CN113532422B - Multi-sensor track fusion method based on distance map and data cleaning - Google Patents

Multi-sensor track fusion method based on distance map and data cleaning Download PDF

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CN113532422B
CN113532422B CN202110784798.3A CN202110784798A CN113532422B CN 113532422 B CN113532422 B CN 113532422B CN 202110784798 A CN202110784798 A CN 202110784798A CN 113532422 B CN113532422 B CN 113532422B
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CN113532422A (en
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徐丽
贾我欢
申林山
钱婧捷
李悦齐
闫鑫
张旭
张舜祁
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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Abstract

A multi-sensor track fusion method based on distance map and data cleaning belongs to the technical field of multi-sensor information fusion. The invention aims to solve the problem that the calculated amount and the fusion precision are unbalanced in the conventional multi-sensor track fusion method. The invention takes the distance of the sampling points as the basis for judging whether the two tracks are related at the moment, constructs the distance graph on the basis, and completes track association by pruning the distance graph, thereby better showing the association relationship between the tracks and obtaining higher association precision with smaller time cost. And the data of the associated track is cleaned by using the Grabbs criterion, outliers in the sensor track are removed, higher fusion precision is achieved by using less fusion time, and technical support is provided for the problem of multi-sensor track fusion. The invention can be applied to the fusion of multi-sensor tracks.

Description

Multi-sensor track fusion method based on distance map and data cleaning
Technical Field
The invention belongs to the technical field of multi-sensor information fusion, and particularly relates to a multi-sensor track fusion method based on a distance map and data cleaning.
Background
In recent years, with the rapid development of information science and sensor technology, how to integrate the measurements obtained by multiple sensors to improve the accuracy and efficiency of a track fusion system has become a challenging topic. The flight path fusion problem takes the fusion of flight path correlation and flight path state estimation as a technical core, and the fusion of the flight path correlation and the flight path state estimation forms a basic process of the flight path fusion.
The key to solve the problem of track association is the selection of an association policy and the establishment of an association criterion. The track association algorithm can be generally divided into two categories according to the method used by the algorithm: a statistical-based track correlation method and a fuzzy mathematics-based track correlation method. The track association problem is converted into a hypothesis test problem by a statistic-based track association method, the track state estimation of the sensor nodes is assumed to obey specific statistical distribution, the track state estimation difference between the sensor nodes is used as test statistic, a statistical hypothesis is established, and whether the tracks are associated or not is judged according to a predetermined threshold value. The statistical-based track association method is simple in concept and easy to implement, but it needs to be assumed that the sensor data obeys a typical distribution rule, and the distribution rule of the sensor data is often unknown in practical application.
The track association has a certain ambiguity, and the ambiguity can be represented by using a membership function of fuzzy mathematics, namely, the degree of similarity of two tracks is described by using membership. The track association method based on fuzzy mathematics selects or designs an associated membership function to calculate the membership degree of the track from the same target so as to judge whether the two tracks are associated or not. The track correlation method based on fuzzy mathematics is suitable for the environment with dense targets and large system errors, and is widely applied to actual engineering. However, such methods generally have high algorithm complexity, so that the fusion system is heavy in burden, and membership functions need to be given subjectively. Because the complexity of the track correlation method based on fuzzy mathematics is high, it is difficult to obtain high correlation precision with small time cost.
The track state estimation fusion takes the target state estimation of each local sensor as a processing object, and the target state estimation of the sensors is subjected to fusion processing by a certain track state estimation fusion method, so that the system track is obtained. The most representative track state estimation Fusion methods are Measurement Fusion (MF), elementary Fusion (SF), and Weighted Covariance Fusion (WCF). The measurement fusion method has simple idea, small calculated amount and lower precision, and is suitable for simple estimation. The greatest advantage of the first-class fusion method is high speed, but it assumes that the sensor tracks are uncorrelated, and the sensor tracks are actually correlated due to the common process noise, so the SF method gets a non-optimal solution. The weighted covariance fusion method considers the correlation of local tracks, so the accuracy is higher, but the calculation amount is larger. Researches find that most track state estimation fusion methods have imbalance between calculated amount and fusion precision, namely the high-precision fusion method usually consumes higher calculation resources, and the system track obtained by the fusion method with small calculated amount is usually lower in precision.
