CN111708982B - Association complexity measurement method in target tracking problem - Google Patents

Association complexity measurement method in target tracking problem Download PDF

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CN111708982B
CN111708982B CN202010560329.9A CN202010560329A CN111708982B CN 111708982 B CN111708982 B CN 111708982B CN 202010560329 A CN202010560329 A CN 202010560329A CN 111708982 B CN111708982 B CN 111708982B
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刘冰
王艺
贺峰
邢姗姗
李美剑
陈超
王树刚
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Strategic Early Warning Research Institute Of People's Liberation Army Air Force Research Institute
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Abstract

The invention relates to a method for measuring association complexity in a target tracking problem,belonging to the field of target tracking data processing. In order to solve the problem that the complexity of stable and accurate tracking of a high maneuvering target cannot be described quantitatively, the target maneuvering complexity in the target tracking problem is defined as the allowable upper limit E of a filtering position estimation error not greater than a tracking estimation error at a certain moment 0 And the ratio of the theoretical maximum allowable sigma of the measured positioning error to satisfy this condition, i.e. E 0 And/sigma. Under a Kalman filtering framework, a calculation formula of the complexity is deduced by innovatively introducing a method of state updating error reduction factor lambda, and specific algorithm steps are given. The algorithm is utilized to provide a unified and standardized identification standard for the scene difficulty of the target tracking problem, quantitatively analyze the influence of the scene parameters on the target tracking problem, and support scientific and reasonable algorithm equivalent test experimental design.

Description

Association complexity measurement method in target tracking problem
Technical Field
The invention belongs to the field of target tracking data processing, and particularly relates to a method for measuring correlation complexity in a target tracking problem.
Background
The filtering algorithm is an algorithm for inhibiting random noise of observation data by introducing a motion model, however, the motion model is difficult to be completely matched with actual motion when a target does complex high-mobility actions, the model error is large, and the estimation error is large, even the filtering is divergent. The stable and accurate tracking of the high maneuvering target is a difficult problem in the field of target tracking, and the complexity of the method is a comprehensive action result of coupling of factors such as maneuvering characteristics of the target, detection data rate of a sensor, measurement errors and the like. However, at present, there is no unified and standardized definition for the complexity of the maneuvering target tracking problem itself, so that different researches define maneuvering targets under the own speech system, the complexity of the researched problems cannot be described quantitatively, and the problem of knowing who researches is difficult to say is more complicated.
Disclosure of Invention
Technical problem to be solved
The invention aims to solve the technical problem of how to provide a method for measuring the association complexity in the target tracking problem so as to overcome the problem that the complexity of stably and accurately tracking a high maneuvering target cannot be described quantitatively.
(II) technical scheme
In order to solve the above technical problem, the present invention provides a method for measuring association complexity in a target tracking problem, which comprises the following steps:
step 1, inputting T k-1 Time of day state estimation covariance
Figure BDA0002545865340000011
Step 2, calculating a state transition matrix, wherein delta t is a data updating time step length of target tracking;
Figure BDA0002545865340000021
step 3, calculating the target tracking data updating time T k-1 To T k Velocity mean change vector
Figure BDA0002545865340000022
Wherein n is a group satisfying T k-1 ≤t j ＜T k T of the condition j Number of (c), v (t) k ) N is the motion velocity vector of the target;
Figure BDA0002545865340000023
Figure BDA0002545865340000024
step 4, estimating a state transition error covariance matrix Q of the maneuvering motion;
Figure BDA0002545865340000025
step 5, calculating T k State prediction covariance of time of day
Figure BDA0002545865340000026
Figure BDA0002545865340000027
Step 6, calculating to meet the position error demand threshold E 0 The required position error reduction ratio at the time k;
Figure BDA0002545865340000028
wherein
Figure BDA0002545865340000029
Is composed of
Figure BDA00025458653400000210
3 × 3 arrays at the upper left corner;
step 7, calculating a threshold value E meeting the position error requirement 0 The measured positioning covariance of (a);
Figure BDA00025458653400000211
wherein I is an identity matrix;
step 8, outputting T k Complexity of the time;
Figure BDA00025458653400000212
step 9, updating a state estimation covariance matrix;
Figure BDA0002545865340000031
wherein H is (I) 3×3 0 3×3 ) T ；
And step 10, calculating each sampling moment in the analysis data time period, and stopping the calculation, otherwise, returning to the step 1.
