CN110187336B - Multi-station radar site positioning and joint tracking method based on distributed PHD - Google Patents

Multi-station radar site positioning and joint tracking method based on distributed PHD Download PDF

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CN110187336B
CN110187336B CN201910573146.8A CN201910573146A CN110187336B CN 110187336 B CN110187336 B CN 110187336B CN 201910573146 A CN201910573146 A CN 201910573146A CN 110187336 B CN110187336 B CN 110187336B
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杨晓波
柴雷
吴若凡
杨琪
李溯琪
易伟
孔令讲
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University of Electronic Science and Technology of China
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    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a multi-station radar site location and joint tracking method based on distributed PHD, which comprises the following steps: s1, receiving the echo signal, and performing local tracking filtering processing; s2, calculating a Cherenov information divergence formula between the posteriori of every two radars; s3, constructing an optimization problem model; s4, solving the optimization model to obtain position parameters of all radars relative to other radar sites; s5, selecting a multi-sensor information fusion criterion; s6, changing the combined posterior distribution into an edge density function, and obtaining a fused posterior density function according to a multi-sensor information fusion criterion; and S7, transmitting the fused posterior density function back to each local radar in a mixed Gaussian form. The invention can utilize a plurality of radars to measure the information of the target under the condition of unknown accurate positions of the multi-station radar, simultaneously carry out the station location of the multi-station radar, the tracking of multiple targets and the information fusion, and has the characteristics of small calculated amount, high convergence speed and the like.

Description

Multi-station radar site positioning and joint tracking method based on distributed PHD
Technical Field
The invention belongs to the technical field of radar target tracking, and particularly relates to a multi-station radar site location and joint tracking method based on distributed PHD.
Background
In modern war, tracking targets by using multi-station radar union widely distributed in war area is a research hotspot in radar tracking field. Compared with a single radar, the multi-station radar can obtain more dimensions and wider range of information about the target, so that the detection performance of the target and the robustness of the system are improved. When the multi-station radar is used for carrying out joint tracking on a target, the accurate position of the multi-station radar needs to be known so as to carry out operations such as spatial alignment and the like during information fusion. However, in an actual scenario, due to positioning errors and the like, the system cannot provide an accurate position of the radar, which causes performance deterioration when the multi-station radar system performs joint tracking on the target. Therefore, the efficient multi-station radar site location and joint tracking method has important theoretical value and practical significance.
Some researchers have conducted research and obtained corresponding research results aiming at the problem of multi-station radar site location and joint tracking, and most of the current results are based on a maximum likelihood and expectation-maximization method, in which method, the position information of the radar is contained in a joint likelihood function formed by using a plurality of radar measurements, and the position information of the radar can be obtained by maximizing the likelihood function. In the patent "worship, li 26107, philosophy, pan, combined multisensor registration and multi-target tracking, china, 108519595a, 2018-03-20", such a method is used and multi-target tracking is performed using a GLMB filter. However, this method needs to collect all measurement information from all radars, so in a high-density clutter environment, constructing a joint likelihood function causes a huge communication burden, and this method adopts a centralized fusion architecture, resulting in poor robustness of the whole system. A radar joint tracking and self-positioning method based on posterior information is proposed in documents "m.unney, b.mulgrew, and d.e.clark," a Cooperative approach to sensor localization in distributed networks, "IEEE trans.signal process, vol.64, No.5, pp.1187-1199, oct.2016", but this method uses high-dimensional particles to represent local posterior, so that a large number of particles need to be transmitted between multiple radars to estimate posterior information, which causes a great communication burden, and information transmitted between sensors uses belief propagation technology, which is not suitable for a ring-shaped multi-sensor network structure.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a multi-station radar site location and joint tracking method based on distributed PHD, which can utilize the measurement information of a plurality of radars to a target under the condition of unknown accurate positions of the multi-station radars, simultaneously perform site location, multi-target tracking and information fusion of the multi-station radars, and has the characteristics of small calculated amount, high convergence speed and the like.
The purpose of the invention is realized by the following technical scheme: a multi-station radar site location and joint tracking method based on distributed PHD comprises the following steps:
s1, receiving an echo signal, and performing local tracking filtering processing by adopting a probability hypothesis density filter;
s2, transmitting the posterior density function represented by the mixed Gaussian similarity to other radar sites, and calculating a Cherenov information divergence formula between the posterior of every two radars;
s3, constructing an optimization problem model by utilizing the Cherenov information divergence related to the two radar positions established in the step S2;
s4, solving the optimization model by using a particle swarm algorithm to further obtain a position parameter of the radar j relative to the radar i; carrying out the same operation on all the two radars to obtain the position parameters of all the radars relative to other radar sites;
s5, selecting a multi-sensor information fusion criterion;
s6, combining the posterior distribution into an edge density function according to the position parameters of all radars relative to other radar sites, and obtaining a fused posterior density function according to the multi-sensor information fusion criterion;
and S7, transmitting the fused posterior density function back to each local radar in a mixed Gaussian form.
