CN109581305B - Multi-radar error correction method based on historical data - Google Patents

Abstract

The invention discloses a multi-radar error correction method based on historical data. Secondly, clustering the radar tracks by using the idea of hierarchical clustering to obtain a clustering tree representing the incidence relation among the tracks. And thirdly, based on the clustering tree obtained by hierarchical clustering, finding out the segmentation points by using a K-means algorithm to obtain the association relation of the radar track. And finally, correcting the system error of the radar by using a differential evolution algorithm.

Description

Multi-radar error correction method based on historical data

Technical Field

The invention belongs to the field of radar data analysis, and particularly relates to a multi-radar error correction method based on historical data.

Background

In modern and future wars, precision tracking and accurate combat are the subject of the wars. Precision percussion weapons are being developed in various countries. The purpose of radar detection of an aerial target is to indicate direction and position for accurate striking and guide own airplanes or air defense weapons to intercept incoming missiles or airplanes, but only under the condition that the radar detection accuracy is high enough, the performance of the precision guided weapons can be fully exerted, and the radar accuracy can also be guaranteed to realize accurate striking, so that modern wars put forward higher and higher requirements on the detection accuracy of radars. However, the radar precision test is only carried out in the model machine development stage at present, and due to the influence of various factors, the radar precision in batch production is difficult to be ensured to be consistent with the model machine development, so that the error correction has wide application prospect.

At present, radar correction methods at home and abroad are mainly divided into two categories of static correction and dynamic correction; the static correction is mainly a static test method which takes a fixed object as a reference target, for example, equipment such as a test tower and a level meter is used for testing each error of the radar one by one and obtaining a radar error precision value through theoretical calculation. At present, static test methods at home and abroad are mature, but static test requires corresponding instruments and equipment to be installed on a radar, and the test precision is poor, so that the method only can be used for testing the precision of the radar in a static state, and cannot reflect the actual error of the radar in normal operation.

At present, the dynamic test method has high cost and various defects. Countries such as the united states and russia use satellite-based methods to perform detection accuracy testing of remote radars, and even transmit satellites specifically for radar testing. In the test, a certain specific satellite is detected and tracked by using a radar, radar detection data is compared with satellite orbit data, and radar detection precision is calculated; the method has the advantages that the method can reflect the actual error of the radar in normal operation, but is only suitable for the remote radar with the detection distance of thousands of kilometers, and the conventional radar with the detection distance of hundreds of kilometers cannot be tested due to the limitation of the detection power of the radar. Another commonly used dynamic test method is to use an aircraft for testing, in which the aircraft is arranged for radar accuracy testing by fine planning, known as flight control. The detected airplane flies to the radar station and the back radar station in a specific distance range and at different heights, meanwhile, flight data are recorded or monitored by using higher-precision equipment on the airplane, and the flight data are compared with the radar detection data after the flight is finished, so that the detection precision of the radar is judged. The method is mature, but multiple repeated tests are generally carried out, the problems that the flight test is complicated in limited conditions and multiple programs, the influence of various factors on the air route and the flight plan arrangement are added in the middle of the test, the test can be completed only in a few months, a large amount of manpower and material resources are wasted, even if the detection precision is found to be not satisfactory, the operation is still a matter after a few months, and the method is difficult to popularize and use in the radar production process.

Disclosure of Invention

Aiming at the defects of the prior art, a set of multi-radar error correction technology based on historical data needs to be researched, the method is suitable for the current conditions of most national air defense systems, the cost of radar error correction is reduced, the radar accuracy is improved, and the altitude condition quality is simply and effectively improved.

The technical problem (or purpose) to be solved by the invention is to provide a multi-radar error correction technology based on historical data, which can mutually correct and obtain error parameters of various radars according to historical measurement data of the multiple radars under the condition of not increasing any hardware equipment, and improve the detection precision and the air condition quality of the radars.

The technical scheme is as follows: firstly, historical data are sampled and processed in an interpolation mode, and similarity among tracks is defined; secondly, acquiring an incidence relation of the radar track by utilizing the track similarity based on the idea of hierarchical clustering; and finally, calculating the error of the radar by using a differential evolution algorithm. The invention comprises the following steps:

step1, preprocessing a radar track;

step2, defining radar track similarity based on the improved Hausdorff distance;

step3, clustering the radar tracks based on hierarchical clustering to obtain a clustering tree representing the incidence relation among the tracks;

step4, searching reasonable clustering segmentation points in the clustering tree to obtain the association relation of the radar track;

step 5, correcting errors of the multi-radar system by using a differential evolution algorithm based on the incidence relation of the radar tracks;

