CN111679270B - Multipath fusion target detection algorithm under scene with uncertain reflection points - Google Patents

Multipath fusion target detection algorithm under scene with uncertain reflection points Download PDF

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CN111679270B
CN111679270B CN202010456711.5A CN202010456711A CN111679270B CN 111679270 B CN111679270 B CN 111679270B CN 202010456711 A CN202010456711 A CN 202010456711A CN 111679270 B CN111679270 B CN 111679270B
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target
state
reflection point
covariance
measurement
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CN111679270A (en
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唐续
光昌国
王代维
程建
杨阳
董平
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University of Electronic Science and Technology of China
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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
    • 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
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • 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

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  • Radar, Positioning & Navigation (AREA)
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Abstract

The invention discloses a multi-path fusion target detection algorithm under a scene with uncertain reflection points, and belongs to the technical field of radars. The invention estimates the states of the target and the reflection point simultaneously in an iterative way, and uses a batch of data for track initialization in a sliding window way. Each iteration consists of two steps: and (4) predicting and updating. In the prediction stage, the state of the reflection point is predicted through the last iteration estimation state at the last moment, on the basis, the state of the target is estimated through multi-pass grid search global optimal solution, and in the updating stage, the state of the reflection point is re-estimated by using the updated target state. And repeating the steps, wherein the iteration process is based on the given maximum iteration times or judges whether the threshold is exceeded, if the iteration times reach the maximum iteration times or exceed the threshold, the iteration is stopped, and the target position and the position of the reflection point are output. The invention improves the target state estimation precision and effectively detects the low-altitude small target.

Description

Multipath fusion target detection algorithm under scene with uncertain reflection points
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a multi-path fusion target detection algorithm under a scene with uncertain reflection points.
Background
The low-small slow target refers to a small aircraft with low flying height, relatively small volume and low flying speed, and typical low-small slow targets comprise an unmanned aerial vehicle, a model airplane, a paraglider and the like. In recent years, with the development of civil unmanned aerial vehicles in China, the performance of the unmanned aerial vehicles reaches the international first-class level, and the civil unmanned aerial vehicles can be consumed by common people. Meanwhile, some potential safety hazards are brought, for example, small unmanned planes which are not allowed to fly often appear in civil aviation airports, which causes serious influence on normal operation of the airports and even influences take-off and landing of airplanes. In addition, some unmanned aerial vehicles often appear in some activity places, have also seriously influenced the safety guarantee of activity. Therefore, how to effectively manage and control the unmanned aerial vehicle becomes a problem to be solved urgently by the current radar monitoring system.
In order to improve the detection and tracking performance of the target under the low signal-to-noise ratio and high-stray-field scenes, the target information in the measurement received by the sensor should be mined as much as possible in the detection system. In some application scenarios, due to the multipath effect of electromagnetic wave propagation, the sensor can generate multiple target measurements in the same frame in the received echoes. For example, in an urban environment, a high-rise building is visible everywhere, a target is easily shielded for a monitoring system, a visual blind area exists, and electromagnetic wave signals can be directly reflected back to a receiver through the target and can also be reflected back to the receiver through a building when being transmitted, so that the target has multiple transmission paths, and normal detection of the target can be influenced if the electromagnetic wave signals are not processed. In other words, the target signal reflected by other paths is also a part of the target information, and if the part of the target information can be utilized, the target detection performance is inevitably increased. Since the target is moving continuously, the position of the reflection point generally moves along with the movement of the target, and usually, only the approximate position of the building is known, but the specific position of the reflection point in the building is not known.
The existing multi-path-based target detection algorithm assumes that a reflection point is known, and a measurement mode is determined, if the traditional multi-path ML-PMHT (maximum likelihood probability multi-hypothesis tracking) target detection algorithm is used in a scene with unknown reflection points, the target estimation error is increased, false tracks are easy to generate, and the tracking loss rate is high. The existing multi-path ML-PMHT target detection algorithm does not model uncertainty of a reflection point into the algorithm, and measurement errors are increased due to the uncertainty of the initial position of the reflection point, so that the target state obtained through searching and optimizing has a large difference from a real target state, and the log-likelihood ratio (LLR) formed by clutter is easily mistaken as the log-likelihood ratio (LLR) formed by a target, thereby causing false tracks.