Further, the specific implementation method of step S1 is as follows:
the posterior density distribution obtained by each local radar is probability hypothesis density distribution, and is characterized by using a mixed Gaussian form as follows:
Figure BDA0002111251760000021
wherein v isi,k(x) Representing the a posteriori density function from the ith radar at the kth time, x representing the target state variable,
Figure BDA0002111251760000022
representing the Gaussian probability density function, KiRepresenting the number of gaussian components in the a posteriori density function,
Figure BDA0002111251760000023
the weight values of the gaussian components are represented,
Figure BDA0002111251760000024
represents the mean of the gaussian component and,
Figure BDA0002111251760000025
a covariance matrix representing the gaussian component;
since the position information of the radar is contained in the posterior density function when transmitting the posterior information to the other radar stations, the density function transmitted to the other radar station j is actually a joint distribution density function with respect to the target state variable and the radar position:
Figure BDA0002111251760000026
wherein
Figure BDA0002111251760000027
θi,jAnd represents the position of the radar j relative to the radar i when the radar i is taken as a coordinate origin.
Further, the specific implementation method of step S2 is as follows: the chernoff information divergence was calculated between the posteriors of every two radars:
Figure BDA0002111251760000031
wherein Γ (·) represents chernoff information divergence; omegaiDenotes a parameter assigned to the radar i satisfying 0 ≦ ωi≤1，ωi+ωj＝1；Π＝{(vi(x),ωi),(vj(x),ωj) The multiple target states and corresponding weights are contained in the set; n represents the number of targets;
substituting the posterior density distribution represented by the mixed Gaussian form obtained by the probability hypothesis density filter into the Cherenov information divergence to obtain:
Figure BDA0002111251760000032
Γ(θi,j) Representing the position theta between the radar i, ji,jThe resulting divergence of the chernoff information,
Figure BDA0002111251760000033
represents a set of measurements from radar i, j;
substituting the local posterior density information represented by the Gaussian mixture form into a Cherenov divergence formula to obtain:
Figure BDA0002111251760000035
wherein
Figure BDA0002111251760000036
Further, the optimization model constructed in step S3 is:
Figure BDA0002111251760000037
further, in step S5, the multi-sensor information fusion criterion is selected as:
Figure BDA0002111251760000038
wherein v isf,k(x|Zi,k,Zj,k) Representing the fused posterior density function, vi,k(x|Zi,k) And vj,k(x|Zj,k) The posterior probability hypothesis density function, ω, representing radar i and j, respectivelyiAnd ωjRepresenting the weight taken up by the posterior density function at the time of fusion.
Further, the specific implementation method of step S6 is as follows:
knowing the radar position parameter θi,jPosterior, combined posterior distribution vi,k(x,θi,j) Becomes the edge density function vi,k(x|θi,j) And according to the multi-sensor information fusion criterion, obtaining a fused posterior density function as follows:
Figure BDA0002111251760000041
the fused posterior density function is expressed in the form of a mixed gaussian:
Figure BDA0002111251760000042
wherein
Figure BDA0002111251760000043
And if the number of the radars is N, performing the fusion operation for N-1 times by sequentially performing the posterior density function after the multi-radar fusion.
The invention has the beneficial effects that: the invention can utilize the measurement information of a plurality of radars to the target under the condition of unknown accurate positions of the multi-station radars, simultaneously carry out the station location of the multi-station radars, the tracking of multiple targets and the information fusion, and has the characteristics of small calculated amount, high convergence rate and the like.
Drawings
FIG. 1 is a flow chart of a distributed PHD-based multi-station radar site location and joint tracking method of the present invention;
FIG. 2 is a method for representing position parameters of a radar j and a radar n according to the present invention, wherein the position of the radar i is taken as a coordinate origin;
FIG. 3 is a diagram of simulation effects of joint tracking of multiple targets without using site location and using the method, under the condition that the positions of various radars are unknown.
