CN110988833B - Weak target detection and tracking method - Google Patents

Weak target detection and tracking method Download PDF

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CN110988833B
CN110988833B CN201911148279.7A CN201911148279A CN110988833B CN 110988833 B CN110988833 B CN 110988833B CN 201911148279 A CN201911148279 A CN 201911148279A CN 110988833 B CN110988833 B CN 110988833B
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state information
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value
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CN110988833A (en
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胡居荣
祝怡翔
周寒瑜
陆龙
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Hohai University HHU
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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
    • 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
    • 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
    • G01S13/006—Theoretical aspects
    • 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
    • G01S7/414—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

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Abstract

The invention discloses a weak target detection and tracking method based on weighted dynamic programming and Kalman filtering, which utilizes multi-frame data obtained by a sensor to accumulate energy by using a dynamic programming algorithm and selects a path with the maximum energy as a predicted flight path, thereby solving the problem of huge calculated amount caused by adopting an exhaustion method. And when energy accumulation is carried out, weighting processing is carried out by adopting a weighting function, and the zero position of the weighting function is determined by combining with a predicted value given by Kalman filtering. The dynamic programming algorithm after the weighting function and the Kalman filtering processing can effectively solve the energy diffusion problem in the traditional dynamic programming algorithm, so that the accuracy of establishing the flight path is improved.

Description

Weak target detection and tracking method
Technical Field
The invention relates to a weak target detection and tracking method, and belongs to the technical field of target detection and target tracking.
Background
The tracking algorithm before detection is an algorithm which is mainly provided for solving the problem of detection and tracking of a weak target under a clutter background. The algorithm utilizes the sensor to scan for multiple times to obtain data containing noise and targets, joint processing is carried out on the data, and multiple groups of data are fully utilized, so that the weak targets are detected and tracked. In order to implement the pre-detection tracking algorithm, various methods have been proposed, such as a pre-detection tracking algorithm based on particle filtering, a pre-detection tracking algorithm based on dynamic programming, a pre-detection tracking algorithm based on hough transform, and the like.
The pre-detection tracking algorithm based on dynamic programming is an optimization algorithm of an exhaustive method, lists all possible paths, accumulates energy along the paths, and considers that the value obtained by accumulating the energy along the real track is the largest, so that the path with the larger energy accumulation value is more likely to be the real track. The dynamic programming algorithm can effectively reduce the calculated amount and avoid the defect that the calculated amount of an exhaustion method increases exponentially.
Although the pre-detection tracking algorithm based on dynamic programming can greatly reduce the calculation amount compared with an exhaustive method, the traditional dynamic programming algorithm does not limit the range of energy accumulation and does not consider the weight, so that the method has a more serious energy diffusion problem, and further more false tracks are generated.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a weak target detection and tracking method.
In order to solve the technical problem, the invention provides a weak target detection and tracking method, which comprises the steps of obtaining the measured value of each resolution unit in an echo signal at the moment k, and obtaining target state information at the echo moment according to all the measured values at the moment;
initializing a value function and target state information at the moment k-1, wherein the value function represents the accumulated value of the echo signal;
updating the value function and the target state information when k is 2 according to the initialized value function and the target state information;
updating the target state information when k is 3 according to the value function when k is 2, and calculating the motion speed of the target when k is 2 by using the target state information when k is 3 and the target state information when k is 2;
when k is 3, updating the target state information of the current moment through the value function of the previous moment, obtaining the position information of the previous moment through the target state information of the previous moment, processing the motion speed and the position information of the target obtained at the previous moment by adopting a Kalman filtering and direction weighting method, and updating the value function of the current moment;
when k is larger than or equal to 4, a recursion formula is executed, and until the last frame data is processed, the recursion formula sequentially comprises the following steps: updating the record of the target state information at the current moment, estimating the target motion speed at the previous moment, performing Kalman filtering and direction weighting according to the target state information and the target motion speed at the previous moment, updating the search range of the target state information at the next moment, and updating the value function at the current moment;
intercepting the threshold value of the value function to obtain all the values meeting the preset threshold value condition
Figure GDA0003521405680000021
To the above
Figure GDA0003521405680000022
And (4) tracing back the flight path by using the record of the target state information to obtain the flight path obtained at the kth moment.
