CN113093174A - PHD filtering radar fluctuation weak multi-target-based track-before-detect method - Google Patents

PHD filtering radar fluctuation weak multi-target-based track-before-detect method Download PDF

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CN113093174A
CN113093174A CN202110235449.6A CN202110235449A CN113093174A CN 113093174 A CN113093174 A CN 113093174A CN 202110235449 A CN202110235449 A CN 202110235449A CN 113093174 A CN113093174 A CN 113093174A
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target
likelihood
amplitude
radar
complex
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CN113093174B (en
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吴孙勇
李东升
薛秋条
孙希延
纪元法
蔡如华
符强
王守华
严素清
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Guilin University of Electronic Technology
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    • G—PHYSICS
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G01S13/726—Multiple target tracking
    • G—PHYSICS
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • G—PHYSICS
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/415—Identification of targets based on measurements of movement associated with the target
    • G—PHYSICS
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention discloses a PHD filtering radar fluctuation weak multi-target-based track-before-detect method, which solves the problems of target detection and tracking under amplitude fluctuation, researches swerling0,1 and 3 fluctuation target models, and establishes two tracking models of complex likelihood and amplitude likelihood under a PHD-TBD algorithm, wherein the complex likelihood method overcomes the defect that the amplitude likelihood only considers the measured amplitude information and ignores phase information in the calculation process, thereby better utilizing the original target information. In the method, under the condition that the target amplitude fluctuates, the complex likelihood is superior to the amplitude likelihood in the estimation performance of the target position and the number in comparison with the amplitude likelihood, and the calculation efficiency is higher. At low signal-to-noise ratios, complex likelihoods can still effectively detect and track an unknown number of weak targets.

Description

PHD filtering radar fluctuation weak multi-target-based track-before-detect method
Technical Field
The invention relates to the technical field of radar fluctuation weak multi-target detection and tracking, in particular to a PHD filtering radar fluctuation weak multi-target-based pre-detection tracking method.
Background
With the rapid development of modern electronic information technology, the radar target detection technology faces the threat of airplane stealth technology, the radar Reflection Cross Section (RCS) of a stealth target is small due to the development of the stealth technology, a target reflection echo signal is weak, and the echo signal-to-noise ratio (SNR) is low. The traditional detection and tracking method of a moving target is post-detection tracking (DBT), in the method, a threshold value is set for each frame of measured data to judge whether the target exists, and the track of the target is obtained through a tracking algorithm; however, when the signal-to-noise ratio of the echo signal is low, the echo of a weak target is usually lower than a threshold value, detection omission occurs, and the target track is difficult to extract by using single-frame measurement data; if the threshold is lowered, a large number of false alarms are generated and the target trajectory cannot be maintained.
To solve the above problem, one of the methods is to use a track-before-detect (TBD) algorithm. The algorithm performs combined processing on multi-frame data according to the continuity of target motion in space and the relevance of continuous frames of target echo data on time, and realizes target detection and tracking through multi-frame energy accumulation. The traditional TBD method comprises dynamic programming, Hough transformation and the like. However, these methods are large in calculation amount and high in algorithm complexity on one hand, and are only suitable for linear gaussian models on the other hand.
The Particle filter TBD (Particle Filter BD, PF-TBD) algorithm under the Bayesian framework can solve the problems of nonlinearity and non-Gaussian, so that the method is rapidly developed in the field of weak target detection and tracking. The PF-TBD method is limited in that the appearance (new growth) and disappearance (death) of the target are not modeled, and thus when the number of processing targets is unknown and changed, the complexity of the algorithm is increased sharply, and the filter performance is limited.
Disclosure of Invention
The invention aims to provide a PHD filtering radar fluctuation-based pre-detection tracking method for weak multiple targets, and aims to solve the technical problem that the fluctuation of the weak multiple targets cannot be effectively tracked in the prior art.
