CN109581305A - A kind of more radar error calibration methods based on historical data - Google Patents
A kind of more radar error calibration methods based on historical data Download PDFInfo
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Abstract
The invention discloses a kind of more radar error calibration methods based on historical data define the similarity calculation rule between radar track, the similarity based on improved Hausdorff distance definition track first.Secondly, radar track clustering processing is obtained the clustering tree of incidence relation between expression track using the thought of hierarchical cluster.Again, the clustering tree obtained based on hierarchical cluster is found cut-point using K-means algorithm, obtains the incidence relation of radar track.Finally, utilizing the systematic error of differential evolution algorithm amendment radar.
Description
Technical field
The invention belongs to radar data analysis fields, and in particular to a kind of more radar error correction sides based on historical data
Method.
Background technique
In modern and future war, precision tracking and precision strike are the themes of war.Every country is all in development essence
Really strike weapon.The purpose of radar detection aerial target is to point the direction for precision strike and position, guides one's own side's aircraft or anti-
Empty weapons interception attacks guided missile or aircraft, but only in the sufficiently high situation of radar detection precision, precision-guided munitions are
The performance of oneself can be given full play to, it may also be said to which radar accuracy is to realize the guarantee of precision strike, therefore modern war is to radar
Detection accuracy propose increasingly higher demands.But radar accuracy test at present only carries out in the prototype design stage, due to
The influence of various factors, it is difficult to ensure that batch production radar accuracy is consistent with Development Prototype, therefore error correction has widely
Application prospect.
Currently, radar calibration method is broadly divided into static and dynamic calibration two major classes both at home and abroad；Static shift correction mainly with
Fixed object is benchmark target, such as every error of radar is tested and passed through one by one using test tower and level meter equipment
It crosses theoretical calculation and obtains the static test of radar error precision value.Current static test both domestic and external is mature,
But static test needs install corresponding instrument and equipment on radar, and measuring accuracy is poor, can only be directed to radar silence
Accuracy test, cannot reflect radar work normally when actual error.
Currently, dynamic testing method cost is relatively high, and there are various deficiencies.For example the countries such as the U.S., Russia adopt
It is the detection accuracy test that benchmark mesh calibration method carries out long-range radar to satellite, or even specially transmits for radar test
Satellite.In testing, some specific satellite is tracked using radar detection, by GPR Detection Data and satellite orbit data
It is compared, calculates radar detection precision；The advantages of this method is the actual error being able to reflect when radar works normally, still
It is only applicable to the long-range radar of detection range thousands of miles, for detection range hundreds of kilometer normal radar due to radar visit
Surveying power limitation can not be tested.Another common dynamic testing method is tested using aircraft, in test
The test for arranging aircraft to be used for radar accuracy is prepared by precision, that is, usually said inspection flies.Aircraft is detected specific
Distance segment, on different height to radar station, back radar station flight, while record or setting using higher precision on board the aircraft
Flying quality, is compared, therefore, it is determined that the spy of radar by standby monitoring flying quality after the completion of flight with GPR Detection Data
Survey precision.The method comparative maturity, but multiplicating test is generally carried out, flight test restrictive condition multiprogram is cumbersome, examination
The problems such as testing the intermediate influence along with the various factors on course line and flight plan arrangement, which at least needs the several months could
Complete, waste a lot of manpower and material resources, even if having found detection accuracy it is undesirable be also the several months after thing, very
Difficulty is promoted the use of in radar production process.
Summary of the invention
In view of the deficiencies of the prior art, need to develop it is a set of can be based on more radar error correction skills of historical data
Art adapts to majority state air defense system present situation, reduces the cost of radar error correction, improves radar accuracy, simply and effectively
Improve air situation quality.
The technical problems to be solved by the invention (or purpose) are to provide a kind of more radar errors school based on historical data
Positive technology can mutually be corrected according to the historical measurement data of multiple radars and be obtained in the case where not increasing any hardware device
The error parameter for taking each radar improves the detection accuracy and air situation quality of radar.
