CN112484728A - Based on OSPA(2)Multi-sensor multi-target track association and fusion method for distance - Google Patents

Based on OSPA(2)Multi-sensor multi-target track association and fusion method for distance Download PDF

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CN112484728A
CN112484728A CN202011179118.7A CN202011179118A CN112484728A CN 112484728 A CN112484728 A CN 112484728A CN 202011179118 A CN202011179118 A CN 202011179118A CN 112484728 A CN112484728 A CN 112484728A
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刘宇
刘伟峰
李建宁
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Hangzhou Dianzi University
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Abstract

The invention discloses a method based on OSPA(2)A distance multi-sensor multi-target track association and fusion method. The existing method lacks consideration of the characteristics of the whole flight path, and the correlation performance between the flight paths is reduced. Firstly, establishing a system model to obtain an estimated track set; then based on OSPA(2)Measuring the distance between each estimated track set by the distance to obtain the estimated track sets belonging to the same target; and finally, carrying out track fusion on the estimated track set belonging to the same target by adopting a federal filter fusion method. The method can accurately obtain the estimated track set belonging to the same target, and the obtained final track has RMSE position error lower than that of all single sensors, so that higher precision can be obtained.

Description

Based on OSPA(2)Multi-sensor multi-target track association and fusion method for distance
Technical Field
The invention belongs to the field of track association and fusion, and relates to a method based on OSPA(2)(OSPA on OSPA, optimal sub-mode distribution on optimal sub-mode distribution) distance-to-multi-sensor multi-target track association and fusion method.
Background
In reality, the situation that a plurality of sensors track a plurality of targets frequently occurs, so that the track of one target usually has a plurality of tracks. Meanwhile, due to the existence of the conditions of space alignment, time alignment, different target observation precision and the like, a plurality of groups of tracks of a plurality of sensors are obtained. In view of the above situation, how to accurately obtain estimated track sets belonging to the same target in a plurality of estimated track sets has become an important matter. Conventionally, the tracks are correlated according to the distance of the geometric distance between the tracks, so that a great number of tracks belonging to the same target are judged, and the correlation between the tracks is easy to reduce. It is necessary to find a new track association method by combining historical track point information as much as possible.
How to accurately correlate the track sets has become an important issue. In general, it is desirable to consider that the estimated track obtained is not lost, and that the track termination is not delayed. However, in practical situations, when tracking a target, a phenomenon that a flight path is lost at a certain time, recovered later and finally delayed due to a flight path termination may occur due to a certain complex situation. Where the track is lost, two possibilities may arise. The first condition is as follows: continuing to estimate the trajectory using the same identity as originally specified, the likelihood that the target still exists is preserved. If future observations confirm its presence, the track will appear with the same identity; case two: instead of using the same identity recovery trail, the target is assigned a new identity. If its presence is later confirmed, a new flight path is established with the new identity, resulting in failure to maintain a consistent estimate of the target identity.
Disclosure of Invention
The invention aims to provide a method for associating multiple sensors with multiple targets, which aims to solve the problem that the association performance between tracks is reduced due to the lack of consideration of the characteristics of the whole track and the problem that the association performance between the tracks is reduced due to the fact that the prior art only carries out association according to the information of track points at the current moment, and provides a method based on OSPA (open shortest Path first)(2)A distance-to-multi-sensor multi-target track association and fusion method.
The method comprises the following steps:
establishing a system model to obtain an estimated track set;
step (2) is based on OSPA(2)Measuring the distance between each estimated track set by the distance to obtain the estimated track sets belonging to the same target;
and (3) carrying out track fusion on the estimated track set belonging to the same target by adopting a federal filter fusion method.
Further, the step (1) is specifically: respectively obtaining estimated track sets of I sensors and J targets by adopting a track-oriented multi-hypothesis tracking algorithm; establishing a system model, wherein the mathematical description of a state equation, a deviation equation and a measurement equation is as follows:
Figure BDA0002749628050000021
wherein k is a time series, xkAnd xk+1State vectors at time k and at time k +1, Ak+1,kBeing a state transition matrix, bkAnd bk+1Input matrices for time k and k +1, Bk+1,kIs the coefficient matrix corresponding to the input matrix,
Figure BDA0002749628050000022
is the observation vector of the ith sensor at time k,
Figure BDA0002749628050000023
the matrix is observed for the state of the ith sensor at time k,
Figure BDA0002749628050000024
is the coefficient matrix of the ith sensor at time k, wk、
Figure BDA0002749628050000025
The system state noise vector, the system offset noise vector, and the measurement noise vector of the I-th sensor at time k, I being 1,2, …, I, respectively. The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are all zero mean Gaussian white noise sequences.