In order to achieve the above object, the present invention provides a PHD filtering radar fluctuation-based weak multi-target tracking-before-detection method, which comprises the following steps:
s1: initializing system parameters, and reading original measurement data of a kth-1 moment and a kth moment in a radar receiver;
s2: dividing scenes, and utilizing original measurement data at the moment of k-1 to adapt to a new target in each small scene;
s3: respectively calculating complex likelihood and amplitude likelihood of three amplitude fluctuation types aiming at complex measurement data and square measurement data obtained at the moment k, and giving out SMC (surface Mount device) realization of PHD (phase Shift keying) filtering under amplitude fluctuation;
s4: extracting target states and target numbers according to the posterior information;
s5: and (5) enabling K to be K +1, judging whether K is greater than K, if yes, finishing the algorithm, and if not, returning to the step two.
The system parameters include:
sampling interval T, current time K, total target motion time K, and scanning area [ r ] of radar in polar coordinatesmin,rmax]×[θmin,θmax]Measurement data Z in a Radar reception tracking scenek and Zk-1Consider a range and azimuth surveillance radar covering a defined area in polar coordinates, for which the transmitted pulse is assumed to be of bandwidth B and duration TεLinear frequency-modulated signal, speed of light c, distance resolution unit
Figure BDA0002959829220000021
For angles, consider N at the radar receiveraA linear phased array of antennas is provided,at an interval of
Figure BDA0002959829220000022
Where λ is the wavelength of the carrier frequency and the angular resolution is
Figure BDA0002959829220000023
Dividing scenes, and in the step of utilizing the original measurement data at the k-1 moment to self-adapt to the new targets in each small scene:
if N is presentr×NθIf it is larger, the scene N will ber×NθIs divided into
Figure BDA0002959829220000024
A scene, consider generating N within each scenefilterParticles, the number of particles in the whole scene is n1×n2×Nfilter；
Setting a measurement cut-off threshold ThCut offSorting the measurements in each scene in descending order, selecting the intensity above a threshold ThCut offMeasured at a value lower than ThCut offThe measurement of (a) is regarded as false detection measurement, and the position information of each measurement is (n)r,nθ)；
The position information (n) of each measurementr,nθ) Converting the target position into a planar rectangular coordinate system and recording the target position as (z)x,zy)；
At each (z)x,zy) And generating particles nearby, calculating the likelihood of each particle in the scene, then performing resampling to select the particles with higher weight in the scene, and performing normalization processing on the selected particle weight.
Respectively calculating complex likelihood and amplitude likelihood of three amplitude fluctuation types aiming at complex measurement data and square measurement data obtained at the moment k, and giving out SMC realization of PHD filtering under amplitude fluctuation:
calculating the amplitude likelihood when the target does not exist;
respectively calculating amplitude likelihood with amplitude fluctuation types of swerling0,1 and 3;
calculating a complex likelihood when the target is absent;
and respectively calculating the complex likelihood of the amplitude fluctuation types of swerling0,1 and 3.
At the time k-1:
using a set of band weights
Figure BDA0002959829220000031
Particles of (2)
Figure BDA0002959829220000032
Representing the posterior density of the PHD, predicting and updating the set of weighted particles
Figure BDA0002959829220000033
For complex measurement and square measurement, the likelihood of different amplitude fluctuation is different, in the target tracking process, the target amplitude can influence the target echo strength, the target with high echo strength can inhibit the target with low echo strength, and the likelihood higher than the threshold value is considered to be assigned as the highest likelihood.
And when the target amplitude fluctuation type is swerling 3, judging after calculating the particle weight, if the particle weight is infinite, keeping the state of the predicted particle unchanged, not updating the particle, and assuming that the particle weight is 0.
The step of extracting the target state and the target number according to the posterior information comprises the following steps:
calculating the target number, and resampling samples;
determining updated particle weights
Figure BDA0002959829220000034
And if the sum is more than 0, clustering the resampled particles by using a K-means method, deleting the weight sum and being lower than a threshold Thk-meansThe sum of the weights is higher than a threshold Thk-meansThe particle group(s) is considered as an estimated target state, and if the particle group(s) is smaller than 0, it is considered that there is no target in the scene at that time.