the step1 comprises the following steps: filtering the radar track (reference: Kalman R E.A. new approach trajectory filtering and prediction schemes [ J ]]Journal of basic Engineering,1960,82(1):35-45.), interpolation process comprising: the interpolation is uniformly interpolated according to the time difference between the front and the rear points, and the two points of the interpolation are set as p₁(x₁,y₁,t₁)，p₂(x₂,y₂,t₂) Wherein x is₁,y₁Respectively representing a point p in a Cartesian coordinate system centered at the system center₁Abscissa and ordinate of (a), t₁As track point p₁Time stamp of x₂,y₂Are respectively expressed in the systemPoint p in cartesian coordinate system with heart as center of circle₂Abscissa and ordinate of (a), t₂As track point p₂The time stamp of (2) is interpolated as follows:

p′_i(x_i,y_i,t_i)＝(p₂-p₁)×i/n+1+p₁wherein n is the interpolation number, i is the corresponding interpolation number, i is more than or equal to 1 and less than or equal to n, p'_iIndicates the new insertion point, x_i,y_iRespectively represents a lower point p 'of a Cartesian coordinate system with the system center as the center'_iAbscissa and ordinate of (a), t_iIs a waypoint p'_iThe time stamp of (c).

The step2 comprises the following steps:

each radar track is regarded as a series of point sets, the point sets of the two radar tracks are set as a point set A and a point set B respectively, and A is { a ═ a₁,a₂,…,a_p},B＝{b₁,b₂,…,b_m}，a_iIs the ith point in the point set A, i takes the value of 1-p, b_jJ is the jth point in the point set B, the value of j is 1-m, the improved Hausdorff distance h (A, B) and the calculation mode of h (B, A) are as follows:

wherein | | | a_i-b_jI is a_i,b_jEuclidean distance between two points, | b_i-a_jI is b_i,a_jThe Euclidean distance between two points;

considering the time factor, redefining the euclidean distance between two points is as follows:

wherein

And t is_aCorresponding point a_iTime of (t)_bCorresponding point b_jAnd setting the radar track reporting period as T, wherein the delta T is the set error time value, and the delta T needs to satisfy the condition that the delta T is less than T/2.

The step3 comprises the following steps:

step 3-1, regarding each radar track as a category as a first layer of a clustering tree in an initial condition, and calculating pairwise similar distances of all categories to form a similar matrix according to the step2 by taking an initial state as a starting point;

step 3-2, searching the minimum value in the similar distance matrix, clustering the corresponding track categories into one type, generating a new layer serving as the next layer of the clustering tree, and recording the minimum value of the current distance matrix and the corresponding track categories;

and 3-3, recalculating the similar distance matrix according to the merged category state, judging whether the ending condition is reached, if all tracks are of one type or the current minimum similar distance is larger than a threshold (the maximum error caused by the radial and angle errors of the radar can be estimated to be 2-3 times as the threshold), ending the clustering, and returning to the 3-2 if the ending condition is not reached.

In step 3-1, if each category is a set of more than two radar tracks, a definition of similar distances between categories containing more than two radar tracks is introduced:

setting two target radar Track sets as T { Track respectively₁,…,Track_n}，T′{Track′₁,…,Track′_mTherein of

Representing a radar Track as a collection of points, Track_nRepresenting the nth target radar Track, Track 'in the set T'_mRepresents the mth target radar Track in the set T', and Track ═ P₁,P₂,...,P_nTherein of

Changing Hausdorff distance and defining similarity between two track setsH (T, T') is as follows:

H(T,T′)＝max(h(T,T′),h(T′,T))

wherein h (T, T '), h (T', T) respectively represents a Track set T { Track }₁,…,Track_nF to T '{ Track'₁,…,Track′_mSimilarity and T '{ Track'₁,…,Track′_mFor T { Track }₁,…,Track_nThe similarity of the points is defined as follows:

h(T,T′)＝max(h(Track_i,T′)),

h (T, T') is max (h (Track)_iT')) is represented in the set T { Track }₁,…,Track_nTrack in and set T '{ Track'₁,…,Track′_mThe most distant similarity of the (c) images,

similar h (T ', T) ═ max (h (Track'_i,T)),

h (T ', T) is max (h (Track'_iT)) is represented in a set T '{ Track'₁,…,Track′_mTrack in and set T { Track }₁,…,Track_n-the farthest similarity of;

the similarity between a single track to a set of tracks is defined as follows:

h(Track_i,T′)＝min(h(Track_i,Track′_j) Therein), wherein

h(Track_iT') is min (h (Track)_i,Track′_j) Track Track representation_iAnd set T '{ Track'₁,…,Track′_mCalculating the nearest similarity of the tracks in the position, and calculating the improved Hausdorff distance between two point sets by referring to the similarity between the tracks;

combining the above definitions gives:

h(T,T′)＝max(min(h(Track_i,Track′_j) ))) wherein

The current definition has the closure of the assembly domain in the track assembly, i.e. satisfies the following property (setting T)₁Another set of tracks similar to T, T'):