Disclosure of Invention
The invention aims to overcome the defect of application of an ML-PMHT algorithm in a multipath environment with uncertain reflection points, and provides a target detection algorithm of maximum likelihood probability multi-hypothesis tracking (ML-PMHT) with high-efficiency multipath information fusion in a scene with uncertain reflection points, in particular a method for detecting a low-altitude small target (such as a small aircraft) based on the multipath characteristics of signals in an urban complex environment and the uncertain propagation characteristics of reflection points. The method of the invention carries out the fusion processing on the multi-path observation information by explicitly modeling the target and the multi-path observation function, thereby detecting the low-altitude small target under the scene of low signal-to-noise ratio, high clutter and uncertain reflection point.
The idea of the method of the invention is to estimate the states of the target and the reflection point simultaneously in an iterative manner. A sliding window approach is used with a batch of data for track initialization. In each iteration, the same measurement set is used. Each iteration consists of two steps: and (4) predicting and updating. In the prediction stage, the state of the reflection point is predicted through the estimation state of the last iteration at the last moment, on the basis, the state of the target is estimated through multi-pass grid search and global optimal solution, and the global optimal of the LLR cannot obtain the real target state because the LLR is calculated by using the estimated reflection point instead of using the position of the real reflection point. In the update phase, the reflection point state is re-estimated using the updated target state. And repeating the steps, wherein the iteration process is based on the given maximum iteration times or judges whether the iteration times exceed the threshold, if the iteration times reach the maximum iteration times or exceed the threshold, the iteration is stopped, and the target position and the position of the reflection point are output. Therefore, the detection of the low-altitude small target under the scene of low signal-to-noise ratio, high clutter and uncertain reflection points in the city is realized.
The technical problem proposed by the invention is solved as follows:
a multipath fusion target detection algorithm under a scene with uncertain reflection points comprises the following steps:
step 1, initializing multipath ML-PMHT algorithm environment parameters:
initializing parameters of the observation environment: monitoring space V, number L of reflection points, initial state of reflection points
Figure BDA0002509472790000021
Represents the mean valueIs composed of
Figure BDA0002509472790000022
Covariance of
Figure BDA0002509472790000026
1 is equal to or more than L, each reflection point corresponds to a path, and the prior probability of measuring the target n through the propagation path L is pin，lMeasuring the prior probability pi from clutter00The current iteration time Iter is 1, and the maximum iteration time is Imax;
the parameter vectors in the target initialization scenario are respectively expressed as:
Figure BDA0002509472790000023
Figure BDA0002509472790000024
Figure BDA0002509472790000025
wherein k is the sampling time number of batch processing, and k is more than or equal to 1 and less than or equal to Nw，NwFor batch length, X is NwTarget state parameter, X, at each instantfIs NwA state parameter of a reflection point at each moment, Z being NwA measurement set of individual moments;
the state vector of the target at time k is represented as:
Xk＝{x1，k，...，xn，k，...，xN，k}n＝1，...，N
the reflection point state vector at time k is represented as:
Figure BDA0002509472790000031
the set of measurements received at time k is represented as:
Figure BDA0002509472790000032
wherein x isn，kThe state of the nth target at the moment k, N is the number of targets,
Figure BDA0002509472790000033
represents the state of the ith reflection point at the time k, L is the number of the reflection points, zk，jRepresents the jth measurement, m, received by sensor k at timekThe number of the measurement received by the sensor k at the moment is represented;
the motion process of the target and the observation equations for different propagation paths are respectively expressed as:
xn，k＝Fn，kxn，k-1+vn，k
Figure BDA0002509472790000034
wherein, Fn，kIs a target motion matrix, xn，0Is the initial state of the motion of the nth object, hlIs xn，kAn observation function via path l; z is a radical ofn，k，lIs xn，kTarget measurements generated by path l; v. ofn，kAnd ωn，l，kThe noise of the target process and the observation noise are respectively Gaussian white noise with the mean value of zero, and the covariance matrixes are respectively Qn，kAnd Rn，l，k；
Step 2, predicting the state and variance of the reflection point:
Figure BDA0002509472790000035
Figure BDA0002509472790000036
wherein,
Figure BDA0002509472790000037
represents the predicted state of the ith reflection point at time k, Fl，kMotion matrix, v, representing reflection pointsl，kRepresenting the process noise of the reflection point, is zero mean Gaussian white noise, and has a covariance matrix of