Further, the measurement value is expressed as:
Figure GDA0003521405680000023
wherein s isij(k) Representing the echo signal of the target, nij(k) Representing a random noise signal, said noise signal obeying a standard normal distribution and, for different instants k, a random noise signal nij(k) Independently distributed, detected target state information is represented as xk(x, y) which contains the position of the object, xk(x, y) is for zij(k) The position information obtained after signal processing is denoted as xk＝F(zij(k) I and j respectively represent the position coordinates of the resolution cell
Further, the value function and the target state information at the time when the initialization k is 1 are respectively expressed as:
Figure GDA0003521405680000031
wherein
Figure GDA0003521405680000032
Indicating an empty set.
Further, when k is 2, the value function is updated: q (x)2)＝max[q(x1)]+zij(2) Then, the target state information is updated: r (2) ═ argmax [ q (x) ]1)]。
Further, when k is 3, the target state information is updated first:
R(3)＝argmax[q(x2)]
and estimating the moving speed of the target when k is 2 by combining the target state information at the previous moment:
Figure GDA0003521405680000033
wherein, vx2Denotes the speed in the x direction, vy, when k is 22Denotes a speed in the y direction when k is 2, x (-) denotes an x coordinate of the extraction · y (-) denotes a y coordinate of the extraction · TTime of flightRepresenting two framesThe time interval in between.
Further, when k is 3, a kalman filter algorithm is executed to predict the target position when k is 3:
P(2)＝E(4)
Figure GDA0003521405680000034
Figure GDA0003521405680000035
Figure GDA0003521405680000036
Figure GDA0003521405680000037
wherein X2 denotes an initial state quantity, P (2) an initial covariance matrix, E (4) denotes a 4-order identity matrix, A denotes a state transition matrix, B denotes an external control matrix, T denotes a matrix transpose, J denotes an external control quantity,
Figure GDA0003521405680000041
denotes a covariance matrix prediction value when K is 3, Q denotes a process noise covariance matrix, S denotes innovation, H denotes an observation matrix, R denotes an observation noise covariance matrix, K denotes a gain,
Figure GDA0003521405680000042
represents the estimated motion velocity and position information of the target at time k-3, where x' (x)3)、y'(x3)、vx'3、vy'3Is x (x)3)、 y(x3)、vx3、vy3The predicted value of (2);
updating the zero position of the directional weighting function, wherein the directional weighting function is:
Figure GDA0003521405680000043
search range D of update status information:
D＝{x|vminT＜|x-x2|＜vmaxt }, said vmaxAnd vminMaximum velocity and maximum velocity of the object movement
Small velocity, x representing all the positions of the targets to be detected in the search area D, x2Represents the determined target position when k is 2;
update k is a function of the value at time 3:
q(x3)＝max[w(θ)q(x2)]+zij(3)
wherein F (z)ij(3))∈D。
Further, when k is larger than or equal to 4, the following steps are executed in a circulating mode until the processing of the last frame data is finished:
(1) and updating the record of the state information at the moment k:
R(k)＝argmax[q(xk-1)]
wherein q (x)k-1) A value function representing a last time instant;
(2) estimating the speed:
Figure GDA0003521405680000051
(3) performing Kalman filtering on the record of the target state information at the current moment:
Figure GDA0003521405680000052
Figure GDA0003521405680000053
Figure GDA0003521405680000054
Figure GDA0003521405680000055
Figure GDA0003521405680000056
Figure GDA0003521405680000057
wherein X (k-1) represents a state quantity at the time of k-1,
Figure GDA0003521405680000058
represents the predicted value of the target state information at the time k-1, P (k-1) represents the covariance matrix at the time k-1,
Figure GDA0003521405680000059
represents a covariance matrix predicted value at the time k-1, E (4) represents an identity matrix of order 4, A represents a state transition matrix, B represents an external control matrix, T represents a matrix transposition, J represents an external control quantity,
Figure GDA00035214056800000510
denotes the covariance matrix prediction value at time K, Q denotes the process noise covariance matrix, S denotes innovation, H denotes the observation matrix, R denotes the observation noise covariance matrix, K denotes gain,
Figure GDA00035214056800000511
indicating the predicted value of the state at time k,
Figure GDA00035214056800000512
represents the observed value at time k-1;
(4) directional weighting:
Figure GDA00035214056800000513
where θ is the predicted azimuth and (x)k-1),y(xk-1))、(x'(xk),y'(xk) Angle of the line connecting the two points;
(5) updating the search range of the next state information:
D＝{x|vminT＜|x-xk-1|＜vmaxT}
(6) update value function:
q(xk)＝max[w(θ)q(xk-1)]+zij(k)
wherein z isij(k)∈D。
Further, threshold interception is carried out to obtain all the states of the Mth moment meeting the following conditions
Figure GDA0003521405680000061
Figure GDA0003521405680000062
Wherein V is a threshold value set according to a certain condition, and M is the total frame number.