H(T,T′)＝H(T′,T)

H(T,T′)+H(T₁,T′)≥H(T+T₁,T′)

H(T+T₁,T′)≥H(T,T′)。

step4 comprises the following steps:

step 4-1: using hierarchical clustering method (ref: Day W H E, Edesbounner H. Effectionalgorithms for acquiring statistical methods [ J ]]Journal of classification,1984,1(1):7-24.) the classification similarity distance corresponding to each layer of the clustering tree is obtained, and a one-dimensional array D [ n ] arranged from small to large is obtained]Where n denotes the number of levels of the clustering tree, D [ i ]]Representing the corresponding similarity of the ith layer, and randomly selecting two initial center points p of the ith and jth layers₁And p₂，p₁＝D[i],p₂＝D[j]；

Step 4-2: for D [ n ]]Are each independently of p₁,p₂Comparison of for

Separately calculate Dk]And p₁And p₂The difference between the two and comparing the magnitudes, if with p₁D [ k ] is smaller]The label is 1, otherwise the label is 2;

step 4-3: for all points marked 1 or 2, p is recalculated₁,p₂，p_i＝∑D[j]M, wherein D [ j]For the parameter labeled i, m is Dj]The number marked i;

step 4-4: repeating the steps 4-2 and 4-3 until p₁,p₂Are smaller than a given threshold (the maximum error caused by the radar radial and angle errors can be estimated to be 2-3 times as the threshold),and obtaining the segmentation points of the clustering tree, thereby obtaining the association relation between the radar tracks.

The step 5 comprises the following steps:

step 5-1: according to the radar track association relation obtained in the step 4-4, calculating the similarity between the radar track of each radar and other associated radar tracks according to the definition in the step 3-1 to comprehensively evaluate radial and angle error parameters of each radar, namely calculating the similarity of different radar tracks of the same target, and if the radar error parameters are smaller than an allowable range (the requirements of the radial and angle errors of the radar can be preset according to needs), not calibrating;

step 5-2: randomly initializing first-generation error parameters of each radar according to the maximum error range of the radar, namely randomly initializing radial and angle errors of each radar;

step 5-3: for the radar error ranking evaluated in step 5-1, the radar with large error (i.e. the similarity between the radar track and other radar tracks of the same target is small) is corrected, the difference algorithm is used to generate a new generation of error parameters (refer to Wang H, Liu T, Bu Q, et al. An algorithm based on high efficiency computing for multi-target tracking of multi-sensor data fusion [ C ]// control conference CCC, 201635 th Chinese. IEEE,2016:5106-, calculating the similarity between the new radar track and other related radar tracks according to the step 5-1, judging whether the current error parameter increases the radar track similarity, if so, keeping the error parameter, otherwise, using the original error parameter;

step 5-4: and traversing the radar list, updating the error parameters of each radar, correcting the radar track by using the new parameters, evaluating the current radar errors, stopping correction if the radar errors are smaller than the allowable range or the maximum calibration times is reached, and otherwise, repeating the step 5-3.

Has the advantages that: the invention can mutually correct and obtain the error parameters of each radar according to the historical measurement data of a plurality of radars under the condition of not increasing any hardware equipment, thereby improving the detection precision and the air condition quality of the radars. Compared with the conventional radar correction methods such as flight inspection and satellite, the technology greatly reduces the implementation cost and time cost, ensures the effect and improves the international market competitiveness of military products of China to a certain extent.

Drawings

The foregoing and other advantages of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

FIG. 1 is a system block diagram of the present invention.

FIG. 2 is a diagram illustrating the effect of hierarchical clustering in the present invention.

Fig. 3 is a flowchart of a radar error correction process in the present invention.

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

The invention provides a multi-radar error correction method based on historical data, which comprises the following steps:

step1, preprocessing a radar track;

step2, defining radar track similarity based on the improved Hausdorff distance;

step3, clustering the radar tracks based on hierarchical clustering to obtain a clustering tree representing the incidence relation among the tracks;

step4, searching reasonable clustering segmentation points in the clustering tree to obtain the association relation of the radar track;

step 5, correcting errors of the multi-radar system by using a differential evolution algorithm based on the incidence relation of the radar tracks;