Figure BDA0002509472790000038
Representing the predicted state covariance of the reflection point/at time k,
Figure BDA0002509472790000039
represents the initial predicted state covariance of the reflection point l;
Figure BDA00025094727900000310
is a Jacobian matrix of the measurement model to the state of the reflection points, wherein
Figure BDA00025094727900000311
To represent
Figure BDA00025094727900000312
About
Figure BDA00025094727900000313
The superscript T represents transposition;
and 3, searching all possible target states according to the predicted reflecting point state:
step 3-1, making N 'equal to 1, the target state set X' is a null vector,
Figure BDA00025094727900000314
step 3-2, searching a single-target LLR global maximum;
Figure BDA00025094727900000315
Figure BDA00025094727900000316
wherein,
Figure BDA0002509472790000041
pl[zk，j|xn′，k]representing the gaussian probability of being centered on the nth' target through path l;
Figure BDA0002509472790000042
wherein,
Figure BDA0002509472790000043
representing a Gaussian probability density function, Gaussian variable zk，jHas a mean value of
Figure BDA0002509472790000044
Covariance of Rn′，l，kAnd has:
Figure BDA0002509472790000045
step 3-3, judging the global maximum of the single-target LLR
Figure BDA0002509472790000046
Whether the detection threshold is larger than the detection threshold or not, if so, confirming
Figure BDA0002509472790000047
In order to achieve the new objective,
Figure BDA0002509472790000048
that is to say, the
Figure BDA0002509472790000049
Adding the vector X 'into the vector X', and turning to the step 3-4; otherwise, ending the detection process and turning to the step 4;
step 3-4. from the measurement set
Figure BDA00025094727900000410
Removing the measurement associated with the confirmed new target, wherein the removal is based on the measurement with the highest posterior association probability of the target to be removed;
ML-PMHT posterior association probability wj，n′，l，kThe calculation formula is as follows:
Figure BDA00025094727900000411
step 3-5, making N '═ N' +1, and going to step 3-2; at the moment, the searching state space is 4N ', and as (N ' -1) targets are confirmed, the searched 4(N ' -1) dimensions are not required to be searched in the new searching process, so that the unknown 4-dimensional state is only required to be searched in the new searching stage;
step 4, updating the state of the reflection point:
step 4-1. calculate the measurement z at time kk，jThe posterior probability of the nth target is derived through the l path:
Figure BDA00025094727900000412
step 4-2, calculating comprehensive measurement of each target under each path
Figure BDA00025094727900000413
And integrated covariance
Figure BDA00025094727900000414
Figure BDA00025094727900000415
Figure BDA0002509472790000051
And 4-3, stacking the Jacobian matrix, the comprehensive measurement and the comprehensive measurement covariance under different paths respectively:
stacking Jacobian matrices:
Figure BDA0002509472790000052
stacking comprehensive measurement:
Figure BDA0002509472790000053
stack measurement covariance:
Figure BDA0002509472790000054
wherein diag represents a diagonalized matrix;
and 4, executing an extended Kalman smoothing algorithm on the reflection points:
step 4-4-1. Forward Filtering
For k 1: Nw，
Figure BDA0002509472790000055
Wherein,
Figure BDA0002509472790000056
for the first reflection point state at time k predicted from the reflection point state at time k-1, FfIs a matrix of the motion of the reflecting points,
Figure BDA0002509472790000057
the state of the first reflection point at the moment k-1;
Figure BDA0002509472790000058
Figure BDA0002509472790000059
wherein,
Figure BDA00025094727900000510
for the measurement obtained by the l-th reflection point for the n' -th new target,
Figure BDA00025094727900000511
stacking to obtain a comprehensive measurement
Figure BDA00025094727900000512
Figure BDA00025094727900000513
Wherein,
Figure BDA00025094727900000514
to predict the predicted ith reflection point covariance,
Figure BDA00025094727900000515
is the first reflection point covariance at time k-1;
Figure BDA00025094727900000516
wherein,
Figure BDA00025094727900000517
is the Kalman gain;
Figure BDA00025094727900000518
wherein,
Figure BDA00025094727900000519
the covariance of the first reflection point after Kalman filtering updating is shown, and I is an identity matrix;
Figure BDA0002509472790000061
wherein,
Figure BDA0002509472790000062
the state of the first reflection point after Kalman filtering updating;
step 4-4-2. backward smoothing
For k ═ Nw-1∶1，
Figure BDA0002509472790000063
Wherein,
Figure BDA0002509472790000064
is the smoothing gain;
Figure BDA0002509472790000065
wherein,
Figure BDA0002509472790000066
the state of the first reflection point after the k moment is smoothed;
Figure BDA0002509472790000067
wherein,
Figure BDA0002509472790000068
the covariance of the first reflection point after the k moment is smoothed;
step 5, enabling the Iter to be equal to the Iter +1, judging whether the Iter is larger than Imax, if so, turning to the step 6, otherwise, turning to the step 2;
and 6, outputting the target state set X' and the state and covariance of the reflection point.