The invention has the beneficial effects that: the method can solve the problems of detection and tracking of weak multi-target fluctuation, and provides a self-adaptive target regeneration algorithm based on measurement likelihood under scene division for solving the problem of target regeneration under the condition that the prior distribution information of the regenerated target state is unknown. Two calculation modes of amplitude likelihood and complex likelihood are given, and PHD-TBD multi-target estimation with amplitude fluctuation types of swerling0,1 and 3 is successfully realized. Compared with the amplitude likelihood, the complex likelihood makes up the defect that the amplitude likelihood only considers the measured amplitude information and ignores the phase information in the calculation process, thereby better utilizing the original information of the target. Compared with the complex likelihood and the amplitude likelihood, the method provided by the invention has the advantages that the complex likelihood is superior to the amplitude likelihood in the estimation performance of the target position and the number, and the calculation efficiency is higher. At low signal-to-noise ratios, complex likelihoods can still effectively detect and track an unknown number of weak targets.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of steps of a PHD filtering-based radar fluctuating weak multi-target tracking-before-detection method.
FIG. 2 is a schematic flow chart of a PHD filtering-based radar fluctuating weak multi-target tracking-before-detection method.
FIG. 3 is a true trajectory of object motion within a simulated scene of the present invention.
FIG. 4 is an OSPA of the complex likelihood and amplitude likelihood algorithm under swerling0 of the invention.
FIG. 5 is a comparison graph of the target potentials of the complex likelihood and amplitude likelihood algorithm under swerling0 of the present invention.
FIG. 6 is an OSPA of the complex likelihood and amplitude likelihood algorithm under swerling 1 of the present invention.
FIG. 7 is a comparison graph of target potentials of complex likelihood and amplitude likelihood algorithms under swerling 1 of the present invention.
FIG. 8 is an OSPA of the complex likelihood and amplitude likelihood algorithm under swerling 3 of the present invention.
FIG. 9 is a comparison graph of the target potentials of the complex likelihood and amplitude likelihood algorithm under swerling 3 of the present invention.
FIG. 10 is an OSPA of different signal-to-noise ratio complex likelihood and square likelihood under swerling0 of the present invention.
FIG. 11 is a graph of the target potential versus different signal-to-noise ratios at different times under swerling0 of the present invention.
FIG. 12 is an OSPA of different signal-to-noise ratio complex likelihood and square likelihood under swerling 1 of the present invention.
FIG. 13 is a graph of the target potential versus different signal-to-noise ratios at different times under swerling 1 of the present invention.
FIG. 14 is an OSPA of different signal-to-noise ratio complex likelihood and square likelihood under swerling 3 of the present invention.
FIG. 15 is a graph of the target potential versus different signal-to-noise ratios at different times under swerling 3 of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
In the description of the present invention, it is to be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on the orientations or positional relationships illustrated in the drawings, and are used merely for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention. Further, in the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
Referring to fig. 1 and fig. 2, the present invention provides a PHD filtering radar fluctuation-based weak multi-target tracking method before detection, including the following steps:
s1: initializing system parameters, and reading original measurement data of a kth-1 moment and a kth moment in a radar receiver;
s2: dividing scenes, and utilizing original measurement data at the moment of k-1 to adapt to a new target in each small scene;
s3: respectively calculating complex likelihood and amplitude likelihood of three amplitude fluctuation types aiming at complex measurement data and square measurement data obtained at the moment k, and giving out SMC (surface Mount device) realization of PHD (phase Shift keying) filtering under amplitude fluctuation;
s4: extracting target states and target numbers according to the posterior information;
s5: and (5) enabling K to be K +1, judging whether K is greater than K, if yes, finishing the algorithm, and if not, returning to the step two.