Further, satisfy all of Mth frame
Figure GDA0003521405680000063
Of the condition
Figure GDA0003521405680000064
And performing track backtracking by using the record of the state information, wherein the track obtained at the kth moment is recorded as TkThe method comprises the following steps:
Figure GDA0003521405680000065
wherein:
Figure GDA0003521405680000066
the invention achieves the following beneficial effects:
the invention solves the problem of huge calculation amount caused by adopting an exhaustion method; when energy accumulation is carried out, weighting processing is carried out by adopting a weighting function, and the zero position of the weighting function is determined by combining a predicted value given by Kalman filtering; the dynamic programming algorithm after the weighting function and the Kalman filtering processing can effectively solve the energy diffusion problem in the traditional dynamic programming algorithm, thereby improving the accuracy of track establishment.
Detailed Description
The invention is further described below. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
A weak target detection and tracking method comprises the following steps:
(1) the echo signal contains N2A resolution unit for recording the measured value of each resolution unit as zij(k) The measured values of all resolution cells at time k form a matrix, which is recorded as:
Z(k)＝{zij(k)}
(1)
wherein i is more than or equal to 0, j is more than or equal to N, zij(k) To resolve the measurement in cell (i, j), it can be expressed as:
Figure GDA0003521405680000071
wherein s isij(k) Representing the echo signal of the target, nij(k) Representing a random noise signal. It is assumed here that the noise signal follows a standard normal distribution and that for different time instants k, a random noise signal nij(k) Independently and equally distributed. Let the detected target state information be xk(x, y) which contains the position of the object, xk(x, y) is for zij(k) The position information obtained after signal processing is denoted as xk＝F(zij(k))。
(2) Determining the maximum velocity v of the movement of an objectmaxAnd minimum velocity vminAnd constructing a value function and a state when k is 1Recording of information, and initializing all of it:
Figure GDA0003521405680000072
(3) when k is 2, updating the value function of each state information to be searched:
q(x2)＝max[q(x1)]+zij(2)
(4)
the record of status information is then updated:
Figure GDA0003521405680000073
(4) when k is 3, firstly updating the record of the state information:
Figure GDA0003521405680000081
and combining the moving speed of the target when the last state position estimation k is 2:
Figure GDA0003521405680000082
(5) when k is 3, from the obtained x2And vx2,vy2Prediction of x using Kalman Filter Algorithm3And corresponding vx3,vy3. Firstly, initializing various parameters of a Kalman filtering algorithm: set its state transition matrix
Figure GDA0003521405680000083
External control matrix
Figure GDA0003521405680000084
Observation matrix
Figure GDA0003521405680000085
Observing a noise covariance matrix
Figure GDA0003521405680000086
Process noise covariance matrix
Figure GDA0003521405680000087
Covariance matrix
Figure GDA0003521405680000088
Initial state quantity
Figure GDA0003521405680000089
External control quantity
Figure GDA00035214056800000810
Then a filtering algorithm is executed:
X(2)＝X2,P(2)＝E(4) (8)
Figure GDA00035214056800000811
Figure GDA0003521405680000091
Figure GDA0003521405680000092
Figure GDA0003521405680000093
here, the predicted value of X3 was obtained
Figure GDA0003521405680000094
It can be expressed as:
Figure GDA0003521405680000095
where x' (x)3)、y'(x3)、vx'3、vy'3Is x (x)3)、y(x3)、vx3、vy3The predicted value of (2).
Using (x' (x)3),y'(x3) And (x)3),y(x3) Two points) update the zero point of the directional weighting function, w (θ) being:
Figure GDA0003521405680000096
because the time interval T between two frames is extremely short, the target can only move forwards and can not return within the time T, and therefore the value of w (theta) is zero when the angle is more than 90 degrees and less than or equal to 180 degrees. The kalman filter gives a predicted value (x' (x) when k is 33),y'(x3) Therefore, the target is considered to be along the line segment (x' (x))3),y'(x3))-(x(x2),y(x2) The likelihood of directional motion is greatest, i.e., θ is defined as the predicted azimuth and (x' (x))3),y'(x3))、(x(x2),y(x2) W (θ) is the largest when θ is 0.