Further, the step (2) is specifically: respectively adopting OSPA according to the obtained estimated track sets of the I sensors and the J targets(2)Measuring the distance between each estimated track set by using the distance to obtain an estimated track set belonging to the same target;
estimated track of jth target obtained by ith sensor
Figure BDA0002749628050000026
Wherein the content of the first and second substances,
Figure BDA0002749628050000027
tracking an estimated state set of a jth target for an ith sensor at time k;
all target tracks obtained by the ith sensor
Figure BDA0002749628050000028
Wherein, JiThe number of target tracks obtained by the ith sensor, U is an aggregation symbol,
Figure BDA0002749628050000029
denotes from J to JiA set of elements of (c);
target track observed by all sensors
Figure BDA00027496280500000210
The target track association is a target track set corresponding to any two different sensors
Figure BDA00027496280500000211
And
Figure BDA00027496280500000212
the distance between the two electrodes is evaluated,
Figure BDA00027496280500000213
Figure BDA00027496280500000214
respectively represent the ith1Person to, i2The number of estimation targets corresponding to each sensor; the OSPA distance is expressed as the distance between two sets:
Figure BDA00027496280500000215
wherein p is the distance order, p is 1,2, c is the horizontal parameter, ΠnIs all permutations of the set {1,2, …, n }, n being
Figure BDA00027496280500000216
The number of the inner elements, pi (l) is the first arrangement, k1、k2Are respectively the ith1Person to, i2The time series corresponding to each of the sensors,
Figure BDA00027496280500000217
for a set of target tracks
Figure BDA00027496280500000218
And
Figure BDA00027496280500000219
the distance between them.
Further, the step (3) is specifically: firstly, information distribution is carried out between each sub-filter and the main filter:
Figure BDA0002749628050000031
in the formula, QkIn order for the process to excite the noise covariance,
Figure BDA0002749628050000032
for the a posteriori estimated covariance matrix of each sub-filter and the main filter at time k,
Figure BDA0002749628050000033
is its covariance matrix, M is the number of sub-filters, MzRepresents a main filter; beta is amAnd if the sub-filter information distribution coefficient is more than 0, distributing coefficients for the sub-filter information, and meeting the information distribution principle:
Figure BDA0002749628050000034
Figure BDA0002749628050000035
distributing coefficients for the main filter information;
Figure BDA0002749628050000036
for the a posteriori state estimates of the sub-filters and the main filter at time k,
Figure BDA0002749628050000037
is a global estimated value;
time updates are made independently between each sub-filter and the main filter:
Figure BDA0002749628050000038
Figure BDA0002749628050000039
in the formula (I), the compound is shown in the specification,
Figure BDA00027496280500000310
for the a priori state estimates of each sub-filter and main filter at time k,
Figure BDA00027496280500000311
for a priori estimation of the covariance, Φ, of each sub-filter and the main filter at time kkBeing a state transition matrix, ΓkT represents transposition for a process noise distribution matrix;
measurement updates are performed in each sub-filter:
Figure BDA00027496280500000312
in the formula (I), the compound is shown in the specification,
Figure BDA00027496280500000313
for the a posteriori estimated covariance of each sub-filter and the main filter at time k +1,
Figure BDA00027496280500000314
the a posteriori state estimates for each sub-filter and main filter at time k +1, H is the state variable to observation transformation matrix, R is the measurement noise covariance,
Figure BDA00027496280500000315
is the measured value of each sub-filter at time k + 1;
and fusing the local estimation information of each sub-filter according to the following formula to obtain the global optimal estimation:
Figure BDA00027496280500000316
Figure BDA00027496280500000317
in the formula (I), the compound is shown in the specification,
Figure BDA00027496280500000318
for a globally optimal a posteriori state estimate at time k +1,
Figure BDA00027496280500000319
the covariance is estimated for the global optimum a posteriori at time k +1,
Figure BDA00027496280500000320
the a priori state estimate of the main filter at time k +1,
Figure BDA00027496280500000321
the covariance is estimated a priori for the main filter at time k + 1.
The method can accurately obtain the estimated track set belonging to the same target, and compared with the target estimated track set of a common single sensor, the RMSE position error of the obtained final track is lower than that of all single sensors. Therefore, the method of the invention can obtain higher precision. Based on OSPA(2)The distance multi-sensor track association method combines historical track point information, completely considers the characteristics of the whole track, avoids the reduction of the association between the tracks, and further accurately and efficiently obtains a track set belonging to the same target; on the basis, a federal filter method is adopted to fuse the flight path sets belonging to the same target, so that the optimal flight path is obtained. Compared with a single-sensor track set, the method reduces the position error of the real track and the estimated track.