Disclosure of Invention
The invention aims to solve the problem that the calculated amount and the fusion precision are unbalanced in the conventional multi-sensor track fusion method, and provides a multi-sensor track fusion method based on a distance map and data cleaning.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a multi-sensor track fusion method based on distance map and data cleaning specifically comprises the following steps:
step 1, utilizing M sensors to jointly observe T0For any two sensors, the two sensors are a sensor s and a sensor l, and at the moment k, the sensor s observes T0The strip track is respectively recorded as
Figure BDA0003158296000000021
Sensor l observes T0The strip track is respectively recorded as
Figure BDA0003158296000000022
Wherein the content of the first and second substances,
Figure BDA0003158296000000023
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor s at the time k0The position of the strip of flight path,
Figure BDA0003158296000000024
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor l at the time k0Strip flight path;
constructing a distance graph of the sensor s and the sensor l at the moment k according to the state vector of the flight path;
step 2, respectively constructing distance graphs of the sensor s and the sensor l at the moments of k +1, k +2, … and k + N < -1 > by adopting the method in the step 1;
performing track association on the sensor s and the sensor l based on the constructed N distance maps;
step 3, repeating the processes of the step 1 and the step 2, and respectively carrying out track association on each two sensors to obtain a track corresponding to each target in the observation data of each sensor;
step 4, data cleaning
Removing outliers in the flight path corresponding to each target respectively to obtain an effective flight path of each target;
and 5, respectively carrying out state estimation fusion on each target according to the obtained effective track to obtain a track fusion result of each target.
The invention has the beneficial effects that: the invention provides a multi-sensor track fusion method based on a distance map and data cleaning, which takes the distance of sampling points as a basis for judging whether two tracks are associated at the moment, constructs the distance map on the basis, and completes track association by pruning the distance map, thereby better showing the association relationship between the tracks and obtaining higher association precision with less time cost. Data cleaning is carried out on the associated track by using the Grubbs (Gzobos) rule, outliers in the sensor track are eliminated, and high fusion precision is achieved with short fusion time, so that the contradiction between the track fusion precision and the calculated amount is balanced, and technical support is provided for the multi-sensor track fusion problem.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a multi-radar detection platform;
in the figure, Multiplatform radio scene represents a multi-Platform Radar scene, Ground represents the Ground, Platform represents a Platform, detectors represents a sensor, and Targets represents a target;
FIG. 3 is a top view of a multi-radar detection system;
FIG. 4 is a comparison of correct correlation rates for different methods;
FIG. 5 is a graph comparing error correlation rates for different methods.
Detailed Description
First embodiment this embodiment will be described with reference to fig. 1. The multi-sensor track fusion method based on distance map and data cleaning in the embodiment specifically comprises the following steps:
step 1, utilizing M sensors to jointly observe T0For any two sensors, the two sensors are a sensor s and a sensor l, and at the moment k, the sensor s observes T0The strip track is respectively recorded as
Figure BDA0003158296000000031
Sensor l observes T0Strip track, respectively marked
Figure BDA0003158296000000032
Wherein the content of the first and second substances,
Figure BDA0003158296000000033
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor s at the time k0The position of the strip of flight path,
Figure BDA0003158296000000034
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor l at the time k0Strip flight path;
constructing a distance graph of the sensor s and the sensor l at the moment k according to the state vector of the flight path;
step 2, respectively constructing distance graphs of the sensor s and the sensor l at the moments of k +1, k +2, … and k + N < -1 > by adopting the method in the step 1;
performing track association on the sensor s and the sensor l based on the constructed N distance maps;
step 3, repeating the processes of the step 1 and the step 2, and respectively carrying out track association on each two sensors to obtain a track corresponding to each target in the observation data of each sensor;
step 4, data cleaning
Removing outliers in the flight path corresponding to each target respectively to obtain an effective flight path of each target;
and 5, respectively carrying out state estimation fusion on each target according to the obtained effective track to obtain a track fusion result of each target.