Further, before the step 1, a step of inputting parameters is further included, where the inputted parameters include:
(1) true value vector x (t) of target motion track k )，k＝1,...,m，t k Sampling time of true value data of the flight path;
(2) motion velocity vector v (t) of object k )，k＝1,...,m；
(3) And updating the time step deltat of the target tracking data.
Further, E 0 The upper limit of position error that is allowed to be reached for tracking filtering.
Further, 0 < C prd (k) < 1, complexity C prd (k) Larger means more complex maneuvering target tracking.
Further, the following steps are also included between step 6 and step 7: calculating a threshold value E meeting the position error requirement 0 Position covariance of
Figure BDA0002545865340000032
(III) advantageous effects
The invention provides an algorithm for measuring the tracking complexity of a maneuvering target in a target tracking problem so as to reflect the difficulty of the target tracking problem from measurement error, data frequency, observation geometry and maneuvering. The invention innovatively defines the target maneuvering complexity in the target tracking problem as the allowable upper limit E of the filtering position estimation error not greater than the tracking estimation error at a certain moment 0 And is fullMeasuring the ratio of the maximum allowable theoretical value sigma of the positioning error, i.e. E, for this condition 0 And/sigma. Under a Kalman filtering framework, a calculation formula of the complexity is deduced by innovatively introducing a method of state updating error reduction factor lambda, and specific algorithm steps are given.
The algorithm provides a unified and standardized scene difficulty identification standard of the target tracking problem, quantitatively analyzes the influence of scene parameters on the target tracking problem, and supports scientific and reasonable algorithm equivalent test experimental design. The algorithm can be applied to target tracking system index demonstration, and belongs to one of basic problems in target tracking algorithm test evaluation in a tracking algorithm test design process.
Drawings
FIG. 1 is a main body implementation step of the associative complexity metric algorithm of the present invention;
FIG. 2 shows traces 1 and 2 in example 1 of the present invention;
FIG. 3 is a graph showing the average variation of the target tracking data at the time of updating and the average variation of the target tracking data at the previous time;
FIG. 4 is a plot of the tracking scene complexity for track 1 at a sensor data rate of 0.1Hz in accordance with the present invention;
FIG. 5 is a complexity curve of four scenarios in embodiment 1 of the present invention;
FIG. 6(1) is a complex curve of trace 1 with respect to three thresholds in example 2 of the present invention;
FIG. 6(2) is a complex curve of trace 2 with respect to three thresholds in example 2 of the present invention;
FIG. 7 is a flow chart of an algorithm for a maneuvering target tracking complexity metric in the target tracking problem of the present invention.
Detailed Description
In order to make the objects, contents and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
Symbol convention:
(1) thickening a body into a vector or matrix
(2) Italics without bolding to scalar quantity
(3) Default vector is column vector, and transpose is added to row vector
(4) I is an identity matrix, I' is a matrix with the last right diagonal of 1 and the rest of 0
Basic principle: (ii):
defining: for a measurement positioning system, when a Kalman filtering method is adopted to estimate a target position, a certain moment ensures that the estimation error of a filtering position is not more than the allowable upper limit E of the tracking estimation error 0 If the allowable theoretical maximum value of the positioning error measured at the moment is sigma, the complexity of the maneuvering target tracking at the moment is defined as
Figure BDA0002545865340000051
Description of the definitions: the definition starts from the working principle of a filtering algorithm, and the filtering position estimation is the maximum likelihood estimation under the condition of comprehensively considering model prediction errors and measurement data errors. By reducing the measured position error σ when the model error increases (target maneuvers), the filtered position estimate error E can be maintained 0 And is not changed. So the closer σ is to E 0 The larger the error of the model (the stronger the target maneuvering), the full failure of the model when the maneuvering complexity reaches the maximum, and the position estimation of the target can be provided only by measuring and positioning, i.e. sigma-E 0 It indicates that the target maneuver complexity is at a maximum at this time. From the above analysis, 0 < C mav ＜1，C mav Larger means more complex maneuvering target tracking.
