CN107643083B - Spatial target interruption track correlation method based on track prediction - Google Patents

Spatial target interruption track correlation method based on track prediction Download PDF

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CN107643083B
CN107643083B CN201710841999.6A CN201710841999A CN107643083B CN 107643083 B CN107643083 B CN 107643083B CN 201710841999 A CN201710841999 A CN 201710841999A CN 107643083 B CN107643083 B CN 107643083B
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track
interruption
space
speed
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修建娟
何友
董凯
崔亚奇
韩蕾蕾
王萌
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Naval Aeronautical University
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Abstract

The invention discloses a track forecast-based spatial target interruption track association method, and belongs to the technical field of track association. The invention aims to effectively improve the continuity and stability of space target tracking and improve the target tracking precision and the effective tracking batch number, and adopts first-order and second-order least square curve fitting to improve the precision of a track forecast initial value point aiming at the speed and the position of the space target respectively, utilizes the position of the track forecast initial value point obtained by variable-order curve fitting, estimates the target acceleration at the moment according to a space target kinetic equation, forecasts the space target motion track by utilizing an Euler extrapolation forecasting method by utilizing the estimated acceleration, and solves the problem of interrupted track correlation by utilizing the space target track forecasting result.

Description

Spatial target interruption track correlation method based on track prediction
Technical Field
The invention belongs to the technical field of target track association, and is suitable for a tracking system with higher track zero fragmentation degree under a complex and dense target environment.
Background
No matter new satellite launching, collision avoidance, space debris management, important space target early warning interception and the like need a high-precision target tracking and track forecasting technology as a basis, the relative motion speed of each target in a complex space target group is low, so that a radar cannot effectively distinguish each target in the target group within a relatively long time, continuous and effective stable measurement cannot be obtained for part of distinguishable targets in the group, further, the tracking result has many short and small tracks, the problems of tracking saturation, low number of effectively tracked targets and the like easily occur, and how to fully utilize the motion characteristics of the space targets to realize mutual feedback and virtuous cycle of tracking and forecasting and improve the tracking and forecasting performances are the key to realize space multi-target high-precision real-time tracking and improve the continuity of space target tracking, Stability, and difficult problems which need to be solved for realizing accurate prediction of the drop point.
Disclosure of Invention
The invention aims to provide a spatial target interruption track correlation method based on track prediction. The method aims to solve the problems that in the space target tracking process, targets are lost in time, the same target is subjected to track initiation for multiple times, multiple lot numbers are given to the same target, the number of batches for effectively tracking the targets is limited and the like.
The invention relates to a track prediction-based spatial target interruption track correlation method, which is characterized in that according to a spatial target kinetic equation, a variable order curve fitting is adopted to obtain an initial value point of track prediction and carry out track prediction on a spatial target, and a track segment correlation threshold before and after interruption is established by using a predicted track to realize short track correlation fusion of the spatial target, and specifically comprises the following technical measures: the method comprises the steps of performing smoothing processing by adopting a curve fitting method in the track forecast initial value point obtaining process, improving the precision of a track forecast initial value point by adopting first-order and second-order least square curve fitting aiming at the speed and the position of a space target respectively, estimating the target acceleration at the moment according to a space target kinetic equation by utilizing the track forecast initial value point position obtained by variable order curve fitting, forecasting the motion track of the space target by utilizing an Euler extrapolation forecasting method according to the estimated acceleration, and establishing track segment correlation positions and speed thresholds before and after interruption by combining the forecasted track to realize the correlation fusion of the tracks before and after the interruption of the space target.
The invention can solve the problems of short flight paths, more flight paths and the like caused by discontinuous space target measurement data in a complex environment by track prediction while tracking the target, improve the number of the targets effectively tracked by a radar system, and improve the continuity, stability and tracking precision of space target tracking.
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FIG. 1 is a flow chart of a spatial target interrupt track correlation method based on track prediction.
Detailed Description
The specific implementation mode of the invention comprises the following steps:
step 1: in order to improve the accuracy of the predicted initial value point of the space target track, a variable-order curve fitting method is adopted to carry out smoothing processing in the process of obtaining the initial value point, the least square curve fitting does not require a fitting curve to pass through all known points, the result obtained in the process of curve fitting can better reflect the objective reality of curve tracks formed by the space target motion, meanwhile, a first-order least square curve fitting method is suitable for processing time-varying state quantities which change linearly, a second-order least square curve fitting method is suitable for processing second-order time-varying state quantities which change nonlinearly, and therefore the accuracy of the predicted initial value point of the track is improved by adopting first-order least square curve fitting for the speed of the space target and adopting second-order least square curve;
step 2: let t be obtained by curve fittingkThe position of an initial track forecast point under the moment geocentric inertial coordinate system is (x)I,yI,zI) Then, the estimated value of the acceleration of the space target at the moment is calculated according to the kinetic equation of the space target
Figure GDA0002439873520000021
Wherein, mu is 3.986004418 × 1014m3·s-2Is a constant of universal gravitation,
Figure GDA0002439873520000022
J2＝1.08264×10-3is the second order band harmonic coefficient of the earth, re6378137m is the equator radius of the earth;
and step 3: t obtained by fitting a curvekTrack forecast initial point speed under moment geocentric inertial coordinate system
Figure GDA0002439873520000023
T is calculated by Euler's extrapolation prediction methodk+1The space target position and the speed predicted value at the moment are respectively
Figure GDA0002439873520000024
Figure GDA0002439873520000025
T obtained by the formulae (2) and (3)k+1T is calculated from the equation (1) by using the predicted values of the target position and velocity in the time spacek+1The estimated value of the target acceleration in the time space is calculated to obtain tk+2Predicting the space target position and speed at different moments by analogy in turn;
and 4, step 4: the position of a space target before interruption, a predicted speed value and a space target track after interruption are aligned at the moment, the space target before interruption is taken as a center and the space target track after interruption is associated in sequence, and an extrapolation state vector of a target track i before interruption at the moment k is set for
Figure GDA0002439873520000026
Is shown, i.e.
Figure GDA0002439873520000031
Wherein: x is the number ofI，yI，zIAnd
Figure GDA0002439873520000033
respectively predicting the spatial target position and the speed before interruption;
corresponding same moment obtained by filtering of target j after interruptionFor the target state vector
Figure GDA0002439873520000034
Is shown by
Figure GDA0002439873520000035
And
Figure GDA0002439873520000036
constructing a location test statistic λij(k)
Figure GDA0002439873520000037
Wherein:
Figure GDA0002439873520000038
and
Figure GDA0002439873520000039
are respectively state vectors
Figure GDA00024398735200000310
Of (2) a corresponding position element xI、yIAnd zI，
Figure GDA00024398735200000311
And
Figure GDA00024398735200000312
are respectively state vectors
Figure GDA00024398735200000313
A corresponding position element;
if the position test statistic lambdaij(k) Is lower than a set check threshold DLimit ofWherein D isLimit ofThe value of (A) is determined and adjusted according to the type of the target in the air and engineering experience, i.e. lambdaij(k)≤DLimit ofJudging that the position correlation inspection of the target track j after the interruption at the moment k and the target i before the interruption is successful;
and 5: if there are multiple target flights after interruption at that momentIf the track meets the requirement of the position correlation test in step 4, the interrupted target track number meeting the position correlation test is given to the set ΛDI.e. by
ΛD＝{j|λij(k)≤DLimit of} (6)
And utilize the set ΛDElement construction velocity test statistic in (1)
Figure GDA00024398735200000314
Wherein:
Figure GDA00024398735200000315
and
Figure GDA00024398735200000316
are respectively state vectors
Figure GDA00024398735200000317
Corresponding velocity element of
Figure GDA00024398735200000318
And
Figure GDA00024398735200000319
Figure GDA00024398735200000320
and
Figure GDA00024398735200000321
respectively, set ΛDThe middle track l corresponds to a corresponding speed element in the state vector;
if velocity test statistic
Figure GDA00024398735200000322
Is lower than a set check threshold VLimit ofJudging that the speed correlation inspection of the target track l after interruption and the target i before interruption is successful;
step 6: if there are still a plurality of target tracks after interruption meeting the speed correlation check requirement with the target i before interruption, that is
Figure GDA00024398735200000323
If the number of elements in (1) is more than ΛVThe track corresponding to the minimum median value is used for being associated with the target track i before interruption;
and 7: and (3) performing association check judgment of the steps 1-6 by utilizing the sliding window check through data of a plurality of continuous moments, wherein m times of the n times of association check meet the check requirement, and if m/n is more than 0.5 and less than 1, judging that the association of the corresponding target track before and after interruption is successful, so that the accuracy rate of the association of the interrupted track of the space target under the complex environment is ensured, and the missing association and the error association caused by the association check judgment of a single moment are reduced.