The invention has the beneficial effects that:
the invention effectively reduces the calculation complexity of the association between the measurement and the target by using the ML-PMHT algorithm characteristic, effectively utilizes the measurement information of a plurality of paths and improves the estimation precision of the target state for the signal multipath and the uncertain propagation characteristic of the reflection point in the urban complex environment. The method can effectively detect the low-altitude small target (such as a small aircraft).
Drawings
FIG. 1 is a geometric diagram of the positions of a target and a sensor in a detection scene of an urban aircraft in an embodiment;
FIG. 2 is a time delay observation clutter map of 10 sampling moments of two targets in a monitored space in an embodiment;
FIG. 3 is a Doppler observation clutter map of 2 two targets in the monitored space at 10 sampling moments in an embodiment;
FIG. 4 is an iterative error plot of target and reflection point state estimates in an embodiment;
FIG. 5 is a graph of the estimated track for the target state in 100 Monte Carlo experiments.
Detailed Description
The invention is further described below with reference to the figures and examples.
The embodiment provides a multipath fusion target detection algorithm under a scene with uncertain reflection points, which comprises the following steps:
step 1, initializing environmental parameters and algorithm parameters, wherein in a detection scene of an urban aircraft, a position geometric diagram of a target and a sensor is shown in fig. 1, in the scene, 2 reflection points, 1 transmitter, 1 receiver and 2 targets exist, that is, L is 2, N is 2, L is 1, 2, and N is 1, 2, and in the scene, a single target generates 3 propagation paths according to an electromagnetic wave propagation sequence:
in the detection scene of the urban small unmanned aerial vehicle, a receiver base station is fixed at 0m, 0m to collect signals reflected by buildings and targets, and a transmitter base station is fixed at minus 500m, 1000m, and the invention belongs to an external radiation source radar and adopts a 4G base station as a transmitting base station.
Doppler observation space Vγ500Hz, Doppler standard deviation σγ＝2Hz, time-delayed observation space V r10 mus, monitoring space VγVrStandard deviation of time delay σr0.03 mu s, false track alarm rate PFA0.02, SNR of 7dB per path, assuming uniform distribution of spurs within a cell, and a batch length N w10, and averaging the number of clutter N at each time instant λ10. The time delay observation clutter maps of 10 sampling moments of 2 two targets in the monitored space are shown in figure 2, and the Doppler observation clutter maps are shown in figure 3.
The interval delta T between sampling moments of the radar system is 2s, the total simulation duration is 10 moments, the maximum iteration time Imax in each batch processing is 10 times, and the current iteration time Iter is 1.
In the sampling process, the motion vectors of the initial states of the 2 targets are respectively:
x1，1＝[-104m 21m/s 1310m -9m/s]
x2，1＝[-100m 20m/s 500m 9m/s]
detecting the existence of two reflection points in the space, the initial state of the reflection point 1
Figure BDA0002509472790000071
Wherein
Figure BDA0002509472790000072
Initial state of reflection point 2
Figure BDA0002509472790000073
Wherein
Figure BDA0002509472790000074
The prior probability of the measurement coming from the target n through the propagation path l is pin，l0.02, the prior probability pi of the measurement originating from clutter00＝0.96。
Step 2, predicting the state and variance of the reflection point:
Figure BDA0002509472790000075
Figure BDA0002509472790000076
wherein,
Figure BDA0002509472790000077
represents the predicted state of the ith reflection point at time k, Fl，kMotion matrix, v, representing reflection pointsl，kRepresenting the process noise of the reflection point, is zero mean Gaussian white noise, and has a covariance matrix of
Figure BDA0002509472790000078
Representing the predicted state covariance of the reflection point/at time k,
Figure BDA0002509472790000079
represents the initial predicted state covariance of the reflection point l;
Figure BDA00025094727900000710
is a Jacobian matrix of the measurement model to the state of the reflection points, wherein
Figure BDA00025094727900000711
To represent
Figure BDA00025094727900000712
About
Figure BDA00025094727900000713
The superscript T represents transposition;
step 3, searching all possible target states according to the predicted reflecting point state to obtain
Figure BDA0002509472790000081
State of new target, n ═ 1, 2;
step 4, updating the state of the reflection point to obtain the first reflection point state after the k moment is smoothed
Figure BDA0002509472790000082
Covariance of first reflection point after smoothing at time k
Figure BDA0002509472790000083
Step 5, enabling the Iter to be equal to the Iter +1, judging whether the Iter is larger than Imax, if so, turning to the step 6, otherwise, turning to the step 2;
and 6, outputting the target state set X' and the state and covariance of the reflection point.