(iii) algorithmic derivation explanations
The following explains a specific derivation calculation method of the complexity of the maneuvering target tracking. Set forth the following tracking system
Equation of motion:
x k ＝F(x k-1 +A k-1 ) (19)
the measurement equation:
z k ＝Hx k +ε， (20)
wherein
Figure BDA0002545865340000052
In order to target the three-dimensional position and velocity,
Figure BDA0002545865340000053
for the state transition matrix, Δ t is the filter time step (sensor data update rate),
Figure BDA0002545865340000061
a target maneuver item is represented that is associated with the maneuver,
Figure BDA0002545865340000062
measuring the position location for the detection system, H ═ I 3×3 0 3×3 ) T To measure the matrix,. epsilon.is the measurement error. A is to be k-1 And ε is considered a random variable, note cov (A) k-1 )＝Q k-1 ，cov(ε)＝R。
According to the Kalman filtering formula
Figure BDA0002545865340000063
Wherein
Figure BDA0002545865340000064
Therefore, it is possible to
Figure BDA0002545865340000065
Wherein
Figure BDA0002545865340000066
The covariance is predicted for the state,
Figure BDA0002545865340000067
the covariance is updated for the state. Are respectively provided with
Figure BDA0002545865340000068
And
Figure BDA0002545865340000069
the upper left corner 3 × 3 sub-matrix of
Figure BDA00025458653400000610
And
Figure BDA00025458653400000611
which are the covariances representing the position estimate. Order to
Figure BDA00025458653400000612
Figure BDA00025458653400000613
Wherein E 0 The upper bound of position error that is allowed to be reached for tracking filtering. The purpose of the equations (5,6) is to determine the ratio lambda of the position covariance to be reduced for the state update at time k based on the prediction covariance at time k and the desired upper bound of the filtering error at time k, and then estimate the coincidence E 0 Maximum position covariance matrix of upper bound of error
Figure BDA00025458653400000614
From this upper bound, the maximum measured covariance that can meet this requirement is calculated below. Because H ═ I, O]Substituting H into equation (4), take the upper left 3 × 3 sub-matrix, so
Figure BDA00025458653400000615
R k Is the measurement error at time k;
order to
Figure BDA00025458653400000616
And because of
Figure BDA00025458653400000617
And
Figure BDA00025458653400000618
reversible, so the demand at time k
Figure BDA00025458653400000619
Is simplified to obtain
Figure BDA00025458653400000620
Order to
Figure BDA00025458653400000621
The complexity of the k time is therefore
Figure BDA00025458653400000622
In addition, the updated covariance is observed as
Figure BDA0002545865340000071
The predicted covariance at the next time instant is
Figure BDA0002545865340000072
Therefore, the time of each moment can be obtained by iterative calculation according to the formulas (1) to (11)
Figure BDA0002545865340000073
Algorithm calculation step
Inputting:
(1) true value vector x (t) of target motion track k )，k＝1,...,m，t k Sampling time of true value data of the flight path;
(2) motion velocity vector v (t) of object k )，k 1.. m, if not x (t) can pass k ) Obtaining difference;
(3) updating time step delta t of data tracked by the target;
(4) a matrix H, a measurement error covariance matrix R and a sensor deployment position S;
the metric algorithm comprises the following steps:
step 1: input T k-1 Time of day state estimation covariance
Figure BDA0002545865340000074
Step 2: computing state transition matrices
Figure BDA0002545865340000075
And step 3: calculating the target tracking data updating time T k-1 To T k Velocity mean change vector
Figure BDA0002545865340000076
Wherein n is T k-1 ≤t j ＜T k T of the condition j Number of (2)
Figure BDA0002545865340000077
Figure BDA0002545865340000078
And 4, step 4: estimating a state transition error covariance matrix Q for a maneuver
Figure BDA0002545865340000081
And 5: calculating T k State prediction covariance at time
Figure BDA0002545865340000082
Figure BDA0002545865340000083
Step 6: calculated to satisfy the position error E 0 The required position error reduction ratio at time k
Figure BDA0002545865340000084
Wherein
Figure BDA0002545865340000085
Is composed of
Figure BDA0002545865340000086
3 x 3 array in the upper left corner.
