CN113390406A - Multi-target data association and positioning method based on passive multi-sensor system - Google Patents

Multi-target data association and positioning method based on passive multi-sensor system Download PDF

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CN113390406A
CN113390406A CN202110666607.3A CN202110666607A CN113390406A CN 113390406 A CN113390406 A CN 113390406A CN 202110666607 A CN202110666607 A CN 202110666607A CN 113390406 A CN113390406 A CN 113390406A
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李万春
王丽
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of electronic countermeasure, and particularly relates to a multi-target data association and positioning method based on a passive multi-sensor system in a non-ideal state. The method of the invention is totally divided into three steps: coarse association, fine association and backtracking. Firstly, error vectors of all position points in a search interval are calculated, and then position points after coarse correlation are judged and screened out according to relevant conditions. And dividing points after coarse association into different clusters by using a DBSCAN clustering algorithm in fine association, finding out a measured value matched with each cluster, and obtaining a position estimation of a target corresponding to each cluster by using a WLS algorithm. And finally, deleting redundant targets corresponding to the same set of measured values according to the mahalanobis distance in backtracking. The method has the advantages that the method can accurately complete the association of the passive multi-sensor multi-target data and finally accurately estimate the positions of a plurality of targets, and is simple and good in effect.

Description

Multi-target data association and positioning method based on passive multi-sensor system
Technical Field
The invention belongs to the technical field of electronic countermeasure, and relates to a multi-target data association and positioning method based on a passive multi-sensor system.
Background
Nowadays, with the continuous development of science and technology, electronic countermeasures among countries are also increasingly developed, and it is very important to reconnaissance of enemy targets to obtain more effective target information. Therefore, the passive multi-sensor reconnaissance system is more and more popular, the system utilizes independent measurement parameters of each sensor for a target in a certain specific space to carry out comprehensive analysis, fully utilizes all the measurement parameters through a series of technical means such as data association, matching, weighting fusion and the like, reduces the influence caused by the problem of one sensor as much as possible, realizes comprehensive and accurate description of the operational environment, and is convenient for a commander to make a more scientific and effective operational strategy. It can be seen that the passive multi-sensor reconnaissance system is more complex than a single sensor, and particularly in a multi-target scene, accurate position estimation of a plurality of targets is obtained by firstly obtaining a measurement value combination of the same target under the plurality of sensors, and only correct matching association is carried out on all measurement data, so that the uncertainty of reconnaissance information can be effectively reduced, the target positioning precision is improved, and the electronic combat performance is improved.
At present, most researches aiming at multi-target data association and positioning algorithms are realized under an ideal state, namely, under the condition of no false alarm and no missing detection. However, in actual signal detection, data obtained through a series of signal processing algorithms are not all data corresponding to a real target with a certain measurement error, for example, when a threshold detection method is adopted, due to the ubiquitous and fluctuating noise, a target which does not exist in practice is judged to be a target, and due to weak signal strength, the signal cannot be extracted from the noise after signal processing, that is, a missing detection situation. Therefore, the method has great research significance for the multi-target positioning problem research under the conditions of false alarm and missing detection.
Disclosure of Invention
Aiming at the problems, the invention provides a multi-target data association and positioning method based on a passive multi-sensor system under a non-ideal state.
The technical scheme adopted by the invention is as follows:
assume that there are M sensors, N targets in the passive multi-sensor reconnaissance system model. Due to false alarms and missed detections in the system, the number of azimuth measurements obtained in each sensor is not necessarily equal to N. The method is totally divided into three steps: coarse association, fine association and backtracking. Firstly, error vectors of all position points in a search interval are calculated, and then position points after coarse correlation are judged and screened out according to relevant conditions. And dividing points after coarse association into different clusters by using a DBSCAN clustering algorithm in fine association, finding out a measured value matched with each cluster, and obtaining a position estimation of a target corresponding to each cluster by using a WLS algorithm. And finally, deleting redundant targets corresponding to the same set of measured values according to the mahalanobis distance in backtracking.
