by one _s)=NUM (Q, l _s), wherein, s=1,2 ..., M, NUM (Q, l _s) element l among the expression candidate association collection Q _sTotal number, for ξ (l _sAssociative combination { the l of)=1 ₁..., l _s..., l _M, put it among the final correct incidence set Z, and contain { l among the deletion candidate association collection Q ₁..., l _s..., l _MThe associative combination of arbitrary element, at current iteration number of times k ₂On to add 1 be k ₂=k ₂+ 1;

8) further candidate association collection Q is screened, if k ₂＜N ₂Then three sensors of picked at random and guarantee that this three sensor groups do not choose in the screening before being combined in utilize the angle of pitch cotangent value of step 1, these three sensor metric data are carried out the angle of pitch detect, can not from candidate association collection Q, delete by the associative combination that detects, return step 7; Otherwise, Q is put into new candidate association collection R, enter step 9;

9) if candidate association collection R is not an empty set,, set up cost function one by one then to associative combination all among the R Wherein, c is e _MnTotal number, choose and make the combination of overall cost minimum as final association results, put into final correct incidence set Z and output as a result of; Otherwise, directly will final correct incidence set Z output.

2. metric data correlating method according to claim 1, wherein step 2) described utilization sets up candidate association collection P by the associative combination that detects, carries out as follows:

At first, establish

I=1,2 ..., K represents a certain associative combination by detecting in i the sensor groups, K represents the number of sensor groups;

Then, choose two adjacent sensor groups L arbitrarily _I-1And L _i, guarantee

The expression empty set, identical sensor has identical measurement in the promptly adjacent sensor groups;

Each sensor measurement { l that will meet at last, above-mentioned condition ₁, l ₂..., l _MBe combined into candidate association collection P, wherein,

Images