Detailed Description
The solution of the invention is that in the multi-station radar site location stage, each radar respectively uses a PHD filter to carry out local filtering and obtain posterior information represented by a Gaussian mixture form, then uses the posterior information to calculate the Cherenov information divergence between every two radars, and uses a particle swarm optimization to optimize so as to minimize the Cherenov information divergence and obtain the relative position between every two radars. And in the joint tracking stage, fusing posterior information by using a generalized covariance crossing criterion under a distributed framework according to the obtained relative position of the radar to obtain a joint tracking result. The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, a multi-station radar site location and joint tracking method based on distributed PHD includes the following steps:
s1, receiving an echo signal, and performing local tracking filtering processing by adopting a probability hypothesis density filter; the specific implementation method comprises the following steps:
the posterior density distribution obtained by each local radar is probability hypothesis density distribution, and is characterized by using a mixed Gaussian form as follows:
Figure BDA0002111251760000051
wherein v isi,k(x) Representing the a posteriori density function from the ith radar at the kth time, x representing the target state variable,
Figure BDA0002111251760000052
representing the Gaussian probability density function, KiRepresenting the number of gaussian components in the a posteriori density function,
Figure BDA0002111251760000053
the weight values of the gaussian components are represented,
Figure BDA0002111251760000054
represents the mean of the gaussian component and,
Figure BDA0002111251760000055
a covariance matrix representing the gaussian component;
since the position information of the radar is contained in the posterior density function when transmitting the posterior information to the other radar stations, the density function transmitted to the other radar station j is actually a joint distribution density function with respect to the target state variable and the radar position:
Figure BDA0002111251760000056
wherein
Figure BDA0002111251760000057
θi,jWhich represents the position of radar j relative to radar i when radar i is taken as the origin of coordinates, as shown in fig. 2.
S2, transmitting the posterior density function represented by the mixed Gaussian similarity to other radar sites, and calculating a Cherenov information divergence formula between the posterior of every two radars; the specific implementation method comprises the following steps: the chernoff information divergence was calculated between the posteriors of every two radars:
Figure BDA0002111251760000059
wherein Γ (·) represents chernoff information divergence; omegaiDenotes a parameter assigned to the radar i satisfying 0 ≦ ωi≤1，ωi+ωj1, this parameter determines the weight of the posterior density function in calculating the divergence of the chernoff information;
Π＝{(vi(x),ωi),(vj(x),ωj)}is a set containing multiple target states and corresponding weights; n represents the number of targets;
substituting the posterior density distribution represented by the mixed Gaussian form obtained by the probability hypothesis density filter into the Cherenov information divergence to obtain:
Figure BDA0002111251760000058
Γ(θi,j) Representing the position theta between the radar i, ji,jThe resulting divergence of the chernoff information,
Figure BDA0002111251760000061
represents a set of measurements from radar i, j;
substituting the local posterior density information represented by the Gaussian mixture form into a Cherenov divergence formula to obtain:
Figure BDA0002111251760000062
wherein
Figure BDA0002111251760000067
S3, constructing an optimization problem model by utilizing the Cherenov information divergence related to the two radar positions established in the step S2: the constructed optimization model is as follows:
Figure BDA0002111251760000063
s4, solving the optimization model by using a particle swarm algorithm to further obtain a position parameter of the radar j relative to the radar i; carrying out the same operation on all the two radars to obtain the position parameters of all the radars relative to other radar sites;
s5, selecting the multi-sensor information fusion criterion as follows:
Figure BDA0002111251760000064
wherein v isf,k(x|Zi,k,Zj,k) Representing the fused posterior density function, vi,k(x|Zi,k) And vj,k(x|Zj,k) The posterior probability hypothesis density function, ω, representing radar i and j, respectivelyiAnd ωjRepresenting the weight taken up by the posterior density function at the time of fusion.
S6, combining the posterior distribution into an edge density function according to the position parameters of all radars relative to other radar sites, and obtaining a fused posterior density function according to the multi-sensor information fusion criterion; the specific implementation method comprises the following steps:
knowing the radar position parameter θi,jPosterior, combined posterior distribution vi,k(x,θi,j) Becomes the edge density function vi,k(x|θi,j) And according to the multi-sensor information fusion criterion, obtaining a fused posterior density function as follows:
Figure BDA0002111251760000065
the fused posterior density function is expressed in the form of a mixed gaussian:
Figure BDA0002111251760000066
wherein
Figure BDA0002111251760000071
And if the number of the radars is N, performing the fusion operation for N-1 times by sequentially performing the posterior density function after the multi-radar fusion.
And S7, transmitting the fused posterior density function back to each local radar in a mixed Gaussian form.
FIG. 3 is a diagram of simulation effects of joint tracking of multiple targets without using site location and using the method, under the condition that the positions of various radars are unknown. As can be seen from the figure, under the same scene, compared with the result that radar site location is not carried out, the method provided by the invention has the advantages that the higher tracking precision can be obtained by carrying out combined tracking on multiple targets.