in step1 of the invention, radar tracks are preprocessed. The radar track is mainly subjected to filtering and interpolation processing, so that the timestamps of track points are consistent, and the realization of a follow-up algorithm is accelerated. The general scanning period of the radar track is 8-12 s, but due to the fact that some errors or the interference exists at the position of a target and the like, the radar track sometimes has a missing point or a large error, and therefore a certain radar track is causedThe position points of the tracks are obviously unavailable, and operations such as interpolation and noise reduction are required to be carried out on the radar track data before subsequent processing, and the interpolation method is mainly introduced here because the radar with distributed layout generally comprises a noise reduction function. The interpolation is uniformly interpolated according to the time difference between the previous point and the next point, the time interval between the interpolated points is 8-12 s, and the two points of the interpolation are set as p₁(x₁,y₁,t₁)，p₂(x₂,y₂,t₂) Wherein x is₁,y₁Respectively representing a point p in a Cartesian coordinate system centered at the system center₁Abscissa and ordinate of (a), t₁As track point p₁Time stamp of x₂,y₂Respectively representing a point p in a Cartesian coordinate system centered at the system center₂Abscissa and ordinate of (a), t₂As track point p₂The time stamp of (2) is interpolated as follows:

p′i(x_i,y_i,t_i)＝(p₂-p₁)×i/n+1+p₁wherein n is the interpolation number, i is the corresponding interpolation number 1 ≦ i ≦ n, p'_iIndicating the new insertion point.

In step2 of the method, radar track similarity is defined based on the improved Hausdorff distance. The track similarity is to quantify the similarity between two track lines, is the basis for determining track correlation and is also a precondition for correct clustering result, and the track line is a track point set with position, height and time. The Hausdorff distance measures the distance between proper subsets in space. Let X and Y be two proper subsets of the metric space M. Then the Hausdorff distance H (X, Y) is the smallest number r such that the closed r neighborhood of X contains Y, which also contains X. This distance function has the set of all proper subsets of M integrated into the metric space and is denoted as F (M). The topology of F (M) is only dependent on the topology of M. If M is not empty, then F (M) is also true.

The Hausdorff distance is a measure describing the degree of similarity between two sets of points, and is a defined form of the distance between two sets of points: assume that there are two sets of point sets a ═ a₁,a₂,…,a_p},B＝{b₁,b₂,…,b_pThen the Hausdorff distance between the two point sets is defined as follows:

h (a, B) ═ max (H (a, B), H (B, a)), where H (a, B), H (B, a) respectively denote the similarity of sets a to B and the similarity of sets B to a, defined as follows:

h(A,B)＝max(min(||a_i-b_j||)),a_i∈A,b_j∈B

h(B,A)＝max(min(||b_i-a_j||)),a_j∈A,b_iis epsilon of B, wherein | a_i-b_jI is a_i(x_i,y_i),b_j(x_j,y_j) Euclidean distance between two points, | b_i-a_jI is a_j(x_j,y_j),b_i(x_i,y_i) The euclidean distance between two points.

Each radar track can be regarded as a series of point sets, and similar distances among the tracks can be obtained according to the definition of the Hausdorff distance. Due to the random error condition, a single point may have a large error to further influence the calculation of the similarity between tracks, and the improved Hausdorff distance calculation mode is as follows:

wherein | | | a_i-b_jI is a_i(x_i,y_i),b_j(x_j,y_j) Euclidean distance between two points, | b_i-a_jI is a_j(x_j,y_j),b_i(x_i,y_i) The euclidean distance between two points.

For the improved Hausdorff distance, the influence of random errors on the similarity can be effectively eliminated, and since some civil aviation routes are similar and only have time difference, the time factor must be considered, and the Euclidean distance between two points is redefined as follows:

wherein

And t is_aCorresponding point a_iTime of (t)_bCorresponding point b_jAnd setting the radar track reporting period as T, wherein the delta T is the set error time value, and the delta T needs to satisfy the condition that the delta T is less than T/2. The similar distance between the two tracks can be conveniently calculated by using the formula.

In step3 of the invention, radar track clustering processing based on hierarchical clustering is carried out. The hierarchical clustering algorithm firstly classifies by establishing a system tree graph, each tree node has subclasses, clustering can be carried out on different levels of the tree to form different cluster families, hierarchical decomposition is carried out on a set of given data objects, and the hierarchical clustering method can be divided into aggregated (aggregative) and split (dynamic) hierarchical clustering according to a decomposition strategy adopted by the hierarchical decomposition.

Clustering by clustering and clustering, using a bottom-up strategy, first taking each object as a class, then combining the classes into a larger class according to the similarity measure until all the objects are in one class or a certain termination condition is met, and referring to fig. 2, wherein r is less than or equal to n-1. Most hierarchical clustering algorithms belong to this class, and they differ only in the definition of class similarity. Here, the term "agglomerative hierarchical clustering" is used, and the term "split hierarchical clustering" is used in contrast to the above-described method and is not described in detail here.