The target motion model is:
x(k+1)＝F(k)x(k)+G(k)u(k)+v(k)
wherein x (k) is a state vector at the time k, x (k +1) is a state vector at the time k +1, F (k) is a state transition matrix, G (k) is an input control matrix, u (k) is an acceleration input matrix, and v (k) is a discrete time white noise sequence;
the measurement equation for sensor i is:
Zi(k)＝H(k)x(k)+wi(k)
wherein Z isi(k) Measured values of sensor i at time k, H (k) is an observation matrix, wi(k) Is zero mean and variance Ri(k) The gaussian of (1) observes noise.
The discrete-time white noise sequence v (k) satisfies: e (v (k)) is 0 and E (v (k))T) Q (k), E (v (k)) represents the mean of v (k), T represents the transpose, and q (k) is a gaussian process noise positive covariance matrix with zero mean.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that, in step 1, a distance map of the sensor s and the sensor l is constructed according to the state vector of the flight path, and the specific process is as follows:
step 1.1, the state vector of the ith flight path of the sensor s at the moment k is as follows: x is the number ofs,i(k)＝[rs,i1(k),rs,i2(k),...,rs,in(k)]T，i＝1,2,…,T0，rs,i1(k),rs,i2(k),...,rs,in(k) Respectively representing the 1 st position characteristic, the 2 nd position characteristic, … and the nth position characteristic of the ith track of the sensor s at the k moment, wherein n represents the number of the characteristics; the state vector of the jth track of sensor l at time k is: x is the number ofl,j(k)＝[rl,j1(k),rl,j2(k),...,rl,jn(k)]T，j＝1,2,…,T0，rl,j1(k),rl,j2(k),...,rl,jn(k) Respectively representing the 1 st position characteristic, the 2 nd position characteristic, … th position characteristic and the nth position characteristic of the jth track of the sensor l at the k moment; the distance d (x) between track i and track j at time ks,i(k),xl,j(k) ) is:
Figure BDA0003158296000000041
wherein T represents transpose;
step 1.2, construct a T0×T0And the element in the ith row and the jth column in the matrix satisfies:
Figure BDA0003158296000000042
wherein, d0In order to be the distance threshold value,
Figure BDA0003158296000000051
intermediate variable Δ ═ δ1,δ2,...,δn]T，δ1Is rs,i1(k) Resolution of δ2Is rs,i2(k) Resolution of δnIs rs,in(k) The resolution of (a);
and constructing an initial distance graph of the sensor s and the sensor l at the moment k based on the constructed matrix, wherein each node in the initial distance graph represents a flight path, and if d (x)s,i(k),xl,j(k))＜d0Then on the section corresponding to track i and track jAdding an edge between the points, and the weight w of the edgeij(k) Is d (x)s,i(k),xl,j(k))；
Step 1.3, when nodes with the degree of existence greater than 1 exist in the initial distance graph of the sensor s and the sensor l at the moment k, pruning is carried out on the initial distance graph, and the principle of reserving the edge with the minimum weight is adopted during pruning, namely, reserving the weight w to minwij(k) And (4) pruning to obtain a final distance map.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the difference between the present embodiment and the first or second embodiment is that, in the step 2, track association is performed on the sensor s and the sensor l based on the constructed N distance maps; the specific process comprises the following steps:
step 2.1, in the distance graph of the sensor s and the sensor l at each moment, if an edge exists between a node i and a node j, the tracks corresponding to the node i and the node j are associated with each other;
step 2.2, calculating the correlation quality Q of the node i and the node jij：
Figure BDA0003158296000000052
Wherein: n' represents the times of correlation of track points corresponding to the nodes i and j in all the N distance graphs of the constructed sensor s and the sensor l;
if the quality of correlation QijIf the distance between the node i and the node j is larger than or equal to the threshold value Q, the tracks corresponding to the node i and the node j are track-related, otherwise, the tracks corresponding to the node i and the node j are not track-related.