Technical solution: first to historical data sampling, interpolation processing, the similarity between track is defined；Secondly, utilizing track
Similarity obtains the incidence relation of radar track based on the thought of hierarchical cluster；Finally, calculating radar using differential evolution algorithm
Error.The present invention the following steps are included:
Step 1, radar track is pre-processed；
Step 2, it is based on improved Hausdorff distance definition radar track similarity；
Step 3, radar track is carried out by clustering processing based on hierarchical cluster, obtains the cluster of incidence relation between expression track
Tree；
Step 4, reasonable cluster segmentation point is found in clustering tree, obtains the incidence relation of radar track；
Step 5, based on the incidence relation of radar track, using differential evolution algorithm to multiple radar system error correction；
Step 1 includes: to be filtered (bibliography: Kalman R E.A new approach to radar track
linear filtering and prediction problems[J].Journal of basic Engineering,
1960,82 (1): 35-45.), interpolation processing, the interpolation processing includes: that interpolation is uniformly inserted according to the time difference of front and back two o'clock
Value, if the two o'clock of interpolation is p1(x1,y1,t1), p2(x2,y2,t2), wherein x1,y1Respectively indicate the flute using system centre as the center of circle
Point p under karr coordinate system1Abscissa and ordinate, t1For track points p1Timestamp, x2,y2It respectively indicates and is with system centre
Point p under the cartesian coordinate system in the center of circle2Abscissa and ordinate, t2For track points p2Timestamp, interpolation method is as follows:
p′i(xi,yi,ti)=(p2-p1)×i/n+1+p1, wherein n is interpolation number, and i is corresponding interpolation number, 1≤i
≤ n, p 'iIndicate new insertion point, xi,yiPoint p ' under respectively indicating using system centre as the cartesian coordinate system in the center of circleiAbscissa
And ordinate, tiFor track points p 'iTimestamp.
Step 2 includes:
Each radar track regards a series of point set as, and the point set for setting two radar tracks is respectively point set A
With point set B, A={ a1,a2,…,ap, B={ b1,b2,…,bm, aiIt is i-th point in point set A, i value is 1~p, bjFor point
Collect in B at j-th point, j value is 1~m, and improved Hausdorff distance h (A, B), h (B, A) calculation is as follows:
Wherein | | ai-bj| | it is ai,bjThe Euclidean distance of point-to-point transmission, | | bi-aj| | it is bi,ajThe Euclidean distance of point-to-point transmission；
Consider that time factor, the Euclidean distance redefined between two o'clock are as follows:
WhereinAnd taCorresponding points aiTime, tbCorresponding points bjTime, Δ T be setting error
Time value sets radar track report cycle as T, and Δ T need to meet Δ T < T/2.
Step 3 includes:
Step 3-1, initial situation thinks that each radar track is first layer of the classification as clustering tree, with initial shape
State is starting point, forms similar matrix according to the similarity distance two-by-two that step 2 calculates all categories；
Step 3-2 finds the minimum value in similarity distance matrix, and corresponding track classification is gathered for one kind, is generated new
One layer, as next layer of clustering tree, record the minimum value and corresponding track classification of current distance matrix；
Step 3-3 recalculates similarity distance matrix according to the class state after merging, judges whether to reach end item
Part, if all tracks, which are greater than threshold value for a kind of or current minimum similarity distance, (can estimate that radar radial direction and angular error are made
At 2~3 times of worst error be used as threshold value), then terminate to cluster, not up to termination condition then return step 3-2.
In step 3-1, if each classification is the set of more than two radar tracks, introduce for including two or more
The definition of similarity distance between the classification of radar track:
If two target radar track set are respectively T { Track1,…,Trackn, T ' { Track '1,…,Track
′m, whereinRepresent the set that a radar track is a mark, TracknIndicate n-th of target radar boat in set T
Mark, Track 'mIndicate m-th of target radar track in set T ', Track={ P1,P2,...,Pn, whereinChange Hausdorff distance, defines the similarity H (T, T ') between two track set, as follows:
H (T, T ')=max (h (T, T '), h (T ', T))
Wherein h (T, T '), h (T ', T) respectively indicate track set T { Track1,…,TracknTo T ' { Track '1,…,
Track′mSimilarity and T ' { Track '1,…,Track′mTo T { Track1,…,TracknSimilarity, be defined as follows
It is shown:
H (T, T ')=max (h (Tracki,T′)),
H (T, T ') i.e. max (h (Tracki, T ')) it indicates in set T { Track1,…,TracknIn track and set
T′{Track′1,…,Track′mFarthest similarity,
Similar h (T ', T)=max (h (Track 'i,T)),
H (T ', T) i.e. max (h (Track 'i, T)) it indicates in set T ' { Track '1,…,Track′mIn track and collection