The steps of the agglomeration hierarchical clustering algorithm are as follows:

step 1: taking an initial state (each radar track is a category) as a starting point, and calculating pairwise similar distances of all categories according to the step2 to form a similar matrix;

step 2: searching the minimum value in the similar distance matrix, gathering the corresponding track types into one type, and recording the minimum value of the current distance matrix and the corresponding track types;

step 3: and updating the similar distance matrix according to the combined category state, judging whether an ending condition is reached, wherein all tracks are of one type or the current minimum similar distance is larger than a certain threshold (the maximum error caused by the radial and angle errors of the radar can be estimated to be 2-3 times as the threshold), and returning to Step2 until the ending condition is not reached until the ending condition is ended.

In the hierarchical clustering algorithm, the initial calculation of the similarity distance between the classes can be according to the method in the step2, because each class corresponds to one flight path, when each class is a set of a plurality of flight paths in the clustering process, the similarity between the sets needs to be defined, and therefore the Hausdorff distance needs to be further expanded; secondly, under the dense target environment, if the target track shapes are similar and no constraint is added according to the method, the targets are difficult to cluster and divide. In order to adapt to a hierarchical clustering algorithm and solve the clustering problem of dense target areas, the definition of the similarity between more than two radar track sets needs to be introduced:

setting two target radar Track sets as T { Track respectively₁,…,Track_n}，T′{Track′₁,…,Track′_mTherein of

Representing a radar Track as a collection of points, Track ═ P₁,P₂,...,P_nTherein of

Changing the Hausdorff distance, defining the similarity H (T, T') between the two track sets as follows:

H(T,T′)＝max(h(T,T′),h(T′,T))

wherein h (T, T '), h (T', T) respectively represents a Track set T { Track }₁,…,Track_nF to T '{ Track'₁,…,Track′_mSimilarity and T '{ Track'₁,…,Track′_mFor T { Track }₁,…,Track_nThe similarity of the points is defined as follows:

h(T,T′)＝max(h(Track_i,T′)),

i.e. in the set T Track₁,…,Track_nTrack in and set T '{ Track'₁,…,Track′_mThe most distant similarity of the (c) images,

similar h (T ', T) ═ max (h (Track'_i,T)),

Is represented in the set T '{ Track'₁,…,Track′_mTrack in and set T { Track }₁,…,Track_n-the farthest similarity of;

the similarity between a single track to a set of tracks is defined as follows:

h(Track_i,T′)＝min(h(Track_i,Track′_j) Therein), wherein

Track_iAnd set T '{ Track'₁,…,Track′_mCalculating the nearest similarity of the tracks in the data, and calculating the similarity between the tracks by referring to the 3 rd point set to calculate the improved Hausdorff distance between the two point sets;

combining the above definitions can result in:

h(T,T′)＝max(min(h(Track_i,Track′_j) ))) wherein

The current definition has the closure of the set domain in the track set, i.e. satisfies the following property (assuming T₁Another set of tracks similar to T, T'):

H(T,T′)＝H(T′,T)

H(T,T′)+H(T₁,T′)≥H(T+T₁,T′)

H(T+T₁,T′)≥H(T,T′)

for a dense target area, if the track trajectories of two targets are similar and occur simultaneously, the situation brings great difficulty to clustering. Generally, the dense target area is also the focal area of radar scanning, which ensures that a plurality of targets in the area are generally detected by the radar. For multiple target tracks scanned by the same radar in the same time period, the target tracks can be considered as different targets, namely, the same target is assumed not to be generated into two radar tracks by the same radar.

In step4 of the invention, reasonable clustering segmentation points are searched in the clustering tree. The clustering result of each layer can be obtained by utilizing hierarchical clustering, and the similarity corresponding to one type of clustering in each layer can be obtained. Because each clustering is to cluster the two most similar flight path sets into one type, and the expanded Hausdorff similarity in the previous step can ensure monotone and non-reducibility in the integrated set domain, the Hausdorff distance of each layer of the corresponding cluster in the whole clustering tree is increased. After the clustering tree is obtained, a proper segmentation point is found, namely a two-classification problem in a one-dimensional space is solved, and the clustering tree is segmented to obtain a clustering result.

The clustering tree is segmented by using the most basic K-means clustering method, wherein K is determined to be 2, and the algorithm steps are as follows:

step 1: using hierarchical clustering method (ref: Day W H E, Edesbounner H. Effectionalgorithms for acquiring statistical methods [ J ]]Journal of classification,1984,1(1):7-24.) the corresponding classification similarity of each layer is obtained, and a one-dimensional array D [ n ] arranged from small to large is obtained]Where n denotes the number of levels of the clustering tree, D [ i ]]Representing the corresponding similarity of the ith layer, and randomly selecting two initial center points p of i and j₁And p₂，p₁＝D[i],p₂＝D[j]；

Step 2: for D [ n ]]Are each independently of p₁,p₂Comparison of for

And p₁Or p₂If the difference is smaller, then D [ i ]]Labeled 1 or 2;

step 3: for all points marked 1 or 2, p is recalculated₁,p₂，p_i＝∑D[j]M, wherein D [ j]For the parameter labeled i, m is Dj]The number marked i;

step 4: repeating the steps 2 and 3 until p₁,p₂And (3) the distance between the two points is less than a given threshold (2-3 times of the maximum error caused by the radial and angle errors of the radar can be estimated as the threshold), so that the segmentation points of the clustering tree can be obtained, and the incidence relation between the radar tracks can be obtained.