Specifically, system parameters are initialized, the system parameters comprise a sampling interval T, a current moment K, a total target movement time K, and a scanning area [ r ] of the radar in a polar coordinatemin,rmax]×[θmin,θmax]Measurement data Z in a Radar reception tracking scenek and Zk-1Consider a range and azimuth surveillance radar covering a defined area in polar coordinates, for which the transmitted pulse is assumed to be of bandwidth B and duration TεLinear frequency-modulated signal, speed of light c, distance resolution unit
Figure BDA0002959829220000051
For angles, consider N at the radar receiveraLinear phased array of antennas with spacing of
Figure BDA0002959829220000052
Where λ is the wavelength of the carrier frequency and the angular resolution is
Figure BDA0002959829220000053
Where, initializing k is 2, bk|k-1(xk|xk-1) and γk(xk) PHD, kappa, representing the target neogenesis and derivation at time kk(z)＝λkC (z) is the false alarm intensity, λkAverage false alarm number, c (z) is false alarm distribution; pD(x) Is the detection probability of the target state, gk(z | x) represents the target-producing measurement likelihood. In multi-target tracking, the PHD multi-target state function D is obtained by updatingk|kIs integrated as the expected value of the target number at time k
Figure BDA0002959829220000061
Specifically, the measurement values received by the radar sensor are composed of the distance and the direction after the distance matching filtering and the adaptive beam forming. Given the ith target state x at time kk,iMeasured value zkGiven by the following nonlinear equation:
Figure BDA0002959829220000062
wherein ,h(xk.i) Indicating by target position (x)k,i,yk,i) Fuzzy function of the ith target at the center, h (x) for simplicityk.i) Is marked as hk,i。nkIs the measurement noise with mean 0 and covariance of complex gaussian Γ;
Figure BDA0002959829220000063
and ρk,iRespectively representing the phase and amplitude of the ith target complex amplitude. Assuming all phases
Figure BDA0002959829220000064
And amplitude pk,1:NkIndependently of each other and of nk and xk.1:Nk. Phase position
Figure BDA0002959829220000065
Is unknown and is distributed uniformly over 0,2 pi) at each moment; for amplitude pk,iComprises the following steps:
Figure BDA0002959829220000066
wherein
Figure BDA00029598292200000611
Are unknown static parameters. There are two expression forms for the k-time radar measurement: one is coherent-accumulated complex measurement zkAnother non-coherent accumulated squared measure is | zk|2。
The blur function for distance matched filtering is:
Figure BDA0002959829220000067
wherein ,|τl|＝2(rk-rl)/c，
Figure BDA0002959829220000068
l∈[0,Nr-1]，
Figure BDA0002959829220000069
The azimuth ambiguity function for adaptive beamforming is:
Figure BDA00029598292200000610
wherein ,Φm＝π[sin(θk)-sin(θm)]，
Figure BDA0002959829220000071
And
Figure BDA0002959829220000072
m∈[0,Nθ-1]，
Figure BDA0002959829220000073
global blur function in range-azimuth unit (l, m):
Figure BDA0002959829220000074
h(xk) Is of size Nc＝Nr×NθNamely:
Figure BDA0002959829220000075
in the traditional radar target detection and tracking problem, threshold processing is firstly carried out on each frame of echo data to form point trace information, then association, filtering and other processing are carried out on the point trace information exceeding the threshold, and finally the track of a target is obtained, so that the tracking of the target is realized. The method of detecting first and tracking second is suitable for the condition that the signal-to-noise ratio is high or the echo amplitude of the target is large, the intensity of the target is far higher than that of the clutter, and the target can be separated from the clutter by setting a large threshold. Under the condition of low signal-to-noise ratio or weak target echo signals, target echoes are annihilated in noise clutter, a single-frame threshold crossing detection method is adopted, target detection omission can be caused due to too high threshold, false alarm rate can be increased due to too low threshold, and target tracks can not be maintained. The TBD method can improve the detection and tracking of the radar weak target from the aspect of signal processing, and the basic idea is to process original data which is not subjected to threshold processing, realize the capability accumulation of the target through multi-frame tracking and fully mine the information of the target in an echo.