Close T { Track1,…,TracknFarthest similarity；
Single track is defined as follows the similarity between track set shown:
h(Tracki, T ') and=min (h (Tracki,Track′j)), wherein
h(Tracki, T ') i.e. and min (h (Tracki,Track′j)) indicate track TrackiWith set T ' { Track '1,…,
Track′mIn track nearest similarity, the similarity calculation between track is with reference to the improvement calculated between two point sets
Hausdorff distance；
In summary definition obtains:
H (T, T ')=max (min (h (Tracki,Track′j))), wherein
Current is defined in track set the closure with set domain, that is, meets following property (setting T1With T, T '
Similar is another track set):
H (T, T ')=H (T ', T)
H(T,T′)+H(T1,T′)≥H(T+T1,T′)
H(T+T1,T′)≥H(T,T′)。
Step 4 includes:
Step 4-1: Hierarchical clustering methods (bibliography: Day W H E, Edelsbrunner H.Efficient is utilized
algorithms for agglomerative hierarchical clustering methods[J].Journal of
Classification, 1984,1 (1): 7-24.) obtain every layer of clustering tree corresponding classification similarity distance, obtain one from
The small one-dimension array D [n] to longer spread, wherein n indicates the number of plies of clustering tree, and D [i] indicates i-th layer of corresponding similarity, at random
Choose i-th, j layer, two initial center point p1And p2, p1=D [i], p2=D [j]；
Step 4-2: for the numerical value in D [n] respectively with p1,p2Compare, forCalculate separately D [k] and p1
And p2Between difference, and compare size, and if p1Difference is small to be labeled as 1 for D [k], otherwise label is；
Step 4-3: for it is all label be or 2 point, recalculate p1,p2, pi=∑ D [j]/m, wherein D [j] be
Labeled as the parameter of i, m is the number that D [j] is labeled as i；
Step 4-4: step 4-2 and step 4-3 is repeated, until p1,p2Respectively less than given threshold value (can estimate radar radial direction
And caused by angular error 2~3 times of worst error as threshold value) to get arrive clustering tree cut-point, to obtain radar track
Between incidence relation.
Step 5 includes:
Step 5-1: the radar track incidence relation obtained according to step 4-4 calculates each radar by definition in step 3-1
Radar track and other associated radar tracks between similarity size with the radial direction and angle of each radar of comprehensive assessment
Error parameter calculates the different radar track similarities of same target, if radar error parameter be less than allowed band (can be with
The radial direction and angular error requirement of radar are previously set as needed) it does not calibrate then；
Step 5-2: according to the worst error range of radar, the first generation error parameter of each radar of random initializtion, i.e.,
Radial direction, the angular error of each radar of random initializtion；
Step 5-3: sorting to the radar error assessed in step 5-1, big (the i.e. radar track and same of first correction error
Similarity between other radar tracks of target is small) radar, using difference algorithm to error cross and variation generate a new generation
Error parameter (bibliography: Wang H, Liu T, Bu Q, et al.An algorithm based on hierarchical
clustering for multi-target tracking of multi-sensor data fusion[C]//Control
Conference (CCC), 2016 35th Chinese.IEEE, 2016:5106-5111.), it is repaired using error parameter of new generation
The just radar track calculates the similarity between new radar track and other associated radar tracks according to step 5-1, judgement
Whether current error parameter increases radar track similarity, and similarity increase then retains the error parameter, otherwise using original
The error parameter come；
Step 5-4: traversal radar list updates the error parameter of each radar, using new parameters revision radar track,
The current each radar error of assessment if it is less than allowed band or reaches maximum calibration number and then stops correcting, otherwise repeats
Step 5-3.
The utility model has the advantages that the present invention can be surveyed in the case where not increasing any hardware device according to the history of multiple radars
Amount data mutually correct the error parameter for obtaining each radar, improve the detection accuracy and air situation quality of radar.This technology is right
There are relatively broad application prospect, technology and conventional out-of-competition testing, satellite etc. in the existing air defence system upgrading of majority state
Radar calibration method is compared, and is greatly reduced cost of implementation, time cost, and effect is guaranteed, is improved me to a certain extent
The competitiveness in the international market of army, state trade product.
Detailed description of the invention
The present invention is done with reference to the accompanying drawings and detailed description and is further illustrated, it is of the invention above-mentioned or
Otherwise advantage will become apparent.
Fig. 1 is system construction drawing of the invention.
Fig. 2 is the effect picture of hierarchical cluster in the present invention.
