CN113390406B

CN113390406B - Multi-target data association and positioning method based on passive multi-sensor system

Info

Publication number: CN113390406B
Application number: CN202110666607.3A
Authority: CN
Inventors: 李万春; 王丽
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2021-06-16
Filing date: 2021-06-16
Publication date: 2022-05-24
Anticipated expiration: 2041-06-16
Also published as: CN113390406A

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 is 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 presence and fluctuation of noise, a target which does not actually exist is determined 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

Redefined as an M L matrix

Where lines that do not satisfy length L are all filled with invalid values at the end. Determining the target detection range and detecting the targetIt is divided into K × J grid points, each grid point (x) is traversed_k,y_j) Azimuth information of each grid point with respect to the M sensors is calculated and expressed as

Definition 1^1×LFor vectors with elements all 1, grid points (x) are calculated_k,y_j) With respect to the error between all the measurements of the sensor, it is positioned:

the physical meaning of the above formula is that the coordinate point (x)_k,y_j) 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

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:

(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 one position (x)Y), two coordinate points located within a range of a dotted line in the grid coordinate graph are regarded as the same target, Δ x and Δ y are ranges of abscissa and ordinate, respectively, and (x)₀,y₀) Then it is taken as the mean point in the same coordinate region, i.e. grid point (x)_k,y_j)。

Let mu be [ x, y ═ y]^TThen for the mth sensor there are:

to f (mu) at mu₀＝[x₀,y₀]^TThe first order Taylor expansion is approximated by:

f(μ)＝f(μ₀)+H(μ-μ₀) (4)

wherein

For any one grid point (x)_k,y_j) 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,...,θ_M]^T. Further, the minimum error vector in the formula (1)

A corresponding set of measurements can be found

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:

where the covariance matrix Σ can be expressed as:

∑＝H₀PH₀ ^T+R (6)

wherein

R＝σ²I_M。

Is easy to know, D²Approximately obeying a chi-square distribution with a degree of freedom of M

The threshold value D with the confidence degree of 90 percent can be known by table lookup_{Sign board}Thus, the target point relationship can be determined as follows:

s2, fine association: the q data points obtained after the coarse correlation are defined as D ═ x₁,x₂,...,x_qAnd 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,...,C_nEach 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 cluster^M×lWhere l represents the number of grid points in the cluster. In the matrix^M×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

Using a weighted minimum of twoThe target position estimated value corresponding to the cluster can be obtained by multiplication (WLS), thereby obtaining all estimated target sets in the fine correlation

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

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

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. 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

Is defined as an M x L matrix

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,y_j) The azimuth information of each grid point relative to M sensors is calculated respectively and expressed as

Definition 1^1×LFor vectors with elements all 1, grid points (x) are calculated_k,y_j) With respect to the error between all measurements of the sensor:

error vector

Is composed of coordinate points (x)_k,y_j) Position information calculation and measurement

The difference between them is taken in all columns of the matrix by rowMinimum value composition;

for any one grid point (x)_k,y_j) By the formula:

obtaining the true azimuth angle theta from the point to all the sensors_(k,j)＝[θ₁,θ₂,...,θ_M]^TThe lower subscript m denotes the mth sensor, (x)_m,y_m) As the coordinates of the m-th sensor, based on the error vector

Finding a corresponding set of measurements

The mahalanobis distance between them is expressed as:

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

The covariance matrix Σ is expressed as:

∑＝H₀PH₀ ^T+R

wherein

R＝σ²I_M，μ₀＝[x_k,y_j]^TAnd Deltax and Deltay are grid points (x) respectively_k,y_j) The horizontal and vertical coordinate ranges of the grid;

setting confidence to 90% threshold D_{Sign board}And carrying out rough association judgment on the target point relation in the following way:

s2, defining the coarsely correlated data set as D ═ { x ═ x₁,x₂,…,x_LAnd 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 with the e as the radius, the MinPts represents the threshold value of the number of sample points in the neighborhood of the sample point, the DBSCAN algorithm clusters the input data points according to the density principle under the condition of unknown real target number, and finally outputs n clusters C ═ C₁,C₂,...,C_n}; matching matrix matchMatrix defining the position of each sensor measurement corresponding to a grid point in the same cluster^M×lWherein l represents the number of grid points in the cluster; in the matrix^M×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

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

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

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.