Updating a search range D of state information, D ═ x | vminT＜|x-x2|＜vmaxT}，
Finally, the update value function:
q(x3)＝max[w(θ)q(x2)]+zij(3) (14)
wherein F (z)ij(3))∈D
(6) When k is more than or equal to 4, the following steps are executed in a circulating way until the processing of the last frame data is finished. Write the step as recursive:
(1) recording of update status information:
Figure GDA0003521405680000101
(2) estimating the speed:
Figure GDA0003521405680000102
(3) kalman filtering:
Figure GDA0003521405680000103
Figure GDA0003521405680000104
Figure GDA0003521405680000105
Figure GDA0003521405680000106
Figure GDA0003521405680000107
Figure GDA0003521405680000108
wherein X (k-1) represents a state quantity at the time of k-1,
Figure GDA0003521405680000109
represents the predicted value of the target state information at the time k-1, P (k-1) represents the covariance matrix at the time k-1,
Figure GDA00035214056800001010
represents a covariance matrix predicted value at the time k-1, E (4) represents an identity matrix of order 4, A represents a state transition matrix, B represents an external control matrix, T represents a matrix transposition, J represents an external control quantity,
Figure GDA00035214056800001011
representing coordination of time kThe variance matrix predictor, Q represents the process noise covariance matrix, S represents innovation, H represents the observation matrix, R represents the observation noise covariance matrix, K represents gain,
Figure GDA00035214056800001012
indicating the predicted value of the state at time k,
Figure GDA0003521405680000111
represents the observed value at time k-1;
(4) directional weighting:
Figure GDA0003521405680000112
where θ is the predicted azimuth and (x)k-1),y(xk-1))、(x'(xk),y'(xk) Angle between the two points.
(5) Updating the search range of the next state information:
D＝{x|vminT＜|x-xk-1|＜vmaxT} (24)
(6) update value function:
q(xk)＝max[w(θ)q(xk-1)]+zij(k) (25)
wherein z isij(k)∈D。
(7) Intercepting a threshold value to find out all the states of the Mth moment meeting the following conditions
Figure GDA0003521405680000113
Figure GDA0003521405680000114
Wherein V is a threshold value set according to a certain condition, and M is the total frame number.
(8) Satisfy all of the Mth frame
Figure GDA0003521405680000115
Of the condition
Figure GDA0003521405680000116
And performing track backtracking by using the record of the state information, wherein the track obtained at the kth moment is recorded as TkThe method comprises the following steps:
Figure GDA0003521405680000117
wherein:
Figure GDA0003521405680000118
the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (4)

1. A weak target detection and tracking method is characterized in that,
acquiring the measured value of each resolution unit in the echo signal at the moment k, and acquiring target state information at the echo moment according to all the measured values at the moment;
initializing a value function and target state information at the moment k-1, wherein the value function represents the accumulated value of the echo signal;
updating the value function and the target state information when k is 2 according to the initialized value function and the target state information;
updating the target state information when k is 3 according to the value function when k is 2, and calculating the motion speed of the target when k is 2 by using the target state information when k is 3 and the target state information when k is 2;
when k is 3, updating the target state information of the current moment through the value function of the previous moment, obtaining the position information of the previous moment through the target state information of the previous moment, processing the motion speed and the position information of the target obtained at the previous moment by adopting a Kalman filtering and direction weighting method, and updating the value function of the current moment;
when k is larger than or equal to 4, a recursion formula is executed, and until the last frame data is processed, the recursion formula sequentially comprises the following steps: updating the record of the target state information at the current moment, estimating the target motion speed at the previous moment, performing Kalman filtering and direction weighting according to the target state information and the target motion speed at the previous moment, updating the search range of the target state information at the next moment, and updating the value function at the current moment;
intercepting the threshold value of the value function to obtain all the values meeting the preset threshold value condition
Figure FDA0003521405670000011
To the above
Figure FDA0003521405670000012
Tracing back the flight path by using the record of the target state information to obtain the flight path obtained at the kth moment;
the measurement values are expressed as:
Figure FDA0003521405670000013
wherein s isij(k) Representing the echo signal of the target, nij(k) Representing a random noise signal, said noise signal obeying a standard normal distribution and, for different instants k, a random noise signal nij(k) Independently distributed, detected target state information is represented as xk(x, y) which contains the position of the object, xk(x, y) is for zij(k) The position information obtained after signal processing is denoted as xk＝F(zij(k) I and j respectively represent the position coordinates of the resolution unit;