In the present embodiment, the tracks observed by the sensors s and l may be associated in a one-to-one correspondence.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment and one of the first to third embodiments is that the specific process of step 4 is:
let xi′,t(k) If the sensor i 'observes the state vector of the target t track at the time k, i' is 1,2, …, M, then the expectation of the associated tracks of the M sensors to the target t at the time k
Figure BDA0003158296000000053
Comprises the following steps:
Figure BDA0003158296000000061
xi′,t(k) the mean variance of (a) is:
Figure BDA0003158296000000062
x is to bei′,t(k) Arranged into order statistic x from small to large1'(k)≤x2'(k)≤…≤xM'(k)，x1'(k)，x2'(k)，…，xM'(k) The 1 st, 2 nd, … th, Mth state vector in the order statistics, and using xM'(k) Calculating the Grabbs coefficient GM'(k)：
Figure BDA0003158296000000063
If it is
Figure BDA0003158296000000064
X is theni′,t(k) Within the confidence limits, otherwise,
Figure BDA0003158296000000065
x is theni′,t(k) Removing the state vector of the suspicious track;
after the state vectors of the suspicious track are removed, the remaining track state vectors are recalculated until all the remaining track state vectors are within the confidence limit, and all effective track state vectors of the target t at the moment k are obtained;
and similarly, all the effective track state vectors of the target t at other moments and all the effective track state vectors of other targets at all the moments are obtained.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is that, in step 5, state estimation fusion is performed on each target according to the obtained effective flight path, and the specific process is as follows:
step 5.1, if all the effective track state vectors of the target t at the moment k comprise the state vectors of the two sensors for observing the track, executing step 5.2; otherwise, if all the effective track state vectors of the target t at the moment k comprise state vectors of the track observed by more than two sensors, executing the step 5.3;
step 5.2, global state estimation of target t at moment k
Figure BDA0003158296000000066
Comprises the following steps:
Figure BDA0003158296000000067
wherein x isi″,t(k) Is the state vector, x, of the target t track observed by the sensor i' at time kj″,t(k) Is that the state vector of the target t track is observed by the sensor j ' at the moment k, i ' and j ' are the sensors corresponding to all the effective track state vectors of the target t at the moment k, Pi″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance of sensor j "at time k;
global error covariance P of target t at time kDCTF(k) Comprises the following steps:
PDCTF(k)＝Pi″(k)[Pi″(k)+Pj″(k)]-1Pj″(k)
step 5.3, calculating the global state estimation of the target t at the moment k and the global error covariance of the target t at the moment k; the specific process is as follows:
step 5.3.1, recording the state vectors of the target t track observed by the sensor i 'at the moment k and the state vectors of the target t track observed by the sensor j' at the moment k as i 'and j' for any two sensors corresponding to the effective track state vector of the target t at the moment k;
Figure BDA0003158296000000071
wherein x isi″,t(k) Is the state vector, x, of the target t track observed by the sensor i' at time kj″,t(k) Is the state vector P of the target t track observed by the sensor j' at the moment ki″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance of sensor j "at time k,
Figure BDA0003158296000000072
is xi″,t(k) And xj″,t(k) The fusion result of (1);
step 5.3.2, mixing
Figure BDA0003158296000000073
Assigned to xi″,t(k) And for any other sensor (any sensor except i 'and j') corresponding to the effective track state vector of the target t at the moment k, assigning the state vector of the target t track observed by the sensor at the moment k to xj″,t(k)；
Step 5.3.3, after assignment, repeatedly executing the processes of step 5.3.1 and step 5.3.2 until state vectors of effective tracks observed by all sensors to the target t at the moment k are fused, and taking the final state vector fusion result as global state estimation of the target t at the moment k;
step 5.3.4, recording any two sensors corresponding to the effective track state vector of the target t at the moment k as i 'and j', and fusing the local error covariance of the sensor i 'at the moment k and the local error covariance of the sensor j' at the moment k;
PDCTF(k)＝Pi″(k)[Pi″(k)+Pj″(k)]-1Pj″(k)
wherein, Pi″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance, P ", of the sensor j" at time kDCTF(k) Is Pi″(k) And Pj″(k) The fusion result of (1);
step 5.3.5, adding PDCTF(k) Assign to Pi″(k) And for any other sensor (any sensor except i 'and j') corresponding to the effective track state vector of the target t at the moment k, assigning the local error covariance of the sensor at the moment k to Pj″(k)；
And 5.3.6, after assignment, repeatedly executing the processes of the step 5.3.4 and the step 5.3.5 until the local error covariance of all the sensors at the moment k is fused, and taking the final local error covariance fusion result as the global error covariance of the target t at the moment k.