Fig. 3 is radar error correction process flow diagram in the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
The present invention provides a kind of more radar error calibration methods based on historical data, comprising the following steps:
Step 1, radar track is pre-processed；
Step 2, it is based on improved Hausdorff distance definition radar track similarity；
Step 3, radar track is carried out by clustering processing based on hierarchical cluster, obtains the cluster of incidence relation between expression track
Tree；
Step 4, reasonable cluster segmentation point is found in clustering tree, obtains the incidence relation of radar track；
Step 5, based on the incidence relation of radar track, using differential evolution algorithm to multiple radar system error correction；
In step 1 of the present invention, radar track is pre-processed.Mainly radar track is filtered, interpolation processing, makes track
Point timestamp is consistent, is conducive to the realization for accelerating subsequent algorithm.The radar track general scan period is 8~12s, but due to one
Perhaps target position has situations such as interference radar track to have sometimes to lose a little or the larger situation of error goes out a little errors
It is existing, cause the location point of certain tracks obviously unavailable, needs to carry out interpolation drop to radar track data before subsequent processing
It the operation such as makes an uproar, interpolation method is mainly introduced here, because generally all including decrease of noise functions for distributed arrangement's radar.Interpolation is pressed
According to the time difference uniform interpolation of front and back two o'clock, between the point after meeting interpolation time interval between 8~12s, if the two of interpolation
Point is p1(x1,y1,t1), p2(x2,y2,t2), wherein x1,y1It respectively indicates using system centre as under the cartesian coordinate system in the center of circle
Point p1Abscissa and ordinate, t1For track points p1Timestamp, x2,y2Respectively indicate the Descartes using system centre as the center of circle
Point p under coordinate system2Abscissa and ordinate, t2For track points p2Timestamp, interpolation method is as follows:
p′i(xi,yi,ti)=(p2-p1)×i/n+1+p1, wherein n is interpolation number, and i is 1≤i of corresponding interpolation number
≤n,p′iIndicate new insertion point.
In step 2 of the present invention, it is based on improved Hausdorff distance definition radar track similarity.Track similarity is just
It is by the similarity degree quantization between two track lines, is the relevant basis of determining track and the correct premise of cluster result
Condition, track line are with position, height, the track point set of time.In Hausdorff distance metric space between proper subclass
Distance.If X and Y are two proper subclass of metric space M.So Hausdorff distance H (X, Y) is that the smallest several r make X
Close r neighborhood include Y, the r neighborhood that closes of Y also includes X.It is empty that this distance function enabled that all proper subclass of M form is integrated into measurement
Between, and it is denoted as F (M).The topology of F (M) is to depend on the topology of M.If M is non-empty, F (M) is also.
Hausdorff distance is to describe a kind of measurement of similarity degree between two groups of point sets, it is the spacing of two point sets
From a kind of form of Definition: assuming that there is two groups of point set A={ a1,a2,…,ap, B={ b1,b2,…,bp, then the two point sets
Between Hausdorff distance definition it is as follows:
H (A, B)=max (h (A, B), h (B, A)), wherein h (A, B), h (B, A) respectively indicate the similarity of set A to B
And the similarity of set B to A, it is defined as follows:
H (A, B)=max (min (| | ai-bj||)),ai∈A,bj∈B
H (B, A)=max (min (| | bi-aj||)),aj∈A,bi∈ B, wherein | | ai-bj| | it is ai(xi,yi),bj(xj,
yj) point-to-point transmission Euclidean distance, | | bi-aj| | it is aj(xj,yj),bi(xi,yi) point-to-point transmission Euclidean distance.
Each radar track can regard a series of point set as, can be navigated according to the definition of Hausdorff distance
Similarity distance between mark.Since there are random error situations, so there may be between large error and then influence track for a single point
The calculating of similarity, improved Hausdorff are as follows apart from calculation:
Wherein | | ai-bj| | it is ai(xi,yi),bj(xj,yj) point-to-point transmission Euclidean distance, | | bi-aj| | it is aj(xj,yj),bi
(xi,yi) point-to-point transmission Euclidean distance.
Influence of the random error to similarity can effectively be excluded for improved Hausdorff distance above, due to having
The similar only time difference of a little civil air routes, it is therefore necessary to consider time factor, the Euclidean distance for redefining point-to-point transmission is as follows
It is shown:
WhereinAnd taCorresponding points aiTime, tbCorresponding points bjTime, Δ T be setting error
Time value sets radar track report cycle as T, and Δ T need to meet Δ T < T/2.It can easily be calculated using above formula
Similarity distance between two tracks.
In step 3 of the present invention, the radar track clustering processing based on hierarchical cluster.Hierarchical clustering algorithm passes through foundation first
Dendrogram is classified, and each tree node has its subclass, and cluster can be clustered in the different levels of tree, is formed different
Collection of sets, hierachical decomposition is carried out to the set of data-oriented object, according to the decomposition strategy that hierarchicabstract decomposition uses, hierarchical clustering method
(agglomerative) of cohesion and (divisive) hierarchical cluster of division can be divided into again.
Agglomerate layered cluster, using bottom-up strategy, first using each object as a class, then according to phase
These classes are merged into biggish class like degree measurement, until all objects are all in a class, or meet some termination
Until when condition, detailed process is shown in Figure 2, wherein r≤n-1.Most hierarchical clustering algorithms belong to this kind, they
It is only different in the definition of class similarity.It is used herein be exactly agglomerate layered cluster, division hierarchical cluster then with it is upper
Method is stated on the contrary, being not described here in detail.