The multi-target data association and positioning algorithm based on the passive multi-sensor system comprises the following steps:
s1, coarse association: in the case of false alarm and missing detection, because the length of the measured data of each sensor may be different, the longest length value is represented by L, and the azimuth angle measurement value set is set
Figure BDA0003117051810000021
Redefined as an M L matrix
Figure BDA0003117051810000022
Where lines that do not satisfy length L are all filled with invalid values at the end. Determining a target detection range, dividing the target detection range into K × J grid points, and traversing each grid point (x)k,yj) The azimuth information of each grid point relative to M sensors is calculated respectively and expressed as
Figure BDA0003117051810000023
Definition 11×LFor vectors with elements all 1, grid points (x) are calculatedk,yj) With respect to the error between all the measurements of the sensor, it is positioned:
Figure BDA0003117051810000024
of the above formulaThe physical meaning is that the coordinate point (x)k,yj) The difference between the calculated value and the measured value of the position information is taken according to the row of the minimum value in all the columns of the matrix to form the error vector of the coordinate point
Figure BDA0003117051810000025
In coarse correlation, in order to make the target on the correlation as close to the real target position as possible, the following two conditions will be satisfied:
(1) considering that in the case of a measurement error satisfying a normal distribution, having a difference between the true target position and the measured value within 3 σ allows a confidence level approaching 100%, where σ represents an azimuth measurement error. In addition, the following basic conditions are constructed under the condition that the existence of the missed detection is considered and the probability that the missed detection exists in the same target simultaneously by a plurality of sensors is low:
Figure BDA0003117051810000026
(2) furthermore, mahalanobis distance between the point to be associated and the corresponding measured value is defined on the basis of the condition that the condition is satisfied, and under the condition that the confidence is satisfied at 90%, the position of the grid point can be regarded as the point of coarse association.
As shown in FIG. 1, for any position (x, y), two coordinate points within a range of a dotted line in the grid coordinate diagram are regarded as the same object, and Δ x and Δ y are ranges of abscissa and ordinate, respectively, and (x, y)0,y0) Then the mean point, i.e., grid point (x), in the same coordinate region is usedk,yj)。
Let mu be [ x, y ═ y]TThen for the mth sensor there are:
Figure BDA0003117051810000027
to f (mu) at mu0＝[x0,y0]TIs subjected to a first-order Taylor expansionThe method is similar to the method:
f(μ)＝f(μ0)+H(μ-μ0) (4)
wherein
Figure BDA0003117051810000031
For any one grid point (x)k,yj) The real value theta of the azimuth angle from the point to all the sensors can be obtained by the formula (3)(k,j)＝[θ1,θ2,...,θM]T. Further, the minimum error vector in the formula (1)
Figure BDA0003117051810000032
A corresponding set of measurements can be found
Figure BDA0003117051810000033
If there is a value in the error vector that does not meet the 3 σ error range, the measured value of its corresponding sensor is removed in the calculation of the mahalanobis distance. Mahalanobis distance is an effective method for calculating the degree of identity of two unknown sample sets, and for the two azimuth vectors, the mahalanobis distance between them can be expressed as:
Figure BDA0003117051810000034
where the covariance matrix Σ can be expressed as:
∑＝H0PH0 T+R (6)
wherein
Figure BDA0003117051810000035
R＝σ2IM。
Is easy to know, D2Approximately obeying a chi-square distribution with a degree of freedom of M
Figure BDA0003117051810000036
The threshold value D with the confidence degree of 90 percent can be known by table lookupSign boardThereby, the target point can be closedThe following determination is made:
Figure BDA0003117051810000037
s2, fine association: the q data points obtained after the coarse correlation are defined as D ═ x1,x2,…,xqAnd setting algorithm parameters (e, MinPts) by utilizing a DBSCAN clustering algorithm, wherein the e represents the neighborhood radius of a certain data sample, namely the neighborhood of the sample point is a circular area taking the e as the radius, and the MinPts represents the threshold value of the number of the sample points in the neighborhood of the sample point. Under the condition of unknown real target number, the DBSCAN algorithm can cluster input data points according to the density principle, and finally outputs n clusters C ═ C1,C2,...,CnEach cluster means that one target estimated position can be obtained.