Drawings
FIG. 1 is a flow chart of the processing of the track-oriented multi-hypothesis tracking algorithm (MHT) in step (1) of the method of the present invention;
FIG. 2 is an OSPA belonging to the same object(2)A distance map;
FIG. 3 is a detailed process diagram of step (3) of the method of the present invention;
FIG. 4 is a diagram of the RMSE position error for the final track.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The method comprises the following steps that (1) an estimated track set of I sensors and J targets is obtained by adopting a track-oriented multi-hypothesis tracking algorithm (MHT); establishing a system model, considering a nonlinear multi-sensor system model with deviation, wherein the noise of the system process is known, and the mathematical description of a state equation, a deviation equation and a measurement equation is as follows:
Figure BDA0002749628050000041
wherein k is a time series, xkAnd xk+1State vectors at time k and at time k +1, Ak+1,kBeing a state transition matrix, bkAnd bk+1Input matrices for time k and k +1, Bk+1,kIs the coefficient matrix corresponding to the input matrix,
Figure BDA0002749628050000042
is the observation vector of the ith sensor at time k,
Figure BDA0002749628050000043
the matrix is observed for the state of the ith sensor at time k,
Figure BDA0002749628050000044
is the coefficient matrix of the ith sensor at time k, wk、
Figure BDA0002749628050000045
The system state noise vector, the system offset noise vector and the measurement noise vector of the ith sensor at time k, i being 1,2, …,I；
The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are all zero mean Gaussian white noise sequences: w is ak～N(0,wk)，
Figure BDA0002749628050000046
As shown in fig. 1, the obtained system measurement data is processed by adopting a track-oriented multi-hypothesis tracking algorithm (MHT) flow, an estimated track set of 5 sensors and 3 targets is obtained, and 50 Monte Carlo (MC) simulations are performed.
Step (2) respectively adopting OSPA according to the obtained estimated track sets of the I sensors and the J targets(2)The distance measures the distance between each estimated track set to obtain the estimated track sets { A1, B1}, { A2, B3}, …, { AJ, BJ }, belonging to the same target.
In this embodiment, the distances between the estimated track sets of the obtained 5 sensors and 3 targets are measured respectively, so as to obtain an estimated track set belonging to the same target. OSPA belonging to the same target(2)The distance map is shown in fig. 2, in which the estimated track sets belonging to the same target are { a1, B1}, { a2, B2}, { A3, B3 }.
Estimated track of jth target obtained by ith sensor
Figure BDA0002749628050000051
Wherein the content of the first and second substances,
Figure BDA0002749628050000052
the estimated state set for the jth target is tracked for the ith sensor at time k.
All target tracks obtained by the ith sensor
Figure BDA0002749628050000053
Wherein, JiThe number of target tracks obtained by the ith sensor, U is an aggregation symbol,
Figure BDA0002749628050000054
denotes from J to JiThe set of elements of (1).
Target track observed by all sensors
Figure BDA0002749628050000055
The target track association is a target track set corresponding to any two different sensors
Figure BDA0002749628050000056
And
Figure BDA0002749628050000057
the distance between the two electrodes is evaluated,
Figure BDA0002749628050000058
Figure BDA0002749628050000059
respectively represent the ith1Person to, i2The number of estimation targets corresponding to each sensor; the OSPA distance is expressed as the distance between two sets:
Figure BDA00027496280500000510
wherein p is the distance order, p is 1,2, c is the horizontal parameter, ΠnIs all permutations of the set {1,2, …, n }, n being
Figure BDA00027496280500000511
The number of the inner elements, pi (l) is the first arrangement, k1、k2Are respectively the ith1Person to, i2The time series corresponding to each of the sensors,
Figure BDA00027496280500000512
for a set of target tracks
Figure BDA00027496280500000513
And
Figure BDA00027496280500000514
the distance between them.
And (3) according to the obtained 5 estimated tracks belonging to the same target, fusing the estimated tracks by adopting a federal filter fusion algorithm, wherein the specific implementation steps are shown in FIG. 3. The RMSE position error map of its final track is shown in fig. 4.