Claims (3)

1. A spatial target interruption track association method based on track prediction is characterized by comprising the following steps:
step 1: in the process of obtaining the initial value point, smoothing the space target speed and position by adopting a curve fitting method;
step 2: let t be obtained by curve fittingkThe position of an initial track forecast point under the moment geocentric inertial coordinate system is (x)I,yI,zI) Then, the estimated value of the acceleration of the space target at the moment is calculated according to the kinetic equation of the space target
Figure FDA0002439873510000011
Wherein, mu is 3.986004418 × 1014m3·s-2Is a constant of universal gravitation,
Figure FDA0002439873510000012
J2＝1.08264×10-3is the second order band harmonic coefficient of the earth, re6378137m is the equator radius of the earth;
and step 3: combination curveT obtained by line fittingkTrack forecast initial point speed under moment geocentric inertial coordinate system
Figure FDA0002439873510000018
T is calculated by Euler's extrapolation prediction methodk+1The space target position and the speed predicted value at the moment are respectively
Figure FDA0002439873510000013
Figure FDA0002439873510000014
T obtained by the formulae (2) and (3)k+1T is calculated from the equation (1) by using the predicted values of the target position and velocity in the time spacek+1The estimated value of the target acceleration in the time space is calculated to obtain tk+2Predicting the space target position and speed at different moments by analogy in turn;
and 4, step 4: the position of a space target before interruption, a predicted speed value and a space target track after interruption are aligned at the moment, the space target before interruption is taken as a center and the space target track after interruption is associated in sequence, and an extrapolation state vector of a target track i before interruption at the moment k is set for
Figure FDA0002439873510000015
Is shown, i.e.
Figure FDA0002439873510000016
Wherein: x is the number ofI,yI,zIAnd
Figure FDA0002439873510000017
respectively predicting the spatial target position and the speed before interruption;
corresponding target state vector of the same moment obtained by filtering of target j after interruption
Figure FDA0002439873510000021
Is shown by
Figure FDA0002439873510000022
And
Figure FDA0002439873510000023
constructing a location test statistic λij(k)
Figure FDA0002439873510000024
Wherein:
Figure FDA0002439873510000025
and
Figure FDA0002439873510000026
are respectively state vectors
Figure FDA0002439873510000027
Of (2) a corresponding position element xI、yIAnd zI，
Figure FDA0002439873510000028
And
Figure FDA0002439873510000029
are respectively state vectors
Figure FDA00024398735100000210
A corresponding position element;
if the position test statistic lambdaij(k) Is lower than a set check threshold DLimit ofWherein D isLimit ofThe value of (A) is determined and adjusted according to the type of the target in the air and engineering experience, i.e. lambdaij(k)≤DLimit ofJudging that the position correlation inspection of the target track j after the interruption at the moment k and the target i before the interruption is successful;
step 5, if a plurality of interrupted target tracks meet the position correlation inspection requirement in the step 4 at the moment, giving the interrupted target track numbers meeting the position correlation inspection to the set ΛDI.e. by
ΛD＝{j|λij(k)≤DLimit of} (6)
And utilize the set ΛDElement construction velocity test statistic in (1)
Figure FDA00024398735100000211
Wherein:
Figure FDA00024398735100000212
and
Figure FDA00024398735100000213
are respectively state vectors
Figure FDA00024398735100000214
Corresponding velocity element of
Figure FDA00024398735100000215
And
Figure FDA00024398735100000216
Figure FDA00024398735100000217
and
Figure FDA00024398735100000218
respectively, set ΛDThe middle track l corresponds to a corresponding speed element in the state vector;
if velocity test statistic
Figure FDA00024398735100000219
Is lower than a set check threshold VLimit ofJudging that the speed correlation inspection of the target track l after interruption and the target i before interruption is successful;
step 6: if there are still a plurality of target tracks after interruption meeting the speed correlation check requirement with the target i before interruption, that is
Figure FDA00024398735100000220
If the number of elements in (1) is more than ΛVAnd the track corresponding to the minimum median value is used for being associated with the target track i before interruption.
2. The method for associating the interrupted flight path of the spatial target based on the trajectory prediction as claimed in claim 1, wherein the specific method for performing the smoothing process on the speed and the position of the spatial target by adopting the curve fitting method in the step 1 is as follows:
and adopting first-order least square curve fitting for the space target speed and second-order least square curve fitting for the position.
3. The method for associating the interrupted flight path of the spatial target based on the track forecast as claimed in claim 1, further comprising the step 7: and (3) performing the correlation inspection of the step (1) to the step (6) by utilizing the data of a plurality of continuous moments of the sliding window inspection, wherein m times of the n times of correlation inspection meet the inspection requirements, and if m/n is more than 0.5 and less than 1, judging that the corresponding target track correlation inspection before and after interruption is successful.
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CN109872372B (en) * 2019-03-07 2021-04-09 山东大学 Global visual positioning method and system for small quadruped robot
CN109945869B (en) * 2019-03-08 2022-07-19 南京理工大学 One-step extrapolation prediction method for variable acceleration motion in target track data preprocessing
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