Furthermore, the PHD filtering algorithm based on the RFS simplifies the multi-target state space into a single-target state space by transmitting the first moment of the multi-target posterior probability density distribution, thereby reducing the calculation complexity to a great extent and having the possibility of actual operation. The prediction and update equations for PHD filtering are as follows:
Figure BDA0002959829220000076
for updating equation Dk|k，PD(x) Is the detection probability associated with the target state; for TBD algorithmThat is, there is no detection process before the update step, assuming that the measurement values contain all the target information; thus PD(x) 1, so the updated equation becomes:
Figure BDA0002959829220000081
the intensity information in each cell is independent of each other for a given target state, so that the multiple-target a posteriori probability density p (z)k|Xk) Can be expressed as the product of the edge probability density function:
Figure BDA0002959829220000082
specifically, in step 2, if N is presentr×NθIf it is larger, the scene N will ber×NθIs divided into
Figure BDA0002959829220000083
A scene; consider generating N within each scenefilterParticles, the number of particles in the whole scene is n1×n2×Nfilter；
Setting a measurement cut-off threshold ThCut offSorting the measurements in each scene in descending order, selecting the intensity above a threshold ThCut offMeasured at a value lower than ThCut offThe measurement of (a) is regarded as false detection measurement, and the position information of each measurement is (n)r,nθ)；
Using the distance and angle quantity formula and formula
Figure BDA0002959829220000084
And
Figure BDA0002959829220000085
converted into distance and orientation, and then according to the formula zx＝rcosθ,zyConverting the position under the polar coordinate into position information under the plane rectangular coordinate by rsin theta;
at each (z)x,zy) Position information (x) of a nearby generation target statei,yi)，v＝U(vmin,vmax) Generating velocity information for a target state
Figure BDA0002959829220000086
Where U represents a uniform distribution, i.e., one particle is generated near each measurement, noted
Figure BDA0002959829220000087
For each particle xiCalculating likelihood on the scene, and then performing resampling to select particles with higher weight in the scene; and normalizing the selected particle weight.
Specifically, in step three, the amplitude likelihood p (| z) when the target is not present is calculatedk|2)：
Figure BDA0002959829220000088
Respectively calculating the amplitude likelihood of the amplitude fluctuation type under swerling0,1 and 3:
Figure BDA0002959829220000091
Figure BDA0002959829220000092
Figure BDA0002959829220000093
wherein ,
Figure BDA0002959829220000094
calculating the complex likelihood p (z) when the target is not presentk)：
Figure BDA0002959829220000095
Respectively calculating the complex likelihood of the amplitude fluctuation type under swerling0,1 and 3:
Figure BDA0002959829220000096
Figure BDA0002959829220000097
Figure BDA0002959829220000098
wherein ,I0(. cndot.) is a first type of modified Bessel function.
Specifically, for time k-1, a set of weighting factors is used
Figure BDA0002959829220000099
Particles of (2)
Figure BDA00029598292200000910
The posterior density representing PHD, i.e.:
Figure BDA00029598292200000911
predicted particle:
Figure BDA0002959829220000101
wherein ,
Figure BDA0002959829220000102
and bk(·|zk) Is the proposed density, Lk-1Particles that are targets for survival at time k-1Number, JkIs the number of particles of the new object at time k. The predicted intensity Dk-1|kComprises the following steps:
Figure BDA0002959829220000103
wherein ：
Figure BDA0002959829220000104
Figure BDA0002959829220000105
wherein ,
Figure BDA0002959829220000106
is in a state of
Figure BDA0002959829220000107
The probability of survival of the target from time k-1 to time k;
Figure BDA0002959829220000108
is in the state xk-1A derived probability density of (a);
Figure BDA0002959829220000109
is the birth probability density.
The update SMC of the PHD can be expressed as:
Figure BDA00029598292200001010
Figure BDA00029598292200001011
wherein ：
Figure BDA00029598292200001012
specifically, for complex measurement and square measurement, the likelihood of different amplitude fluctuations is different, in the target tracking process, the target amplitude affects the target echo strength, the target with high echo strength tends to suppress the target with low strength, and the likelihood higher than the threshold is considered to be the highest likelihood.
Note that, as can be seen from the measurement equation, the echo signal of the target is a sinc function, and the likelihood ratio of the target existing position at this time is very high; when the target amplitude fluctuates, the intensities of echo signals are different, in order to solve the tracking problem of multiple targets under the condition and simultaneously solve the target matching tracking of different intensities, the likelihood ratio is larger than the threshold ThLIs assigned the highest likelihood, i.e.:
Lsw(Lsw≥ThL)＝max(Lsw)。
specifically, when the target amplitude fluctuation type is swerling 3, the particle weight sum may be infinite, and this may cause that the target cannot be tracked at a subsequent time; to cope with this phenomenon, a judgment is made after the particle weight calculation, and if the particle weight sum is infinite, the predicted particle state is kept unchanged, the particle is not updated, and the particle weight is assumed to be 0.