And in the same way, respectively fusing all the effective track state vectors of the target t at other moments, and respectively fusing all the effective track state vectors of the other targets at all the moments. Particularly, if the effective track state vector of a certain target at a certain moment only comprises a track state vector observed by one sensor, the track state vector does not need to be fused, and the track estimation result of the target at the moment is directly obtained.
According to the method, the track fusion center carries out track association based on the distance map and state estimation fusion based on data cleaning on the local track fusion center to obtain the system track.
Fig. 2 shows a multi-platform Radar scene (Multiplatform radio scene). Set up 6 sensors in the many radar detection systems and survey, wherein 2 airborne platform, 4 ground platform set up ground platform in close position. Clearly distinguishable from the top view of fig. 3. Azimuth resolution, elevation resolution and range resolution of each radar platform are respectively set to 1 degree, 5 degrees and 30m, and corresponding radar azimuth deviation fraction, elevation deviation fraction and range deviation fraction are shown in table 1. The deviation score is expressed as the lower limit of the accuracy of the corresponding attribute, the measurement sampling interval is set to 1s, and the duration sampling time is 100 s. The object 1 performs curvilinear motion, and the object 2 performs uniform linear motion.
TABLE 1 Radar platform accuracy and bias score settings
Figure BDA0003158296000000081
FIG. 4 and FIG. 5 show the average correct correlation (P) of 200 simulations using the correlation sequential method (RS), the independent dual threshold method (IDT) and the distance map track correlation method (DG), respectivelyc) Curve and error correlation rate (P)e) Curve line.
Table 2 counts the average association time of performing track association simulation 200 times on each target by using a correlation sequential method, an independent double-threshold method and a distance chart track association method.
TABLE 2 correlation time comparison
Figure BDA0003158296000000091
From the experimental results, it can be seen that the correct correlation rate of the correlation sequential method is the lowest, and the speed is very low, so that the method is not suitable for processing the data of the laser triangulation distance measuring sensor; compared with the distance map track correlation method, the independent double thresholds have lower correct correlation rate and longer correlation time. Therefore, the distance chart track correlation method achieves higher correct correlation rate.
According to the method, the track fusion center performs track association based on the distance map and state estimation fusion based on data cleaning on the sensor track to obtain the system track with higher precision. Table 3 shows the mean error comparison between the fusion method based on Data Cleaning (DCTF) and the Measurement Fusion (MF), the elementary fusion (SF) and the Weighted Covariance Fusion (WCF) according to the present invention.
TABLE 3 average error comparison of DCTF with MF, SF, WCF
Figure BDA0003158296000000092
Table 4 counts the average calculation time for the track state estimation fusion of all targets using MF method, SF method, WCF method and the method of the present invention (DCTF).
TABLE 4 comparison of fusion times between DCTF and MF, SF, WCF methods
Figure BDA0003158296000000093
As can be seen from tables 3 and 4, the track state estimation fusion method of the present invention can obtain higher fusion accuracy with less fusion time. With slightly higher fusion time than the SF method, fusion accuracy close to that of the WCF method is obtained.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.