Steps are as follows for agglomerate layered clustering algorithm:
Step1: with original state (each radar track is a classification) for starting point, all categories are calculated according to step 2
Similarity distance two-by-two form similar matrix；
Step2: finding the minimum value in similarity distance matrix, and corresponding track classification is gathered for one kind, record currently away from
From the minimum value of matrix and corresponding track classification；
Step3: according to the class state after merging, similarity distance matrix is updated, judges whether to reach termination condition, owned
Track, which is greater than some threshold value for a kind of or current minimum similarity distance, (can estimate maximum caused by radar radial direction and angular error
2~3 times of error are used as threshold value), not up to termination condition then returns to Step2, until terminating.
In hierarchical clustering algorithm, the similarity distance between initial calculation class can be according to method in step 2, because each
Class corresponds to a track, at this time will phase between definition set when class each in cluster process is the set of multiple tracks
Like degree, therefore Hausdorff distance needs to further expand；Secondly, under intensive target environment, if targetpath shape is similar
It throws the reins in the manner described above, it is difficult to clustering target.In order to adapt to hierarchical clustering algorithm and solve intensive target area
Clustering problem, need to introduce for the definition comprising similarity between more than two radar track set:
If two target radar track set are respectively T { Track1,…,Trackn, T ' { Track '1,…,Track
′m, whereinRepresent the set that a radar track is a mark, Track={ P1,P2,...,Pn, whereinChange Hausdorff distance, defines the similarity H (T, T ') between two track set, as follows:
H (T, T ')=max (h (T, T '), h (T ', T))
Wherein h (T, T '), h (T ', T) respectively indicate track set T { Track1,…,TracknTo T ' { Track '1,…,
Track′mSimilarity and T ' { Track '1,…,Track′mTo T { Track1,…,TracknSimilarity, be defined as follows
It is shown:
H (T, T ')=max (h (Tracki,T′)),I.e. in set T { Track1,…,TracknIn
Track and set T ' { Track '1,…,Track′mFarthest similarity,
Similar h (T ', T)=max (h (Track 'i,T)),It indicates in set T ' { Track '1,…,
Track′mIn track and set T { Track1,…,TracknFarthest similarity；
Single track is defined as follows the similarity between track set shown:
h(Tracki, T ') and=min (h (Tracki,Track′j)), whereinThat is track TrackiWith collection
Close T ' { Track '1,…,Track′mIn track nearest similarity, the similarity calculation between track calculates two with reference to the 3rd article
Improvement Hausdorff distance between a point set；
In summary it defines available:
H (T, T ')=max (min (h (Tracki,Track′j))), wherein
Current is defined in track set the closure with set domain, that is, meets following property (assuming that T1With T, T '
Similar is another track set):
H (T, T ')=H (T ', T)
H(T,T′)+H(T1,T′)≥H(T+T1,T′)
H(T+T1,T′)≥H(T,T′)
For heavy dense targets region, if two its track tracks of target are inherently similar and occur simultaneously, situation in this
Great difficulty can be brought to cluster.In general, heavy dense targets region is also the key area of radar scanning, this guarantees,
Multiple targets in this region generally can all be arrived by radar detection.The same radar is swept retouched in same time period it is a plurality of
Targetpath can be assumed that it as different targets, that is, assume that the same target will not be generated two radar boats by the same radar
Mark.
In step 4 of the present invention, reasonable cluster segmentation point is found in clustering tree.It is every layer available using hierarchical cluster
Cluster result and every layer in gather for a kind of corresponding similarity.Because cluster is by two most like track collection every time
Conjunction gathers for one kind, and the Hausdorff similarity extended in step before can guarantee monotonic nondecreasing in integration set domain,
Therefore every layer of corresponding cluster Hausdorff distance is incremental in entire clustering tree.It obtains clustering tree to do later being exactly to look for
To suitable cut-point, as one two classification problems in the one-dimensional space, segmentation clustering tree obtains cluster result.