The invention utilizes the posterior density function of each radar instead of the measurement information of each radar to calculate the positions of the multi-base radar, thereby greatly reducing the information transmission load among the radars. In addition, in the invention, the relative position information between the radars is obtained by calculating the dispersion of the Cherenov information between the posterior of every two radars, so that the high-dimensional information calculation problem is subjected to dimension reduction processing, and the calculation amount of the system is greatly reduced. In addition, when the Cherenov information divergence is expressed in a mixed Gaussian form, the obtained optimization function model related to the radar position information is a non-convex optimization problem, and the optimization method based on the gradient is not applicable any more, so that the particle swarm optimization is adopted to solve the problem.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (5)

1. A multi-station radar site location and joint tracking method based on distributed PHD is characterized by comprising the following steps:
s1, receiving an echo signal, and performing local tracking filtering processing by adopting a probability hypothesis density filter;
s2, transmitting the posterior density function represented by the mixed Gaussian similarity to other radar sites, and calculating a Cherenov information divergence formula between the posterior of every two radars; the specific implementation method comprises the following steps: the chernoff information divergence was calculated between the posteriors of every two radars:
Figure FDA0002707376350000011
wherein Γ (·) represents chernoff information divergence; omegaiDenotes a parameter assigned to the radar i satisfying 0 ≦ ωi≤1，ωi+ωj＝1；Π＝{(vi(x),ωi),(vj(x),ωj) The multiple target states and corresponding weights are contained in the set; n represents the number of targets;
substituting the posterior density distribution represented by the mixed Gaussian form obtained by the probability hypothesis density filter into the Cherenov information divergence to obtain:
Figure FDA0002707376350000012
Γ(θi,j) Representing the position theta between the radar i, ji,jThe resulting divergence of the chernoff information,
Figure FDA0002707376350000013
represents a set of measurements from radar i, j;
substituting the local posterior density information represented by the Gaussian mixture form into a Cherenov divergence formula to obtain:
Figure FDA0002707376350000014
wherein
Figure FDA0002707376350000015
S3, constructing an optimization problem model by utilizing the Cherenov information divergence related to the two radar positions established in the step S2;
s4, solving the optimization model by using a particle swarm algorithm to further obtain a position parameter of the radar j relative to the radar i; carrying out the same operation on all the two radars to obtain the position parameters of all the radars relative to other radar sites;
s5, selecting a multi-sensor information fusion criterion;
s6, combining the posterior distribution into an edge density function according to the position parameters of all radars relative to other radar sites, and obtaining a fused posterior density function according to the multi-sensor information fusion criterion;
and S7, transmitting the fused posterior density function back to each local radar in a mixed Gaussian form.
2. The method for multi-station radar site location and joint tracking based on distributed PHD as claimed in claim 1, wherein the step S1 is implemented by:
the posterior density distribution obtained by each local radar is probability hypothesis density distribution, and is characterized by using a mixed Gaussian form as follows:
Figure FDA0002707376350000021
wherein v isi,k(x) Representing the a posteriori density function from the ith radar at the kth time, x representing the target state variable,
Figure FDA0002707376350000022
representing the Gaussian probability density function, KiRepresenting the number of gaussian components in the a posteriori density function,
Figure FDA0002707376350000023
the weight values of the gaussian components are represented,
Figure FDA0002707376350000024
represents the mean of the gaussian component and,
Figure FDA0002707376350000025
a covariance matrix representing the gaussian component;
since the position information of the radar is contained in the posterior density function when transmitting the posterior information to the other radar stations, the density function transmitted to the other radar station j is actually a joint distribution density function with respect to the target state variable and the radar position:
Figure FDA0002707376350000026
wherein
Figure FDA0002707376350000027
θi,jAnd represents the position of the radar j relative to the radar i when the radar i is taken as a coordinate origin.
3. The distributed PHD-based multi-station radar site location and joint tracking method according to claim 1, wherein the optimization model constructed in step S3 is:
Figure FDA0002707376350000028
4. the distributed PHD-based multi-station radar site location and joint tracking method according to claim 1, wherein in step S5, the multi-sensor information fusion criterion is selected as:
Figure FDA0002707376350000029
wherein v isf,k(x|Zi,k,Zj,k) Representing the fused posterior density function, vi,k(x|Zi,k) And vj,k(x|Zj,k) The posterior probability hypothesis density function, ω, representing radar i and j, respectivelyiAnd ωjRepresenting the weight taken up by the posterior density function at the time of fusion.
5. The method for multi-station radar site location and joint tracking based on distributed PHD as claimed in claim 1, wherein the step S6 is implemented by:
knowing the radar position parameter θi,jPosterior, combined posterior distribution vi,k(x,θi,j) Becomes the edge density function vi,k(x|θi,j) And according to the multi-sensor information fusion criterion, obtaining a fused posterior density function as follows:
Figure FDA0002707376350000031
the fused posterior density function is expressed in the form of a mixed gaussian:
Figure FDA0002707376350000032
wherein
Figure FDA0002707376350000033
Figure FDA0002707376350000034
Figure FDA0002707376350000035
And if the number of the radars is N, performing the fusion operation for N-1 times by sequentially performing the posterior density function after the multi-radar fusion.
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