Claims (3)

1. A multi-sensor track fusion method based on distance map and data cleaning is characterized by specifically comprising the following steps:
step 1, utilizing M sensors to jointly observe T0For any two sensors, the two sensors are a sensor s and a sensor l, and at the moment k, the sensor s observes T0The strip track is respectively recorded as
Figure FDA0003627848480000011
Sensor l observes T0Strip track, respectively marked
Figure FDA0003627848480000012
Wherein the content of the first and second substances,
Figure FDA0003627848480000013
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor s at the time k0The position of the strip of the flight path,
Figure FDA0003627848480000014
respectively, the 1 st track, the 2 nd track, …, and the Tth track observed by the sensor l at the time k0Strip flight path;
constructing a distance graph of the sensor s and the sensor l at the moment k according to the state vector of the flight path; the specific process comprises the following steps:
step 1.1, the state vector of the ith track of the sensor s at the moment k is as follows: x is a radical of a fluorine atoms,i(k)＝[rs,i1(k),rs,i2(k),...,rs,in(k)]T，i＝1,2,…,T0，rs,i1(k),rs,i2(k),...,rs,in(k) Respectively representing the 1 st position characteristic, the 2 nd position characteristic, … and the nth position characteristic of the ith track of the sensor s at the k moment, wherein n represents the number of the characteristics; the state vector of the jth track of sensor l at time k is: x is the number ofl,j(k)＝[rl,j1(k),rl,j2(k),...,rl,jn(k)]T，j＝1,2,…,T0，rl,j1(k),rl,j2(k),...,rl,jn(k) Respectively representing the 1 st position characteristic, the 2 nd position characteristic, … th position characteristic and the nth position characteristic of the jth track of the sensor l at the k moment;
the distance d (x) between track i and track j at time ks,i(k),xl,j(k) ) is:
Figure FDA0003627848480000015
wherein T represents transpose;
step 1.2, construct a T0×T0And the element in the ith row and the jth column in the matrix satisfies:
Figure FDA0003627848480000016
wherein d is0In order to be the distance threshold value,
Figure FDA0003627848480000017
intermediate variable delta ═ delta1,δ2,...,δn]T，δ1Is rs,i1(k) Resolution of δ2Is rs,i2(k) Resolution of δnIs r ofs,in(k) The resolution of (a);
and constructing an initial distance graph of the sensor s and the sensor l at the moment k based on the constructed matrix, wherein each node in the initial distance graph represents a flight path, and if d (x)s,i(k),xl,j(k))＜d0Adding an edge between the nodes corresponding to the track i and the track j, and adding the weight w of the edgeij(k) Is d (x)s,i(k),xl,j(k))；
Step 1.3, when nodes with the degree of existence greater than 1 exist in the initial distance graph of the sensor s and the sensor l at the moment k, pruning is carried out on the initial distance graph, and the principle of reserving the edge with the minimum weight is adopted during pruning, namely, reserving the weight w to minwij(k) The final distance map is obtained after pruning;
step 2, respectively constructing distance graphs of the sensor s and the sensor l at the moments of k +1, k +2, … and k + N < -1 > by adopting the method in the step 1;
performing track association on the sensor s and the sensor l based on the constructed N distance maps;
step 3, repeating the processes of the step 1 and the step 2, and respectively carrying out track association on each two sensors to obtain a track corresponding to each target in the observation data of each sensor;
step 4, data cleaning
Removing outliers in the flight path corresponding to each target respectively to obtain an effective flight path of each target;
the specific process of the step 4 is as follows:
let xi′,t(k) If the sensor i 'observes the state vector of the target t track at the time k, i' is 1,2, …, M, then the expectation of the associated tracks of the M sensors to the target t at the time k
Figure FDA0003627848480000021
Comprises the following steps:
Figure FDA0003627848480000022
xi′,t(k) the mean variance of (a) is:
Figure FDA0003627848480000023
x is to bei′,t(k) Arranged into order statistic x from small to large1'(k)≤x2'(k)≤…≤xM'(k)，x1'(k)，x2'(k)，…，xM'(k) Respectively, the 1 st, 2 nd, … th and Mth state vectors in the order statistics, and using xM'(k) Calculating the Grabbs coefficient GM'(k)：
Figure FDA0003627848480000024
If it is
Figure FDA0003627848480000025
X is theni′,t(k) Within the confidence limits, otherwise,
Figure FDA0003627848480000026
x is theni′,t(k) Removing the state vector of the suspicious track;
after the state vectors of the suspicious track are removed, the remaining track state vectors are recalculated until all the remaining track state vectors are within the confidence limit, and all effective track state vectors of the target t at the moment k are obtained;
similarly, all effective track state vectors of the target t at other moments and all effective track state vectors of other targets at all moments are obtained;
and 5, respectively carrying out state estimation fusion on each target according to the obtained effective track to obtain a track fusion result of each target.