Fig. 4 gives an iterative error map of the target and reflection point state estimates. It can be seen that the estimation errors of the target and the reflection point become smaller and smaller with the increase of the iteration times, after 4 iterations, the estimation errors of the target and the reflection point are basically converged, and the errors in the subsequent iterations fluctuate within a small range, so that the iterative algorithm is effective. The method is characterized in that the initial reflection point error is large in the iteration process, so that the estimated target state error is large, the state of the reflection point is updated through the estimated target state along with the iteration, the updated state of the reflection point is used for being brought into a likelihood formula, the target state is estimated more accurately, the estimated position of the reflection point is continuously close to the position of a real reflection point after several iterations, and the purpose of improving the estimation accuracy is achieved.
In fig. 5, the blue solid line indicates the target initialization result of 100 times of multi-target detection under the scenes of low signal-to-noise ratio, high clutter and uncertain reflection points, and the number of threshold-crossing times of the statistical result on the two targets is 100. The result shows that the initialization result is very close to the real track of the target, and the problem of target detection in the scene is solved.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and are not limited, and all equivalent changes and modifications made in the claims of the present invention should be covered by the present invention.

Claims (1)

1. A multipath fusion target detection algorithm under a scene with uncertain reflection points is characterized by comprising the following steps:
step 1, initializing multipath ML-PMHT algorithm environment parameters:
initializing parameters of the observation environment: monitoring space V, number L of reflection points, initial state of reflection points
Figure FDA0002509472780000011
Figure FDA0002509472780000012
Represents a mean value of
Figure FDA0002509472780000013
Covariance of
Figure FDA0002509472780000014
1 is equal to or more than L, each reflection point corresponds to a path, and the prior probability of measuring the target n through the propagation path L is pin,lMeasuring the prior probability pi from clutter00The current iteration time Iter is 1, and the maximum iteration time is Imax;
the parameter vectors in the target initialization scenario are respectively expressed as:
Figure FDA0002509472780000015
Figure FDA0002509472780000016
Figure FDA0002509472780000017
wherein k is the sampling time number of batch processing, and k is more than or equal to 1 and less than or equal to Nw，NwFor batch length, X is NwTarget state parameter, X, at each instantfIs NwA state parameter of a reflection point at each moment, Z being NwA measurement set of individual moments;
the state vector of the target at time k is represented as:
Xk＝{x1,k,...,xn,k,...,xN,k}n＝1,...,N
the reflection point state vector at time k is represented as:
Figure FDA0002509472780000018
the set of measurements received at time k is represented as:
Figure FDA0002509472780000019
wherein x isn,kThe state of the nth target at the moment k, N is the number of targets,
Figure FDA00025094727800000110
represents the state of the ith reflection point at the time k, L is the number of the reflection points, zk,jRepresents the jth measurement, m, received by sensor k at timekThe number of the measurement received by the sensor k at the moment is represented;
the motion process of the target and the observation equations for different propagation paths are respectively expressed as:
xn,k＝Fn,kxn,k-1+νn,k
Figure FDA00025094727800000111
wherein, Fn,kIs a target motion matrix, xn,0Is the initial state of the motion of the nth object, hlIs xn,kAn observation function via path l; z is a radical ofn,k,lIs xn,kTarget measurements generated by path l; v isn,kAnd ωn,l,kThe noise of the target process and the observation noise are respectively Gaussian white noise with the mean value of zero, and the covariance matrixes are respectively Qn,kAnd Rn,l,k；
Step 2, predicting the state and variance of the reflection point:
Figure FDA0002509472780000021
Figure FDA0002509472780000022
wherein,
Figure FDA0002509472780000023
represents the predicted state of the ith reflection point at time k, Fl,kMotion matrix, v, representing reflection pointsl,kRepresenting the process noise of the reflection point, is zero mean Gaussian white noise, and has a covariance matrix of
Figure FDA0002509472780000024
Figure FDA0002509472780000025
Representing the predicted state covariance of the reflection point/at time k,
Figure FDA0002509472780000026