Matching matrix matchMatrix defining the position of each sensor measurement corresponding to a grid point in the same clusterM×lWhere l represents the number of grid points in the cluster. In the matchMatrixM×lThe measured value corresponding to the position with the highest occurrence frequency is taken out line by line and used as the measured value set of the target position corresponding to the cluster
Figure BDA0003117051810000041
The target position estimation value corresponding to the cluster can be obtained by using a weighted least square method (WLS), so that all estimation target sets in the fine correlation are obtained
Figure BDA0003117051810000042
Thus, for each cluster, its corresponding target estimated position can be obtained from the matched azimuth measurements. In addition, the angle difference of matching is still limited during matching, if the angle difference does not satisfy the threshold of 3 σ, the matching value is set as invalid matching, and if the invalid matching value becomes the highest number of occurrence frequencies among the matching values of a certain sensor, the measurement value of the sensor is removed in the position estimation process.
S3, backtracking: for the estimated target set obtained in the fine correlation
Figure BDA0003117051810000043
In order to remove redundant false estimation targets generated by the same real target, measurement value matching comparison is carried out between every two estimation targets, if half or more of the matched measurement values are found to be the same, the estimation targets are considered to be generated by the same target, the Mahalanobis distance calculation formula in the same mode (5) is used for comparing the two undetermined targets, and the estimation position of the target with the smaller Mahalanobis distance is selected. Fig. 2 is a flow chart of the proposed algorithm.
And (3) outputting: position estimation of multiple targets
Figure BDA0003117051810000044
The method has the advantages that the method can accurately correlate the multi-target data and finally accurately estimate the position of the target, and is simple and good in effect.
Drawings
FIG. 1 is a schematic diagram of a range of associated targets;
FIG. 2 is a flow chart of a passive multi-sensor multi-target location algorithm;
FIG. 3 is a diagram of a simulated scene target location distribution;
FIG. 4 is a diagram illustrating a multi-objective coarse correlation result;
FIG. 5 is a density clustering effect diagram based on DBSCAN;
FIG. 6 is a diagram illustrating multi-target location estimation.
Detailed Description
The present invention will be described in detail with reference to examples below:
in this embodiment, Matlab is used to verify the above method for performing multi-target data association and positioning based on the passive multi-sensor system by using azimuth measurement values, and for the sake of simplicity, the following assumptions are made for the algorithm model:
1. both the sensor and the target are in the XY plane;
2. all engineering errors are superposed into the distance errors;
3. the target is assumed to be stationary or at a very low speed of motion.
Assuming that the target detection area is a rectangular area of 100km × 80km, the target search interval is 1km, the number of targets to be examined is 4, the coordinates thereof are (50,30), (50,60), (30,40), (70,40), the number of sensors is 5, the coordinates thereof are (10,10), (90,10), (10,80), (90,80), (60,5), and the units are km. The sensor to target location profile for this scenario is shown in fig. 3.
The passive multi-sensor system has the multi-target positioning effect:
if false alarm and missing detection exist, the false alarm probability Pf is 0.8/rad, and the detection probability Pd is 0.9, as shown in fig. 4, the result of the algorithm after coarse correlation is performed when the angle measurement error is 0.5 °. Fig. 5 and 6 are the results of DBSCAN clustering and final target position estimation, respectively. As can be seen from fig. 4 and 5, after the coarse correlation, points very close to the real target are screened, and there are no noise points. And the points belonging to different targets can be accurately distinguished by utilizing the advantages of the DBSCAN algorithm. As can be seen from fig. 6, the algorithm achieves effective estimation on 4 real targets, the positioning accuracy is high, and no false target point occurs, which indicates that the algorithm achieves good processing for false alarm and missed detection.