In order to improve the classification accuracy, the following improvements are made on the basis of a K-means algorithm: 1) the Hausdorff distance of radar tracks obviously not being the same target is set to be a fixed larger value when the Hausdorff distance of the radar tracks is calculated, so that the radar tracks can be easily clustered into a class when being clustered, for example, the tracks have no overlapping time regions or the tracks found by the same radar have the same time region; 2) setting a confidence rate, namely obtaining two types of division lines through a K-means algorithm, effectively controlling the division lines to improve the classification accuracy, wherein the division lines need to be adjusted, otherwise, clustering deviation can occur when a radar has a large error.

In step 5 of the invention, the error of the multi-radar system is corrected by using a differential evolution algorithm. By randomly initializing radial and angle errors, carrying out differential evolution for each generation, and preferentially selecting an error parameter of each radar until the required precision is met or iteration is carried out to the maximum generation. The differential evolution algorithm comprises the following steps:

step 1: according to the radar track association relation obtained in the step4, calculating the similarity between the radar track of each radar and other associated radar tracks according to the definition in the step 2/3 to comprehensively evaluate radial and angle error parameters of each radar, namely calculating the similarity of different radar tracks of the same target, and if the radar error parameters are smaller than an allowable range (the requirements of the radial and angle errors of the radar can be preset according to requirements), not calibrating;

step 2: according to the maximum error range of the radar, the radial and angle errors (first generation error parameters) of each radar are initialized randomly;

step 3: sequencing the estimated radar errors in Step1, firstly correcting the radar with large error (namely the similarity between the radar track and other radar tracks of the same target is small), generating a new generation of error parameters (references: Wang H, Liu T, Bu Q, et al. An algorithm based on high efficiency computing for multi-target tracking of multi-sensor data fusion [ C ]// control conference CCC, 201635 th Chinese. IEEE,2016:5106 5111.) by using the new generation of error parameters to correct the radar track, calculating the similarity between the new radar track and other associated radar tracks according to 5-1, judging whether the current error parameters increase the similarity of the radar tracks, if the similarity increases, keeping the error parameters, otherwise, using the error parameters;

step 4: and traversing the radar list, updating the error parameters of each radar, correcting the radar track by using the new parameters, evaluating the current radar error, stopping correction if the radar error is smaller than the allowable range or reaches the maximum calibration times, and otherwise, repeating Step 3.

Examples

In most national air defense systems, different radars have larger or smaller system errors, and aiming at the problems of high cost, difficulty in implementation, low precision and the like of the existing static and dynamic radar error correction method, the invention provides a multi-radar correction method for historical data, which can effectively improve the detection precision of each radar and improve the air situation quality under the condition of not increasing a new hardware structure.

The processing flow of the invention is shown in fig. 1-3, and mainly comprises the following steps:

1. preprocessing a radar track;

preprocessing filters radar tracks (reference: Kalman R E.A new approach to linear filtering and prediction schemes [ J ]. Journal of basic Engineering,1960,82(1):35-45.) and interpolates to make track point timestamps consistent, which is beneficial to accelerating the realization of subsequent algorithms. Due to the fact that some errors or interference exists at the position of a target and the like, radar tracks sometimes have lost points or have large errors, and position points of some tracks are obviously unavailable, interpolation processing needs to be conducted, and interpolation is conducted uniformly according to time.

2. Defining radar track similarity based on the improved Hausdorff distance;

the Hausdorff distance is a method for defining the incidence relation between different point sets, and based on the Hausdorff distance, a new Hausdorff is defined to measure the similarity between radar tracks (track point sets) with time and position information and define the similarity between the radar track sets, which is a premise for calculating the radar track clustering relation and is also the basic theory of the patent.

3. Radar track clustering processing based on hierarchical clustering;

the hierarchical clustering algorithm is a clustering idea, each radar track is taken as a target to be taken as an initial layer, each layer selects the most similar track set to be combined into one class, and the currently combined similarity value is recorded. And finally, combining all tracks into one type or reaching a threshold value (in the embodiment, according to the radial error of the radar, 10km, the angle error of-5 degrees is the range of the angle error of the radar, and the radar tracks with the value 2 times larger than the range are regarded as different targets), and finally obtaining a complete hierarchical clustering tree.