Specifically, step four includes calculating the number of targets
Figure BDA0002959829220000111
Resample samples
Figure BDA0002959829220000112
To obtain
Figure BDA0002959829220000113
Determining updated particle weights
Figure BDA0002959829220000114
And if the sum is larger than 0, clustering the resampled particles by using a K-means method, deleting the weight sum and being lower than a threshold Thk-meansThe particle population of (a); the sum of the weights is higher than a threshold Thk-meansThe particle group(s) is considered as an estimated target state, and if the particle group(s) is smaller than 0, it is considered that there is no target in the scene at that time.
The first embodiment is as follows:
this example uses MATLAB software version 2014(a) for simulation testing.
Referring to FIG. 2, the five objects shown are set to move, and a two-dimensional motion scene is considered, with the state of each object defined as
Figure BDA0002959829220000115
wherein (xk,yk) and
Figure BDA0002959829220000116
respectively the position and velocity of the object in a cartesian coordinate system.
Position (x)k,yk) In polar coordinate p ═ rmin,rmax]×[θmin,θmax]Within the scene, rmin,rmax and θmin,θmaxMinimum and maximum target ranges and orientations, respectively;
speed of rotation
Figure BDA0002959829220000117
In the region:
Figure BDA0002959829220000118
wherein vmin and vmaxRespectively, a minimum and a maximum target speed.
And (3) evolving the target state according to uniform linear motion:
xk＝Fxk-1+vk
receiving 100 frames of image at a sensor scanning time interval T of 1s, wherein
Figure BDA0002959829220000119
Figure BDA0002959829220000121
Process noise vkObeying a gaussian distribution with a covariance of:
Figure BDA0002959829220000122
noise standard deviation sigmav5m, the probability of survival of the target is ps,k(x)＝0.98。
For the simulation of the target, vmin＝200m/s，vmax800m/s, signal-to-noise ratio of
Figure BDA0002959829220000123
It is given.
For the simulation of radar measurements, rmin＝100km，rmax＝120km，θmin＝-75°，θmax＝75°，Nr＝300，Nθ＝100，σ20.5, noise covariance of
Figure BDA0002959829220000124
B＝150KHz，Te＝6.67×10-5s，Na＝50，λ＝3cm，c＝3×108m/s，Δr＝500m，Δθ＝1.45°。
Attached: the track condition of the five targets of the present embodiment
Figure BDA0002959829220000125
The performance of the evaluation algorithm adopts an optimal sub-mode to allocate distance (OSPA), OSPA measurement can evaluate target number estimation error and target position estimation error of a multi-target filter, and two finite sets X are given as { X ═ X-1,x2,…xm} and Y＝{y1,y2,…ynOSPA is defined as follows:
Figure BDA0002959829220000126
wherein ,dc(X,Y)＝min{c,db(X,Y)}，
Figure BDA0002959829220000131
c is greater than 0 and is used for punishing the estimation deviation of the target number, and p is an order and is used for punishing the multi-target state estimation deviation. In the simulation experiment, p is set to 3 and c is set to 1000. The smaller the OSPA value, the more accurate the target number and state estimation.
Simulation results and analysis: 5 targets are set to do uniform linear motion in a scene, and the original track of the targets is shown in figure 2. In the simulation, the complex likelihood and the square likelihood in the method are compared, and in order to better reflect the effectiveness of the tracking effect of the algorithm, the tracking performance is illustrated by carrying out OSPA error statistics and potential estimation statistics on 50 Monte Carlo experiments.
Referring to fig. 3, OSPA corresponding to the amplitude likelihood and the complex likelihood under swerling0 is compared, and it can be seen from the graph that OSPA of the complex likelihood is lower than the amplitude likelihood from the appearance of the target to the disappearance of the target. When the new target appears, the OSPA will suddenly increase, because the adaptive new algorithm is caused by using the previous measurement, and has a certain delay. As can be seen from fig. 4, the mean potential estimates under the two methods are relatively close. The effect difference between the complex likelihood and the amplitude likelihood is not obvious under the constant amplitude, but the average operation time of the complex likelihood is 139 seconds, the average operation time of the amplitude likelihood is 1281 seconds, and the operation time of the amplitude likelihood is almost 9.22 times of the complex likelihood.