Claims (1)

1. A multi-target data association and positioning method based on a passive multi-sensor system is characterized in that the data association and positioning method comprises the following steps:
s1, obtaining the measurement data of the target through the sensor, expressing the length of the longest measurement data obtained as L, and measuring the azimuth angle
Figure FDA0003117051800000011
Is defined as an M x L matrix
Figure FDA0003117051800000012
Wherein lines which do not satisfy length L are completely filled with invalid values at the end; defining a target detection plane, dividing it into K × J grid points, and traversing each grid point (x)k,yj) The azimuth information of each grid point relative to M sensors is calculated respectively and expressed as
Figure FDA0003117051800000013
Definition 11×LFor vectors with elements all 1, grid points (x) are calculatedk,yj) With respect to the error between all measurements of the sensor:
Figure FDA0003117051800000014
error vector
Figure FDA0003117051800000015
Is composed of coordinate points (x)k,yj) Position information calculation and measurement
Figure FDA0003117051800000016
The difference value between the two is formed by taking the minimum value in all the columns of the matrix according to the rows;
for any one grid point (x)k,yj) By the formula:
Figure FDA0003117051800000017
obtaining the true azimuth angle theta from the point to all the sensors(k,j)＝[θ1,θ2,...,θM]TThe lower subscript m denotes the mth sensor, (x)m,ym) As the coordinates of the m-th sensor, based on the error vector
Figure FDA0003117051800000018
Finding a corresponding set of measurements
Figure FDA0003117051800000019
The mahalanobis distance between them is expressed as:
Figure FDA00031170518000000110
in particular, for values in the error vector that do not satisfy the 3 σ error range, the measured values of the corresponding sensors need to be discarded in the mahalanobis distance calculation, σ represents the azimuth angle measurement error, and the 3 σ error range means that
Figure FDA00031170518000000111
The covariance matrix Σ is expressed as:
∑＝H0PH0 T+R
wherein
Figure FDA0003117051800000021
R＝σ2IM，μ0＝[xk,yj]TAnd Deltax and Deltay are grid points (x) respectivelyk,yj) The horizontal and vertical coordinate ranges of the grid;
setting confidence to 90% threshold DSign boardAnd carrying out rough association judgment on the target point relation in the following way:
Figure FDA0003117051800000022
s2, defining the coarsely correlated data set as D ═ { x ═ x1,x2,...,xLAnd defining algorithm parameters (e, MinPts) by using a DBSCAN clustering algorithm, wherein the e represents the neighborhood radius of a certain data sample, namely the neighborhood of the sample point is a circular area taking the e as the radius, and the MinPts represents the number of sample points in the neighborhood of the sample pointAnd (3) counting threshold, clustering the input data points by the DBSCAN algorithm under the condition of unknown real target number according to the density principle, and finally outputting n clusters C ═ C1,C2,...,Cn}; matching matrix matchMatrix defining the position of each sensor measurement corresponding to a grid point in the same clusterM×lWherein l represents the number of grid points in the cluster; in the matchMatrixM×lThe measured value corresponding to the position with the highest occurrence frequency is taken out line by line and used as the measured value set of the target position corresponding to the cluster
Figure FDA0003117051800000023
The target position estimation value corresponding to the cluster can be obtained by utilizing a weighted least square method, so that all estimation target sets with fine correlation are obtained
Figure FDA0003117051800000024
Obtaining a corresponding target estimated position of each cluster through a matched azimuth angle measured value, simultaneously limiting a matched angle difference during matching, setting a matched value as invalid matching if the matched value does not meet a 3 sigma error range, and removing the measured value of a certain sensor in the position estimation process if the invalid matching value in the matched value of the sensor becomes a number with the highest occurrence frequency;
s3, for the estimation target set obtained in the fine correlation
Figure FDA0003117051800000025
And performing measurement value matching comparison between every two estimated targets, if half or more of the matched measurement values are the same, determining that the estimated targets are generated by the same target, comparing the two undetermined targets through a Mahalanobis distance calculation formula, and selecting the estimated position with the smaller Mahalanobis distance as the estimated position of the target, thereby obtaining the final position estimation value of the multiple targets.
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