Divide clustering tree using most basic K-means clustering method herein, wherein K is determined as 2, and algorithm steps are as follows:
Step1: Hierarchical clustering methods (bibliography: Day W H E, Edelsbrunner H.Efficient is utilized
algorithms for agglomerative hierarchical clustering methods[J].Journal of
Classification, 1984,1 (1): 7-24.) every layer of corresponding classification similarity is obtained, it obtains one and arranges from small to large
One-dimension array D [n], wherein n indicate clustering tree the number of plies, D [i] indicate i-th layer of corresponding similarity, randomly select i, j two
A initial center point p1And p2, p1=D [i], p2=D [j]；
Step2: for the numerical value in D [n] respectively with p1,p2Compare, forWith p1Or p2Difference is smaller,
D [i] is then labeled as 1 or 2；
Step3: for it is all label be or 2 point, recalculate p1,p2, pi=∑ D [j]/m, wherein D [j] is mark
It is denoted as the parameter of i, m is the number that D [j] is labeled as i；
Step4: Step2 and Step3 is repeated, until p1,p2Respectively less than given threshold value (can estimate radar radial direction and angle
Caused by error 2~3 times of worst error as threshold value) to get the cut-point for arriving clustering tree, between available radar track
Incidence relation.
In order to improve the accuracy of classification, following improvement has been done on the basis of K-means algorithm: 1) for being clearly not same
The radar track of one target calculate its Hausdorff apart from when be set to a fixed biggish numerical value, in this way poly-
It can be easy to gather when class and there is no the track of overlapping time region or the discovery of same radar with identical for one kind, such as track
Time zone etc.；2) a confidence rate is set, that is, after K-means algorithm obtains the cut-off rule of two classifications, effectively
Control cut-off rule will improve the accuracy of classification, otherwise this cut-off rule will adjust that there are may go out when large error in radar
Now cluster deviation.
In step 5 of the present invention, using differential evolution algorithm to multiple radar system error correction.Pass through random initializtion radial direction
And angular error, every generation carry out differential evolution, preferentially choose the error parameter of each radar, until meet the required accuracy or
Until iterating to maximum algebra.Steps are as follows for differential evolution algorithm:
Step1: the radar track incidence relation obtained according to step 4 is calculated the thunder of each radar by definition in step 2/3
Up to the similarity size between track and other associated radar tracks with the radial direction and angular error of each radar of comprehensive assessment
Parameter calculates the different radar track similarities of same target, if radar error parameter (can basis less than allowed band
Need to be previously set the radial direction and angular error requirement of radar) it does not calibrate then；
Step2: according to the worst error range of radar, radial direction, the angular error (first generation of each radar of random initializtion
Error parameter)；
Step3: sorting to the radar error assessed in Step1, first correction error big (the i.e. radar track and same target
Other radar tracks between similarity it is small) radar, error of new generation is generated to error cross and variation using difference algorithm
Parameter (bibliography: Wang H, Liu T, Bu Q, et al.An algorithm based on hierarchical
clustering for multi-target tracking of multi-sensor data fusion[C]//Control
Conference (CCC), 2016 35th Chinese.IEEE, 2016:5106-5111.), it is repaired using error parameter of new generation
The just radar track, the similarity between new radar track and other associated radar tracks is calculated according to 5-1, and judgement is current
Error parameter increase radar track similarity, similarity increase then retains the error parameter, otherwise using original
Error parameter；
Step4: traversal radar list updates the error parameter of each radar, using new parameters revision radar track, comments
Estimate current each radar error, if it is less than allowed band or reaches maximum calibration number and then stop correcting, otherwise repeat
Step3。
Embodiment
In majority state air defense system, different radars will appear either large or small systematic error, for it is existing it is static,
Dynamic radar error calibration method is there are the problems such as at high cost, realization is difficult, precision is not high, and the invention proposes a kind of historical datas
More radar calibration methods, the detection accuracy of each radar can be effectively improved in the case where not increasing new hardware configuration, improve
Air situation quality.
Process flow of the invention is as shown in Figures 1 to 3, mainly comprises the steps that
1, radar track is pre-processed；
Pretreatment is filtered (bibliography: Kalman R E.A new approach to linear to radar track
filtering and prediction problems[J].Journal of basic Engineering,1960,82(1):
35-45.), interpolation processing keeps track points timestamp consistent, is conducive to the realization for accelerating subsequent algorithm.Due to some errors or
There is situations such as interference in target position, and radar track has sometimes to be lost a little or the larger situation of error occurs, and causes certain
The location point of track is obviously unavailable, it is therefore desirable to interpolation processing is done, according to time uniform interpolation.
2, it is based on improved Hausdorff distance definition radar track similarity；
Hausdorff distance is a kind of method for defining incidence relation between different point sets, extends definition based on this
New Hausdorff with measure with having time, location information radar track (track point set) between similarity, and define
Similarity between radar track set, this is the basis reason of the premise for calculating radar track clustering relationships and this patent
By.
3, the radar track clustering processing based on hierarchical cluster；
Hierarchical clustering algorithm is a kind of Clustering, is a target as initiation layer using each radar track, every layer choosing takes
Most like track set is merged into one kind, and records the similarity value currently merged.All tracks are finally merged into one kind
Or reaches threshold value (according to the radial error 10km of radar in embodiment, angular error -5~5 degree are radar angular error model
Enclose, radar track of 2 times more than this value range is considered different target), finally obtain complete hierarchical cluster tree.