Referring to fig. 5, the OSPA pair comparing the complex likelihood and the amplitude likelihood under the PHD filtering under swerling 1 shows that the estimation of the target location information by the complex likelihood has a good effect than the amplitude likelihood. Please refer to fig. 6, the reason for the too high amplitude likelihood OSPA is mainly that for the estimation of the target potential, the amplitude likelihood estimates more wrong position information in the initial process, and these false detections are mostly at the radar edge, and the target phase information of the amplitude likelihood loss causes that the target maximum potential cannot be reached at the estimation time; the amplitude likelihood estimation under swerling 1 has poor effect. The complex likelihood average run time is 132 seconds and the amplitude likelihood average run time is 347 seconds.
Referring to fig. 7 and 8, under swerling 3 condition, PHD-TBD complex likelihood contrast amplitude likelihood loss is minimal. swerling 3 describes the target characteristics consisting of many weaker scatterers and one particularly strong scatterer. For swerling 3, if the particle weight and infinity are satisfied, the particle state is kept unchanged, and the particle weight is replaced by a number as small as possible, so that the problem that the target track cannot continue due to particle and infinity is solved, but the update of the target state is abandoned, and the estimation of the target number and the estimation of the state are affected. The swerling 3 complex likelihood average running time under PHD is 177 seconds, while the amplitude likelihood average running time is 452 seconds.
Referring to fig. 9 and 10, the amplitude likelihood of 5dB snr under swerling0 can be estimated almost completely incorrectly, while the complex likelihood tracking performance of 5dB is good; the tracking effect of the complex likelihood is not much affected in case of a reduced signal-to-noise ratio.
Referring to fig. 11 and 12, in the case of the waving type swerling 1, decreasing the signal-to-noise ratio may cause the number of targets estimated by the amplitude likelihood to increase at the initial time, while the number of targets estimated and the target position estimated are less affected for the entire time than the complex likelihood.
As can be seen from fig. 13 and fig. 14, the estimation of the number of complex likelihood targets in swerling 3 may cause inaccurate estimation of the number of targets along with the reduction of the signal-to-noise ratio, and may generate a certain missing detection, but the influence of the complex likelihood on the reduction of the signal-to-noise ratio is smaller than the error caused by the amplitude likelihood.
In conclusion, the method can solve the problems of detection and tracking of weak multi-target fluctuation, and provides a self-adaptive target regeneration algorithm based on measurement likelihood under scene division for solving the problem of target regeneration under the condition that the prior distribution information of the regenerated target state is unknown. Two calculation modes of amplitude likelihood and complex likelihood are given, and PHD-TBD multi-target estimation with amplitude fluctuation types of swerling0,1 and 3 is successfully realized. Compared with the amplitude likelihood, the complex likelihood makes up the defect that the amplitude likelihood only considers the measured amplitude information and ignores the phase information in the calculation process, thereby better utilizing the original information of the target. Compared with the complex likelihood and the amplitude likelihood, the method provided by the invention has the advantages that the complex likelihood is superior to the amplitude likelihood in the estimation performance of the target position and the number, and the calculation efficiency is higher. At low signal-to-noise ratios, complex likelihoods can still effectively detect and track an unknown number of weak targets.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. A PHD filtering radar fluctuation weak multi-target based track-before-detect method is characterized by comprising the following steps:
s1: initializing system parameters, and reading original measurement data of a kth-1 moment and a kth moment in a radar receiver;
s2: dividing scenes, and utilizing original measurement data at the moment of k-1 to adapt to a new target in each small scene;
s3: respectively calculating complex likelihood and amplitude likelihood of three amplitude fluctuation types aiming at complex measurement data and square measurement data obtained at the moment k, and giving out SMC (surface Mount device) realization of PHD (phase Shift keying) filtering under amplitude fluctuation;
s4: extracting target states and target numbers according to the posterior information;
s5: and (5) judging whether K is greater than K and is equal to K +1, if yes, finishing the algorithm, and if not, returning to S2.