And 7: calculating the satisfied position error E 0 Position covariance of
Figure BDA0002545865340000087
And 8: calculating a satisfied position error E 0 Measured positioning covariance of
Figure BDA0002545865340000088
And step 9: output T k Complexity of time of day
Figure BDA0002545865340000089
Step 10: updating state covariance matrix
Figure BDA00025458653400000810
Step 11:returning to the step 1, calculating the next detection time T k Of the system.
Example 1
The embodiment specifically describes a complexity comparison of an association complexity measurement algorithm in a target tracking problem, which is provided by the invention, for analyzing tracking difficulty in different tracking scenes, and a simulation test is performed.
The problems are as follows: under the conditions that the positioning error threshold is 2km and the sensor data rate is 0.1Hz and 1Hz, the complexity comparison analysis of the tracking problems corresponding to four scenes for tracking maneuvering tracks 1 and 2 with two different degrees shown in figure 2 is carried out, wherein the left side is track 1, and the right side is track 2.
Step 1: first, the sensor data rate is calculated to be 0.1Hz, and the tracking scene complexity for track 1 is calculated.
1.1, setting up
Figure BDA0002545865340000091
Wherein
Figure BDA0002545865340000092
The setting of the numerical value can be properly set according to the positioning error threshold value of 2km, and the difference of the setting only causes the scene complexity numerical value to be different in the early tracking period but is not related to the initial value soon.
1.2 setting Δ t to 10, then
Figure BDA0002545865340000093
1.3 calculating the velocity average change vector of the target tracking data at the updating time and the last time according to the data of the track 1
Figure BDA0002545865340000094
As shown in fig. 3.
1.4 estimating State transition error covariance matrix for maneuvering
Figure BDA0002545865340000095
1.5 calculating T k State prediction covariance at time
Figure BDA0002545865340000096
Figure BDA0002545865340000097
1.6 to satisfy the position error E 0 Required position error reduction ratio at time k of 2000
Figure BDA0002545865340000101
Wherein
Figure BDA0002545865340000102
Is composed of
Figure BDA0002545865340000103
3 x 3 array in the upper left corner.
1.7: calculating a position covariance satisfying position error 2000
Figure BDA0002545865340000104
1.8: calculating a measurement positioning covariance that satisfies a position error of 2000
Figure BDA0002545865340000105
1.9: output T k Complexity of time of day
Figure BDA0002545865340000106
1.10: updating state covariance matrix
Figure BDA0002545865340000107
1.11: returning to the step 1, calculating the next detection time T k Of the system. Fig. 4 shows a tracking scene complexity curve for trace 1 at a sensor data rate of 0.1 Hz.
Step 2: and (3) calculating the data rate of the sensor to be 0.1Hz according to the method in the step 1, and tracking scene complexity of the track 2.
And step 3: and (3) calculating the data rate of the sensor to be 1Hz according to the method in the step 1, and tracking scene complexity of the track 1.
And 4, step 4: and (4) calculating the tracking scene complexity of the track 2 according to the method of the step 1, wherein the data rate of the sensor is 1 Hz.
And 5: the four scene complexity curves calculated in steps 1 to 4 are plotted on a unified scale and compared for analysis, as shown in fig. 5. The complexity of the maneuvering motion of the track 1 is higher than that of the track 2, under the condition that the data rate of the sensor is 0.1Hz, the tracking complexity of the track 1 is kept above 0.65, the tracking complexity of the track 2 near a corner is similar to that of the track 1, and the tracking complexity of other time periods is below 0.35. It is shown that at a sensor data rate of 0.1Hz, the tracking complexity for trace 1 is significantly greater than the tracking complexity for trace 2. At a sensor data rate of 1Hz, although trajectory 1 maneuver complexity is greater than trajectory 2, the two tracking complexity measures are not as far apart, with trajectory 1 tracking complexity being slightly greater than trajectory 2 tracking complexity. In addition, comparing the tracking complexity of trace 1 with the sensor 0.1Hz and 1Hz data, the former is significantly larger than the latter, while for trace 2, the tracking complexity with the sensor 0.1Hz and 1Hz data, the former is significantly larger than the latter only in the turn segment, while the other segments are identical. Therefore, the measurement algorithm of the invention can carry out unified measurement on scenes matched with different sensors and target tracks under the given positioning error requirement threshold value, thereby carrying out unified comparison.