The federal filter in the federal filter fusion algorithm is a two-stage filter, and the output of the common reference system can be directly transmitted to the main filter and can also be output to each sub-filter as an observed value. However, each subsystem can only correspond to the output of the sub-filter, and the local estimation value (common state) of each sub-filter and the covariance matrix thereof are sent to the main filter and are fused together with the estimation value of the main filter to obtain the global optimal estimation.
Information is distributed between each sub-filter and the main filter:
Figure BDA00027496280500000515
in the formula, QkIn order for the process to excite the noise covariance,
Figure BDA0002749628050000061
for the a posteriori estimated covariance matrix of each sub-filter and the main filter at time k,
Figure BDA0002749628050000062
is its covariance matrix, M is the number of sub-filters, MzRepresents a main filter; beta is amAnd if the sub-filter information distribution coefficient is more than 0, distributing coefficients for the sub-filter information, and meeting the information distribution principle:
Figure BDA0002749628050000063
Figure BDA0002749628050000064
distributing coefficients for the main filter information;
Figure BDA0002749628050000065
estimation of the A posteriori states of the sub-filters and the main filter at time kThe value of the one or more of,
Figure BDA0002749628050000066
is a global estimate.
Time updates are made independently between each sub-filter and the main filter:
Figure BDA0002749628050000067
Figure BDA0002749628050000068
in the formula (I), the compound is shown in the specification,
Figure BDA0002749628050000069
for the a priori state estimates of each sub-filter and main filter at time k,
Figure BDA00027496280500000610
for a priori estimation of the covariance, Φ, of each sub-filter and the main filter at time kkBeing a state transition matrix, ΓkFor the process noise distribution matrix, T represents transpose.
Since the main filter has no measurements, the main filter has no measurement updates. Measurement updates are performed in each sub-filter:
Figure BDA00027496280500000611
in the formula (I), the compound is shown in the specification,
Figure BDA00027496280500000612
for the a posteriori estimated covariance of each sub-filter and the main filter at time k +1,
Figure BDA00027496280500000613
the a posteriori state estimates for each sub-filter and main filter at time k +1, H is the state variable to observation transformation matrix, R is the measurement noise covariance,
Figure BDA00027496280500000614
is the measurement of each sub-filter at time k + 1.
And fusing the local estimation information of each sub-filter according to the following formula to obtain the global optimal estimation:
Figure BDA00027496280500000615
Figure BDA00027496280500000616
in the formula (I), the compound is shown in the specification,
Figure BDA00027496280500000617
for a globally optimal a posteriori state estimate at time k +1,
Figure BDA00027496280500000618
the covariance is estimated for the global optimum a posteriori at time k +1,
Figure BDA00027496280500000619
the a priori state estimate of the main filter at time k +1,
Figure BDA00027496280500000620
the covariance is estimated a priori for the main filter at time k + 1.

Claims (5)

1. Based on OSPA(2)The distance multi-sensor multi-target track association and fusion method is characterized by comprising the following steps:
establishing a system model to obtain an estimated track set;
step (2) is based on OSPA(2)Measuring the distance between each estimated track set by the distance to obtain the estimated track sets belonging to the same target;
and (3) carrying out track fusion on the estimated track set belonging to the same target by adopting a federal filter fusion method.
2. The OSPA-based system of claim 1(2)The distance multi-sensor multi-target track association and fusion method is characterized in that the step (1) specifically comprises the following steps:
respectively obtaining estimated track sets of I sensors and J targets by adopting a track-oriented multi-hypothesis tracking algorithm; establishing a system model, wherein the mathematical description of a state equation, a deviation equation and a measurement equation is as follows:
Figure FDA0002749628040000011
wherein k is a time series, xkAnd xk+1State vectors at time k and at time k +1, Ak+1,kBeing a state transition matrix, bkAnd bk+1Input matrices for time k and k +1, Bk+1,kIs the coefficient matrix corresponding to the input matrix,
Figure FDA0002749628040000012
is the observation vector of the ith sensor at time k,
Figure FDA0002749628040000013
the matrix is observed for the state of the ith sensor at time k,
Figure FDA0002749628040000014
is the coefficient matrix of the ith sensor at time k, wk、
Figure FDA0002749628040000015
The system state noise vector, the system offset noise vector, and the measurement noise vector of the I-th sensor at time k, I being 1,2, …, I, respectively.