4. Searching reasonable clustering segmentation points in the clustering tree;

the hierarchical clustering can be used to obtain the clustering result of each layer, and the similarity corresponding to the clustering of each layer. Because each clustering is to cluster the two most similar flight path sets into one type, and the expanded Hausdorff similarity in the previous step can ensure monotone and non-reducibility in the integrated set domain, the Hausdorff distance of each layer of the corresponding cluster in the whole clustering tree is increased. And dividing to a proper division point, namely, solving a two-classification problem in a one-dimensional space, and realizing the classification by using a K-means algorithm.

5. Correcting errors of the multi-radar system by using a differential evolution algorithm;

the differential evolution algorithm is a random optimization algorithm. Because a plurality of radars are mutually corrected, firstly, the errors of all the radars are evaluated and sequenced, and the radars with large errors are corrected; secondly, initializing error parameters of each radar as first-generation error parameters, obtaining new error parameters through cross variation of the parameter set, comparing the parameters before and after, and preferentially recording the new error parameters as second-generation error parameters of the radar; thirdly, correcting each radar track by using the new error parameters, evaluating the new error parameters of each radar, sequencing and preparing to correct the third-generation error parameters; and finally, if the radar error meets a threshold value (in the embodiment, if the radar radial error is less than 0.5km and the angle error ranges from-0.5 degrees to 0.5 degrees, the calibration is considered to be finished) or the evolution reaches the maximum times, stopping error correction. The specific process is shown in FIG. 3.

The present invention provides a multi-radar error correction method based on historical data, and a plurality of methods and ways for implementing the technical solution are provided, the above description is only a preferred embodiment of the present invention, it should be noted that, for those skilled in the art, a plurality of modifications and embellishments can be made without departing from the principle of the present invention, and these modifications and embellishments should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (7)

1. A multi-radar error correction method based on historical data is characterized by comprising the following steps:

step1, sampling radar historical track data, and then preprocessing the radar historical track data;

step2, defining radar track similarity based on the improved Hausdorff distance;

step3, clustering the radar tracks based on hierarchical clustering to obtain a clustering tree representing the incidence relation among the tracks; when each radar track is in one category, calculating pairwise similar distances of all categories to form a similar matrix by taking an initial state as a starting point according to the step2, and if each category is a set of more than two radar tracks, introducing a definition of similarity between the sets of more than two radar tracks;

step4, searching reasonable clustering segmentation points in the clustering tree to obtain the association relation of the radar track;

and 5, correcting errors of the multi-radar system by using a differential evolution algorithm based on the incidence relation of the radar tracks.

2. The method of claim 1, wherein step1 comprises: filtering and interpolating radar historical track data, wherein the interpolation comprises the following steps: the interpolation is uniformly interpolated according to the time difference between the front and the rear points, and the two points of the interpolation are set as p₁(x₁,y₁,t₁)，p₂(x₂,y₂,t₂) Wherein x is₁,y₁Respectively representing a point p in a Cartesian coordinate system centered at the system center₁Abscissa and ordinate of (a), t₁As track point p₁Time stamp of x₂,y₂Respectively representing a point p in a Cartesian coordinate system centered at the system center₂Abscissa and ordinate of (a), t₂As track point p₂The time stamp of (2) is interpolated as follows:

p′_i(x_i,y_i,t_i)＝(p₂-p₁)×i/n+1+p₁wherein n is the interpolation number, i is the corresponding interpolation number, i is more than or equal to 1 and less than or equal to n, p'_iIndicates the new insertion point, x_i,y_iRespectively represents a lower point p 'of a Cartesian coordinate system with the system center as the center'_iAbscissa and ordinate of (a), t_iIs a waypoint p'_iThe time stamp of (c).

3. The method of claim 2, wherein step2 comprises:

each radar track is regarded as a series of point sets, the point sets of the two radar tracks are set as a point set A and a point set B respectively, and A is { a ═ a₁,a₂,…,a_p},B＝{b₁,b₂,…,b_m}，a_iIs the ith point in the point set A, i takes the value of 1-p, b_jJ is the jth point in the point set B, the value of j is 1-m, the improved Hausdorff distance h (A, B) and the calculation mode of h (B, A) are as follows:

wherein | | | a_i-b_jI is a_i,b_jEuclidean distance between two points, | b_i-a_jI is b_i,a_jThe Euclidean distance between two points;

considering the time factor, redefining the Euclidean distance between two points is as follows:

wherein

And t is_aCorresponding point a_iTime of (t)_bCorresponding point b_jAnd setting the radar track reporting period as T, wherein the delta T is the set error time value, and the delta T needs to satisfy the condition that the delta T is less than T/2.