Example 2
For two tracks 1 and 2 with different maneuvering strengths, a sensor with a data rate of 0.1Hz is adopted for observation, and when the positioning error removing requirement threshold values are respectively 500m, 1000m and 2000m, the complexity of a scene on a tracking algorithm is analyzed.
The method of embodiment 1 is adopted to calculate the complexity curves of six scenes respectively, three types corresponding to the track 1 are drawn in one graph, and three types corresponding to the track 2 are drawn in one graph for analysis. As can be seen from fig. 6(1), for track 1, as the positioning error requirement threshold is decreased (i.e., the requirement for positioning accuracy is higher), the scene complexity curve is consistently raised, which indicates that track 1 is consistently changed along with the positioning error requirement threshold in the whole course. As can be seen from fig. 6(2), for track 2, only the turning maneuver section has the characteristics of track 1, while in the non-maneuver section, the scene is not sensitive to the complexity of target tracking with respect to the positioning error requirement threshold, which indicates that the tracking of the non-maneuver target is a simple problem.
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 (5)

1. A method for measuring correlation complexity in a target tracking problem is characterized by comprising the following steps:
step 1, inputting T k-1 Time of day state estimation covariance
Figure FDA0002545865330000011
Step 2, calculating a state transition matrix, wherein delta t is a data updating time step length of target tracking;
Figure FDA0002545865330000012
step 3, calculating the updating time T of the target tracking data k-1 To T k Velocity averagingVariation vector
Figure FDA0002545865330000013
Wherein n is T k-1 ≤t j ＜T k T of the condition j Number of (c), v (t) k ) N is a motion velocity vector of the target;
Figure FDA0002545865330000014
Figure FDA0002545865330000015
step 4, estimating a state transition error covariance matrix Q of the maneuvering motion;
Figure FDA0002545865330000016
step 5, calculating T k State prediction covariance at time
Figure FDA0002545865330000017
Figure FDA0002545865330000018
Step 6, calculating to meet the position error demand threshold value E 0 The required position error reduction ratio at the time k;
Figure FDA0002545865330000019
wherein
Figure FDA00025458653300000110
Is composed of
Figure FDA00025458653300000111
3 × 3 matrix in the upper left corner;
step 7, calculating a threshold value E meeting the position error requirement 0 The measured positioning covariance of (a);
Figure FDA00025458653300000112
wherein I is an identity matrix;
step 8, outputting T k Complexity of the time;
Figure FDA0002545865330000021
step 9, updating a state estimation covariance matrix;
Figure FDA0002545865330000022
wherein H is (I) 3×3 0 3×3 ) T ；
And step 10, calculating each sampling moment in the analysis data time period, and stopping the calculation, otherwise, returning to the step 1.
2. The method of correlating complexity metrics in a target tracking problem as claimed in claim 1 further comprising the step of inputting parameters prior to said step 1, said inputted parameters comprising:
(1) true value vector x (t) of target motion track k )，k＝1,...,m，t k Sampling time of true track data;
(2) motion velocity vector v (t) of object k )，k＝1,...,m；
(3) And updating the time step deltat of the target tracking data.
3. As claimed inThe method for measuring the association complexity in the target tracking problem of 1 is characterized in that E 0 The upper limit of position error that is allowed to be reached for tracking filtering.
4. The method of correlating complexity metrics in an object tracking problem as recited in claim 1 in which 0 < C prd (k) < 1, complexity C prd (k) Larger means more complex maneuvering target tracking.
5. The method for correlating complexity metrics in a target tracking problem as claimed in claim 1, further comprising the steps between step 6 and step 7 of: calculating a threshold value E meeting the position error requirement 0 Position covariance of
Figure FDA0002545865330000023
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CN106933106A (en) * 2016-05-26 2017-07-07 哈尔滨工程大学 A kind of method for tracking target based on fuzzy control Multiple Models Algorithm
CN108414995A (en) * 2018-03-12 2018-08-17 中国人民解放军国防科技大学 Gauss-Newton filtering based target tracking method under nonlinear model

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