2. The multi-sensor track fusion method based on distance map and data cleaning according to claim 1, characterized in that in step 2, track association is performed on the sensor s and the sensor l based on the constructed N distance maps; the specific process comprises the following steps:
step 2.1, in the distance graph of the sensor s and the sensor l at each moment, if an edge exists between a node i and a node j, the tracks corresponding to the node i and the node j are associated with each other;
step 2.2, calculating the correlation quality Q of the node i and the node jij：
Figure FDA0003627848480000031
Wherein: n' represents the times of correlation of track points corresponding to the nodes i and j in all the N distance graphs of the constructed sensor s and the sensor l;
if the quality of correlation QijIf the number of the nodes is larger than or equal to the threshold value Q, the tracks corresponding to the nodes i and j are track-related, otherwise, the tracks corresponding to the nodes i and j are not track-related.
3. The multi-sensor track fusion method based on distance map and data cleaning as claimed in claim 2, wherein in step 5, the state estimation fusion is performed on each target according to the obtained effective track, and the specific process is as follows:
step 5.1, if all the effective track state vectors of the target t at the moment k comprise the state vectors of the two sensors for observing the track, executing step 5.2; otherwise, if all the effective track state vectors of the target t at the moment k comprise state vectors of the track observed by more than two sensors, executing the step 5.3;
step 5.2, global state estimation of target t at time k
Figure FDA0003627848480000032
Comprises the following steps:
Figure FDA0003627848480000033
wherein x isi″,t(k) Is the state vector, x, of the target t track observed by the sensor i' at time kj″,t(k) Is that the state vector of the target t track is observed by the sensor j ' at the moment k, i ' and j ' are the sensors corresponding to all the effective track state vectors of the target t at the moment k, Pi″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance of sensor j "at time k;
global error covariance P of target t at time kDCTF(k) Comprises the following steps:
PDCTF(k)＝Pi″(k)[Pi″(k)+Pj″(k)]-1Pj″(k)
step 5.3, calculating the global state estimation of the target t at the moment k and the global error covariance of the target t at the moment k; the specific process is as follows:
step 5.3.1, recording the state vectors of the target t track observed by the sensor i 'at the moment k and the state vectors of the target t track observed by the sensor j' at the moment k as i 'and j' for any two sensors corresponding to the effective track state vector of the target t at the moment k;
Figure FDA0003627848480000041
wherein x isi″,t(k) Is the state vector, x, of the target t track observed by the sensor i' at time kj″,t(k) Is the state vector P of the target t track observed by the sensor j' at the moment ki″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance of sensor j "at time k,
Figure FDA0003627848480000042
is xi″,t(k) And xj″,t(k) The fusion result of (1);
step 5.3.2, mixing
Figure FDA0003627848480000043
Is assigned to xi″,t(k) And for any other sensor corresponding to the effective track state vector of the target t at the moment k, assigning the state vector of the target t track observed by the sensor at the moment k to xj″,t(k)；
Step 5.3.3, after assignment, repeatedly executing the processes of step 5.3.1 and step 5.3.2 until state vectors of effective tracks observed by all sensors to the target t at the moment k are fused, and taking the final state vector fusion result as global state estimation of the target t at the moment k;
step 5.3.4, recording any two sensors corresponding to the effective track state vector of the target t at the moment k as i 'and j', and fusing the local error covariance of the sensor i 'at the moment k and the local error covariance of the sensor j' at the moment k;
PDCTF(k)＝Pi″(k)[Pi″(k)+Pj″(k)]-1Pj″(k)
wherein, Pi″(k) Is the local error covariance, P ", of the sensor i" at time kj″(k) Is the local error covariance, P ", of the sensor j" at time kDCTF(k) Is Pi″(k) And Pj″(k) The fusion result of (1);
step 5.3.5, adding PDCTF(k) Assign to Pi″(k) And for any other sensor corresponding to the effective track state vector of the target t at the moment k, assigning the local error covariance of the sensor at the moment k to Pj″(k)；
And 5.3.6, after assignment, repeatedly executing the processes of the step 5.3.4 and the step 5.3.5 until the local error covariance of all the sensors at the moment k is fused, and taking the final local error covariance fusion result as the global error covariance of the target t at the moment k.
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