represents the initial predicted state covariance of the reflection point l;
Figure FDA0002509472780000027
is a Jacobian matrix of the measurement model to the state of the reflection points, wherein
Figure FDA0002509472780000028
To represent
Figure FDA0002509472780000029
About
Figure FDA00025094727800000210
The superscript T represents transposition;
and 3, searching all possible target states according to the predicted reflecting point state:
step 3-1, making N 'equal to 1, the target state set X' is a null vector,
Figure FDA00025094727800000211
step 3-2, searching a global maximum value of the single-target LLR;
Figure FDA00025094727800000212
Figure FDA00025094727800000213
wherein,
Figure FDA00025094727800000214
pl[zk,j|xn',k]representing the gaussian probability of being centered on the nth' target through path l;
Figure FDA00025094727800000215
wherein,
Figure FDA00025094727800000216
representing a Gaussian probability density function, Gaussian variable zk,jHas a mean value of
Figure FDA00025094727800000217
Covariance of Rn',l,kAnd has:
Figure FDA00025094727800000218
step 3-3, judging the global maximum of the single-target LLR
Figure FDA00025094727800000219
Whether the detection threshold is larger than the detection threshold or not, if so, confirming
Figure FDA00025094727800000220
In order to achieve the new objective,
Figure FDA00025094727800000221
that is to say, the
Figure FDA00025094727800000222
Adding the vector X 'into the vector X', and turning to the step 3-4; otherwise, ending the detection process and turning to the step 4;
step 3-4. from the measurement set
Figure FDA00025094727800000223
Removing the measurement associated with the confirmed new target, wherein the removal is based on the measurement with the highest posterior association probability of the target to be removed;
ML-PMHT posterior association probability wj,n',l,kThe calculation formula is as follows:
Figure FDA0002509472780000031
step 3-5, making N '═ N' +1, and going to step 3-2;
step 4, updating the state of the reflection point:
step 4-1. calculate the measurement z at time kk,jThe posterior probability of the nth target is derived through the l path:
Figure FDA0002509472780000032
step 4-2, calculating comprehensive measurement of each target under each path
Figure FDA0002509472780000033
And integrated covariance
Figure FDA0002509472780000034
Figure FDA0002509472780000035
Figure FDA0002509472780000036
And 4-3, stacking the Jacobian matrix, the comprehensive measurement and the comprehensive measurement covariance under different paths respectively:
stacking Jacobian matrices:
Figure FDA0002509472780000037
stacking comprehensive measurement:
Figure FDA0002509472780000038
stack measurement covariance:
Figure FDA0002509472780000039
wherein diag represents a diagonalized matrix;
and 4, executing an extended Kalman smoothing algorithm on the reflection points:
step 4-4-1. Forward Filtering
For k 1: Nw，
Figure FDA00025094727800000310
Wherein,
Figure FDA0002509472780000041
for the first reflection point state at time k predicted from the reflection point state at time k-1, FfIs a matrix of the motion of the reflecting points,
Figure FDA0002509472780000042
the state of the first reflection point at the moment k-1;
Figure FDA0002509472780000043
Figure FDA0002509472780000044
wherein,
Figure FDA0002509472780000045
for the measurement obtained by the l-th reflection point for the n' -th new target,
Figure FDA0002509472780000046
stacking to obtain a comprehensive measurement
Figure FDA0002509472780000047
Figure FDA0002509472780000048
Wherein,
Figure FDA0002509472780000049
to predict the predicted ith reflection point covariance,
Figure FDA00025094727800000410
is the first reflection point covariance at time k-1;
Figure FDA00025094727800000411
wherein,
Figure FDA00025094727800000412
is the Kalman gain;
Figure FDA00025094727800000413
wherein,
Figure FDA00025094727800000414
the covariance of the first reflection point after Kalman filtering updating is shown, and I is an identity matrix;
Figure FDA00025094727800000415
wherein,
Figure FDA00025094727800000416
the state of the first reflection point after Kalman filtering updating;
step 4-4-2. backward smoothing
For k ═ Nw-1:1，
Figure FDA00025094727800000417
Wherein,
Figure FDA00025094727800000418
is the smoothing gain;
Figure FDA00025094727800000419
wherein,
Figure FDA00025094727800000420
the state of the first reflection point after the k moment is smoothed;
Figure FDA00025094727800000421
wherein,
Figure FDA00025094727800000422
the covariance of the first reflection point after the k moment is smoothed;
step 5, enabling the Iter to be equal to the Iter +1, judging whether the Iter is larger than Imax, if so, turning to the step 6, otherwise, turning to the step 2;
and 6, outputting the target state set X' and the state and covariance of the reflection point.
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