2. The PHD-filter-based radar fluctuation weak multi-target tracking before detection method according to claim 1, wherein the system parameters include:
sampling interval T, current time K, total target motion time K, and scanning area [ r ] of radar in polar coordinatesmin,rmax]×[θmin,θmax]Measurement data Z in a Radar reception tracking scenek and Zk-1Consider a range and azimuth surveillance radar covering a defined area in polar coordinates, for which the transmitted pulse is assumed to be of bandwidth B and duration TεLinear frequency-modulated signal, speed of light c, distance resolution unit
Figure FDA0002959829210000011
For angles, consider N at the radar receiveraLinear phased array of antennas with spacing of
Figure FDA0002959829210000012
Where λ is the wavelength of the carrier frequency and the angular resolution is
Figure FDA0002959829210000013
3. The PHD-filter-radar-fluctuation-based weak multi-target pre-detection tracking method according to claim 2, wherein scenes are divided, and in the step of self-adapting to new targets in respective small scenes using the raw metrology data at the time k-1:
if N is presentr×NθIf it is larger, the scene N will ber×NθIs divided into
Figure FDA0002959829210000014
A scene, consider generating N within each scenefilterParticles, the number of particles in the whole scene is n1×n2×Nfilter；
Setting a measurement cut-off threshold ThCut offSorting the measurements in each scene in descending order, selecting the intensity above a threshold ThCut offMeasured at a value lower than ThCut offIs regarded as a false detection measurement each timeThe measured position information is (n)r,nθ)；
The position information (n) of each measurementr,nθ) Converting the target position into a planar rectangular coordinate system and recording the target position as (z)x,zy)；
At each (z)x,zy) And generating particles nearby, calculating the likelihood of each particle in the scene, then performing resampling to select the particles with higher weight in the scene, and performing normalization processing on the selected particle weight.
4. The PHD-filtered radar fluctuation-weak multi-target-based track-before-detect method as claimed in claim 3, wherein the step of calculating the complex likelihood and amplitude likelihood of three amplitude fluctuation types respectively for the complex measurement and square measurement data obtained at the time k, and giving the SMC implementation of PHD filtering under amplitude fluctuation is:
calculating the amplitude likelihood when the target does not exist;
respectively calculating amplitude likelihood with amplitude fluctuation types of swerling0,1 and 3;
calculating a complex likelihood when the target is absent;
and respectively calculating the complex likelihood of the amplitude fluctuation types of swerling0,1 and 3.
5. The PHD filtering radar fluctuation-based weak multi-target tracking-before-detection method according to claim 4, wherein at the k-1 moment:
using a set of band weights
Figure FDA0002959829210000021
Particles of (2)
Figure FDA0002959829210000022
Representing the posterior density of the PHD, predicting and updating the set of weighted particles
Figure FDA0002959829210000023
6. The PHD filtering radar based pre-detection tracking method for fluctuating weak multiple targets as claimed in claim 4,
for complex measurement and square measurement, the likelihood of different amplitude fluctuation is different, in the target tracking process, the target amplitude can influence the target echo strength, the target with high echo strength can inhibit the target with low echo strength, and the likelihood higher than the threshold value is considered to be assigned as the highest likelihood.
7. The PHD filtering radar based pre-detection tracking method for fluctuating weak multiple targets as claimed in claim 4,
when the target amplitude fluctuation type is swerling 3, the judgment needs to be carried out after the particle weight is calculated, if the particle weight is infinite, the predicted particle state is kept, the particles are not updated, and the particle weight is assumed to be 0.
8. The PHD-filter-based radar fluctuating weak multi-target tracking method as claimed in claim 5, wherein the step of extracting the target state and the number of targets according to the a posteriori information comprises:
calculating the target number, and resampling samples;
determining updated particle weights
Figure FDA0002959829210000031
And if the sum is more than 0, clustering the resampled particles by using a K-means method, deleting the weight sum and being lower than a threshold Thk-meansThe sum of the weights is higher than a threshold Thk-meansThe particle group(s) is considered as an estimated target state, and if the particle group(s) is smaller than 0, it is considered that there is no target in the scene at that time.
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