4, reasonable cluster segmentation point is found in clustering tree；
With gathering in available every layer of hierarchical cluster of cluster result and every layer for a kind of corresponding similarity.Because
Cluster is to gather two most like track set for one kind every time, and the Hausdorff similarity extended in step before exists
It can guarantee monotonic nondecreasing in integration set domain, therefore every layer of corresponding cluster Hausdorff distance is in entire clustering tree
Incremental.It is divided into suitable cut-point, as one two classification problems in the one-dimensional space are real using K-means algorithm
The now classification.
5, using differential evolution algorithm to multiple radar system error correction；
Differential evolution algorithm is a kind of Stochastic Optimization Algorithms.Since multiple radars mutually correct, each radar is firstly evaluated
Error be ranked up, the big radar of first correction error；Secondly, initializing the error parameter of each radar, missed as the first generation
Poor parameter, thus parameter sets obtain new error parameter, relatively front and back parameter by cross and variation, on the basis of competitive selection to be used as radar
Second generation error parameter；Again, each radar track is corrected using new error parameter, assesses the new error parameter of each radar simultaneously
Sequence prepares correction third generation error parameter；Finally, if radar error meets threshold value (if radar radially misses in embodiment
Difference is less than 0.5km and angular error range at -0.5~0.5 degree, then it is assumed that calibration finishes) or evolution reach maximum times,
Stop error correction.Detailed process, as shown in Figure 3.
The present invention provides a kind of more radar error calibration methods based on historical data, implement the technical solution
There are many method and approach, the above is only a preferred embodiment of the present invention, it is noted that for the common of the art
For technical staff, various improvements and modifications may be made without departing from the principle of the present invention, these are improved and profit
Decorations also should be regarded as protection scope of the present invention.The available prior art of each component part being not known in the present embodiment is subject to reality
It is existing.
Claims (7)
1. a kind of more radar error calibration methods based on historical data, which comprises the following steps:
Step 1, radar track is pre-processed；
Step 2, it is based on improved Hausdorff distance definition radar track similarity；
Step 3, radar track is carried out by clustering processing based on hierarchical cluster, obtains the clustering tree of incidence relation between expression track；
Step 4, reasonable cluster segmentation point is found in clustering tree, obtains the incidence relation of radar track；
Step 5, based on the incidence relation of radar track, using differential evolution algorithm to multiple radar system error correction.
2. the method according to claim 1, wherein step 1 includes: to be filtered to radar track, at interpolation
Reason, the interpolation processing includes: time difference uniform interpolation of the interpolation according to front and back two o'clock, if the two o'clock of interpolation is p1(x1,y1,
t1), p2(x2,y2,t2), wherein x1,y1Point p under respectively indicating using system centre as the cartesian coordinate system in the center of circle1Abscissa and
Ordinate, t1For track points p1Timestamp, x2,y2Point p under respectively indicating using system centre as the cartesian coordinate system in the center of circle2's
Abscissa and ordinate, t2For track points p2Timestamp, interpolation method is as follows:
p′i(xi,yi,ti)=(p2-p1)×i/n+1+p1, wherein n is interpolation number, and i is that corresponding interpolation is numbered, 1≤i≤n,
p′iIndicate new insertion point, xi,yiPoint p ' under respectively indicating using system centre as the cartesian coordinate system in the center of circleiAbscissa and vertical
Coordinate, tiFor track points p 'iTimestamp.
3. according to the method described in claim 2, it is characterized in that, step 2 includes:
Each radar track regards a series of point set as, and the point set for setting two radar tracks is respectively point set A and point
Collect B, A={ a1,a2,…,ap, B={ b1,b2,…,bm, aiIt is i-th point in point set A, i value is 1~p, bjFor in point set B
J-th point, j value is 1~m, and improved Hausdorff distance h (A, B), h (B, A) calculation is as follows:
Wherein | | ai-bj| | it is ai,bjThe Euclidean distance of point-to-point transmission, | | bi-aj| | it is bi,ajThe Euclidean distance of point-to-point transmission；
Consider time factor, the Euclidean distance for redefining point-to-point transmission is as follows:
WhereinAnd taCorresponding points aiTime, tbCorresponding points bjTime, Δ T be setting error time
Value, sets radar track report cycle as T, Δ T need to meet Δ T < T/2.