4. The method of claim 3, wherein step3 comprises:

3-1, when each radar track is in one category, calculating pairwise similar distances of all categories to form a similar matrix by taking an initial state as a starting point according to the step 2;

step 3-2, searching the minimum value in the similar distance matrix, grouping the corresponding track types into one type, and recording the minimum value of the current distance matrix and the corresponding track type;

and 3-3, updating the similar distance matrix according to the combined category state, judging whether an ending condition is reached, ending clustering if all tracks are of one category or the current minimum similar distance is greater than a threshold value, and returning to the 3-2 if the ending condition is not reached.

5. Method according to claim 4, characterized in that in step 3-1, if each class is a set of more than two radar tracks, a definition is introduced for the similarity between the sets of more than two radar tracks:

setting two target radar Track sets as T { Track respectively₁,…,Track_n}，T′{Track′₁,…,Track′_mTherein of

Representing a radar Track as a collection of points, Track_nRepresenting the nth target radar Track, Track 'in the set T'_mRepresents the mth target radar Track in the set T', and Track ═ P₁,P₂,...,P_nTherein of

The improved Hausdorff distance is defined as follows for the similarity H (T, T') between the two track sets:

H(T,T′)＝max(h(T,T′),h(T′,T))

wherein h (T, T '), h (T', T) respectively represents a Track set T { Track }₁,…,Track_nF to T '{ Track'₁,…,Track′_mSimilarity and T '{ Track'₁,…,Track′_mFor T { Track }₁,…,Track_nThe similarity of the points is defined as follows:

h (T, T') is max (h (Track)_iT')) is represented in the set T { Track }₁,…,Track_nTrack in and set T '{ Track'₁,…,Track′_mThe most distant similarity of the (c) images,

h (T ', T) is max (h (Track'_iT)) is represented in a set T '{ Track'₁,…,Track′_mTrack in and set T { Track }₁,…,Track_n-the farthest similarity of;

the similarity between a single track to a set of tracks is defined as follows:

h(Track_i,T′)＝min(h(Track_i,Track′_j) Therein), wherein

h(Track_iT') is min (h (Track)_i,Track′_j) Track Track representation_iAnd set T '{ Track'₁,…,Track′_mThe nearest similarity of the tracks in the Chinese;

combining the above definitions gives:

h(T,T′)＝max(min(h(Track_i,Track′_j) ))) wherein

The current definition has the closure of the set domain in the track set, i.e. satisfies the following properties:

H(T,T′)＝H(T′,T)

H(T,T′)+H(T₁,T′)≥H(T+T₁,T′)

H(T+T₁,T′)≥H(T,T′)，

setting T₁Is another set of tracks.

6. The method of claim 5, wherein step4 comprises:

step 4-1: obtaining the classification similarity corresponding to each layer of the clustering tree by utilizing a hierarchical clustering method to obtain a one-dimensional array D [ n ] arranged from small to large]Where n denotes the number of levels of the clustering tree, D [ i ]]Representing the corresponding similarity of the ith layer, and randomly selecting two initial center points p of the ith and jth layers₁And p₂，p₁＝D[i],p₂＝D[j]；

Step 4-2: for D [ n ]]Are each independently of p₁,p₂Comparison of for

Separately calculate Dk]And p₁And p₂The difference between the two and comparing the magnitudes, if with p₁D [ k ] is smaller]The label is 1, otherwise the label is 2;

step 4-3: for all points marked 1 or 2, p is recalculated₁,p₂，p_i＝∑D[j]M, wherein D [ j]For the parameter labeled i, m is Dj]The number marked i;

step 4-4: repeating the steps 4-2 and 4-3 until p₁,p₂And obtaining the segmentation points of the clustering tree when the values are smaller than the given threshold value, thereby obtaining the association relation between the radar tracks.

7. The method of claim 6, wherein step 5 comprises:

step 5-1: according to the radar track association relation obtained in the step 4-4, calculating the similarity between the radar track of each radar and other associated radar tracks according to the definition in the step 3-1 to comprehensively evaluate radial and angle error parameters of each radar, namely calculating the similarity of different radar tracks of the same target, and if the radar error parameters are smaller than an allowable range, not calibrating;

step 5-2: randomly initializing first-generation error parameters of each radar according to the maximum error range of the radar, namely randomly initializing radial and angle errors of each radar;

step 5-3: sequencing the radar errors evaluated in the step 5-1, firstly correcting the radars with large errors, generating a new generation of error parameters by utilizing a difference algorithm to carry out cross variation on the errors, correcting the radar track by utilizing the new generation of error parameters, calculating the similarity between the new radar track and other related radar tracks according to the step 5-1, judging whether the current error parameters increase the similarity of the radar track or not, if the similarity increases, keeping the error parameters, otherwise, using the original error parameters;

step 5-4: and traversing the radar list, updating the error parameters of each radar, correcting the radar track by using the new parameters, evaluating the current radar errors, stopping correction if the radar errors are smaller than the allowable range or the maximum calibration times is reached, and otherwise, repeating the step 5-3.

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