3. The OSPA-based system of claim 2(2)The distance multi-sensor multi-target track association and fusion method is characterized in that the step (2) specifically comprises the following steps:
respectively adopting OSPA according to the obtained estimated track sets of the I sensors and the J targets(2)Measuring the distance between each estimated track set by using the distance to obtain an estimated track set belonging to the same target;
estimated track of jth target obtained by ith sensor
Figure FDA0002749628040000016
Wherein the content of the first and second substances,
Figure FDA0002749628040000017
tracking an estimated state set of a jth target for an ith sensor at time k;
all target tracks obtained by the ith sensor
Figure FDA0002749628040000021
Wherein, JiThe number of target tracks obtained by the ith sensor is U which is a set symbol,
Figure FDA0002749628040000022
denotes from J to JiA set of elements of (c);
target track observed by all sensors
Figure FDA0002749628040000023
The target track association is a target track set corresponding to any two different sensors
Figure FDA0002749628040000024
And
Figure FDA0002749628040000025
the distance between the two electrodes is evaluated,
Figure FDA0002749628040000026
i1≠i2；
Figure FDA0002749628040000027
respectively represent the ith1Person to, i2The number of estimation targets corresponding to each sensor; the OSPA distance is expressed as the distance between two sets:
Figure FDA0002749628040000028
wherein p is the distance order, p is 1,2, c is the horizontal parameter, ΠnIs all permutations of the set {1,2, …, n }, n being
Figure FDA0002749628040000029
The number of the inner elements, pi (l) is the first arrangement, k1、k2Are respectively the ith1Person to, i2The time series corresponding to each of the sensors,
Figure FDA00027496280400000210
for a set of target tracks
Figure FDA00027496280400000211
And
Figure FDA00027496280400000212
the distance between them.
4. The OSPA-based network element of claim 3(2)The distance multi-sensor multi-target track association and fusion method is characterized in that the step (3) is specifically as follows:
firstly, information distribution is carried out between each sub-filter and the main filter:
Figure FDA00027496280400000213
in the formula, QkIn order for the process to excite the noise covariance,
Figure FDA00027496280400000214
for the a posteriori estimated covariance matrix of each sub-filter and the main filter at time k,
Figure FDA00027496280400000215
is its covariance matrix, M is the number of sub-filters, MzRepresents a main filter; beta is amAnd if the sub-filter information distribution coefficient is more than 0, distributing coefficients for the sub-filter information, and meeting the information distribution principle:
Figure FDA00027496280400000216
Figure FDA00027496280400000217
distributing coefficients for the main filter information;
Figure FDA00027496280400000218
for the a posteriori state estimates of the sub-filters and the main filter at time k,
Figure FDA00027496280400000219
is a global estimated value;
time updates are made independently between each sub-filter and the main filter:
Figure FDA00027496280400000220
Figure FDA00027496280400000221
in the formula (I), the compound is shown in the specification,
Figure FDA00027496280400000222
for the a priori state estimates of each sub-filter and main filter at time k,
Figure FDA00027496280400000223
for a priori estimation of the covariance, Φ, of each sub-filter and the main filter at time kkBeing a state transition matrix, ΓkT represents transposition for a process noise distribution matrix;
measurement updates are performed in each sub-filter:
Figure FDA0002749628040000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002749628040000032
for the a posteriori estimated covariance of each sub-filter and the main filter at time k +1,
Figure FDA0002749628040000033
the a posteriori state estimates for each sub-filter and main filter at time k +1, H is the state variable to observation transformation matrix, R is the measurement noise covariance,
Figure FDA0002749628040000034
is the measured value of each sub-filter at time k + 1;
and fusing the local estimation information of each sub-filter according to the following formula to obtain the global optimal estimation:
Figure FDA0002749628040000035
Figure FDA0002749628040000036
Figure FDA0002749628040000037
in the formula (I), the compound is shown in the specification,
Figure FDA0002749628040000038
for a globally optimal a posteriori state estimate at time k +1,
Figure FDA0002749628040000039
the covariance is estimated for the global optimum a posteriori at time k +1,
Figure FDA00027496280400000310
the a priori state estimate of the main filter at time k +1,
Figure FDA00027496280400000311
the covariance is estimated a priori for the main filter at time k + 1.
5. The OSPA-based system of claim 2(2)The distance multi-sensor multi-target track association and fusion method is characterized by comprising the following steps: and (2) the system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor in the step (1) are zero-mean Gaussian white noise sequences.
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CN113532422A (en) * 2021-07-12 2021-10-22 哈尔滨工程大学 Multi-sensor track fusion method based on distance map and data cleaning
CN114548312A (en) * 2022-03-01 2022-05-27 东南大学 Track association rapid clustering method based on improved OSPA distance index
CN116399327A (en) * 2023-04-10 2023-07-07 烟台欣飞智能系统有限公司 Unmanned aerial vehicle positioning system based on multisource data fusion

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