the value function and the target state information at the moment when the initialization k is 1 are respectively expressed as:
q(x1)＝0,
Figure FDA0003521405670000021
wherein
Figure FDA0003521405670000022
Representing an empty set;
when k is 2, update value function: q (x)2)＝max[q(x1)]+zij(2) Then, the target state information is updated: r (2) ═ argmax [ q (x) ]1)]；
When k is 3, the target state information is updated firstly:
R(3)＝argmax[q(x2)]
and estimating the moving speed of the target when k is 2 by combining the target state information at the previous moment:
Figure FDA0003521405670000023
wherein, vx2Denotes the speed in the x direction, vy, when k is 22Denotes a speed in the y direction when k is 2, x (-) denotes an x coordinate of the extraction · y (-) denotes a y coordinate of the extraction · TTime of flightRepresenting the time interval between two frames;
when k is 3, executing a Kalman filtering algorithm, and predicting the target position when k is 3:
P(2)＝E(4)
Figure FDA0003521405670000024
Figure FDA0003521405670000025
Figure FDA0003521405670000026
Figure FDA0003521405670000027
wherein X2 denotes an initial state quantity, P (2) an initial covariance matrix, E (4) denotes a 4-order identity matrix, A denotes a state transition matrix, B denotes an external control matrix, T denotes a matrix transpose, J denotes an external control quantity,
Figure FDA0003521405670000031
denotes a covariance matrix prediction value when K is 3, Q denotes a process noise covariance matrix, S denotes innovation, H denotes an observation matrix, R denotes an observation noise covariance matrix, K denotes a gain,
Figure FDA0003521405670000032
represents the estimated motion velocity and position information of the target at time k-3, where x' (x)3)、y'(x3)、vx'3、vy'3Is x (x)3)、y(x3)、vx3、vy3The predicted value of (2);
updating the zero position of the directional weighting function, wherein the directional weighting function is:
Figure FDA0003521405670000033
where θ is the predicted azimuth and (x)k-1),y(xk-1))、(x'(xk),y'(xk) Angle of the line connecting the two points;
search range D of update status information: d ═ x | vminT＜|x-x2|＜vmaxT }, said vmaxAnd vminThe maximum speed and the minimum speed of the target motion are adopted, x represents all the positions of the target to be detected in the search area D, and x2Represents the determined target position when k is 2;
update k is a function of the value at time 3:
q(x3)＝max[w(θ)q(x2)]+zij(3)
wherein F (z)ij(3))∈D。
2. The weak target detecting and tracking method according to claim 1, wherein when k ≧ 4, the following steps are performed in a loop until the end frame data is processed:
(1) and updating the record of the state information at the moment k:
R(k)＝argmax[q(xk-1)]
wherein q (x)k-1) A value function representing a last time instant;
(2) estimating the speed:
Figure FDA0003521405670000041
(3) performing Kalman filtering on the record of the target state information at the current moment:
Figure FDA0003521405670000042
Figure FDA0003521405670000043
Figure FDA0003521405670000044
Figure FDA0003521405670000045
Figure FDA0003521405670000046
Figure FDA0003521405670000047
wherein X (k-1) represents a state quantity at the time of k-1,
Figure FDA0003521405670000048
represents the predicted value of the target state information at the time k-1, P (k-1) represents the covariance matrix at the time k-1,
Figure FDA0003521405670000049
represents a covariance matrix predicted value at the time k-1, E (4) represents an identity matrix of order 4, A represents a state transition matrix, B represents an external control matrix, T represents a matrix transposition, J represents an external control quantity,
Figure FDA00035214056700000410
denotes the covariance matrix prediction value at time K, Q denotes the process noise covariance matrix, S denotes innovation, H denotes the observation matrix, R denotes the observation noise covariance matrix, K denotes gain,
Figure FDA00035214056700000411
indicating the predicted value of the state at time k,
Figure FDA0003521405670000051
represents the observed value at time k-1;
(4) directional weighting:
Figure FDA0003521405670000052
where θ is the predicted azimuth and (x)k-1),y(xk-1))、(x'(xk),y'(xk) Angle between the two points;
(5) updating the search range of the next state information:
D＝{x|vminT＜|x-xk-1|＜vmaxT}
(6) update value function:
q(xk)＝max[w(θ)q(xk-1)]+zij(k)
wherein z isij(k)∈D。
3. The weak target detecting and tracking method according to claim 2, wherein threshold interception is performed to obtain all the states of the M-th time point satisfying the following condition
Figure FDA0003521405670000053
Figure FDA0003521405670000054
Wherein V is a threshold value set according to a certain condition, and M is the total frame number.
4. A weak target detecting and tracking method according to claim 3, characterized in that all the fulfils in the mth frame are assigned
Figure FDA0003521405670000055
Of the condition
Figure FDA0003521405670000056
And performing track backtracking by using the record of the state information, wherein the track obtained at the kth moment is recorded as TkThe method comprises the following steps:
Figure FDA0003521405670000057
wherein:
Figure FDA0003521405670000058
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