4. according to the method described in claim 3, it is characterized in that, step 3 includes:
Step 3-1 when each radar track is a classification, using original state as starting point, calculates all categories according to step 2
Similarity distance forms similar matrix two-by-two；
Step 3-2 finds the minimum value in similarity distance matrix, and corresponding track classification is gathered for one kind, record current distance
The minimum value of matrix and corresponding track classification；
Step 3-3 updates similarity distance matrix, judges whether to reach termination condition, if institute according to the class state after merging
Having track is that a kind of or current minimum similarity distance is greater than threshold value, then terminates to cluster, not up to termination condition then return step
3-2。
5. according to the method described in claim 4, it is characterized in that, in step 3-1, if each classification is more than two radars
The set of track is then introduced for the definition comprising similarity between more than two radar track set:
If two target radar track set are respectively T { Track1,…,Trackn, T ' { Track '1,…,Track′m, whereinRepresent the set that a radar track is a mark, TracknIndicate n-th of target radar track in set T, Track 'm
Indicate m-th of target radar track in set T ', Track={ P1,P2,...,Pn, whereinChange
Hausdorff distance defines the similarity H (T, T ') between two track set, as follows:
H (T, T ')=max (h (T, T '), h (T ', T))
Wherein h (T, T '), h (T ', T) respectively indicate track set T { Track1,…,TracknTo T ' { Track '1,…,
Track′mSimilarity and T ' { Track '1,…,Track′mTo T { Track1,…,TracknSimilarity, be defined as follows
It is shown:
H (T, T ') i.e. max (h (Tracki, T ')) it indicates in set T { Track1,…,TracknIn track and set T '
{Track′1,…,Track′mFarthest similarity,
H (T ', T) i.e. max (h (Track 'i, T)) it indicates in set T ' { Track '1,…,Track′mIn track and set T
{Track1,…,TracknFarthest similarity；
Single track is defined as follows the similarity between track set shown:
h(Tracki, T ') and=min (h (Tracki,Track′j)), wherein
h(Tracki, T ') i.e. and min (h (Tracki,Track′j)) indicate track TrackiWith set T ' { Track '1,…,
Track′mIn track nearest similarity；
In summary definition obtains:
H (T, T ')=max (min (h (Tracki,Track′j))), wherein
Current is defined in track set the closure with set domain, that is, meets following property:
H (T, T ')=H (T ', T)
H(T,T′)+H(T1,T′)≥H(T+T1,T′)
H(T+T1, T ') and >=H (T, T '),
Set T1For another track set.
6. according to the method described in claim 5, it is characterized in that, step 4 includes:
Step 4-1: every layer of clustering tree corresponding classification similarity is obtained using Hierarchical clustering methods, one is obtained and arranges from small to large
The one-dimension array D [n] of column, wherein n indicates the number of plies of clustering tree, and D [i] indicates i-th layer of corresponding similarity, randomly selects i-th,
Two initial center point p of j layer1And p2, p1=D [i], p2=D [j]；
Step 4-2: for the numerical value in D [n] respectively with p1,p2Compare, forCalculate separately D [k] and p1And p2It
Between difference, and compare size, and if p1Difference is small to be labeled as 1 for D [k], otherwise label is；
Step 4-3: for it is all label be or 2 point, recalculate p1,p2, pi=∑ D [j]/m, wherein D [j] is label
For the parameter of i, m is the number that D [j] is labeled as i；
Step 4-4: step 4-2 and step 4-3 is repeated, until p1,p2Respectively less than given threshold value is to get the segmentation for arriving clustering tree
Point, to obtain the incidence relation between radar track.
7. according to the method described in claim 6, it is characterized in that, step 5 includes:
Step 5-1: the radar track incidence relation obtained according to step 4-4 is calculated the thunder of each radar by definition in step 3-1
Up to the similarity size between track and other associated radar tracks with the radial direction and angular error of each radar of comprehensive assessment
Parameter calculates the different radar track similarities of same target, do not calibrate if radar error parameter is less than allowed band；
Step 5-2: according to the worst error range of radar, the first generation error parameter of each radar of random initializtion, i.e., at random
Initialize radial direction, the angular error of each radar；
Step 5-3: sorting to the radar error assessed in step 5-1, and the big radar of first correction error utilizes difference algorithm pair
Error cross and variation generates error parameter of new generation, corrects the radar track using error parameter of new generation, counts according to step 5-1
Similarity between new radar track and other associated radar tracks, judges whether current error parameter makes radar navigate
Mark similarity increases, and similarity increase then retains the error parameter, otherwise uses original error parameter；
Step 5-4: traversal radar list updates the error parameter of each radar, utilizes new parameters revision radar track, assessment
Current each radar error if it is less than allowed band or reaches maximum calibration number and then stops correcting, otherwise repeatedly step
5-3。
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