CN111797478A - Strong maneuvering target tracking method based on variable structure multi-model - Google Patents

Strong maneuvering target tracking method based on variable structure multi-model Download PDF

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CN111797478A
CN111797478A CN202010734714.0A CN202010734714A CN111797478A CN 111797478 A CN111797478 A CN 111797478A CN 202010734714 A CN202010734714 A CN 202010734714A CN 111797478 A CN111797478 A CN 111797478A
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李君龙
曹颖
高长生
尹童
张超
陈晓波
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Harbin Institute of Technology
Beijing Institute of Electronic System Engineering
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Abstract

A strong maneuvering target tracking method based on variable structure multi-models relates to the field of target tracking, and aims at the problem that when a high-speed strong maneuvering target in an adjacent space is tracked, the target tracking accuracy is low, and the method comprises the following steps: constructing a dynamic tracking model set by using the dynamic characteristics of the target aircraft, and then acquiring a state equation set of a maneuvering target tracking system; step two: establishing a system measurement model, and obtaining a measurement equation and measurement noise of the system according to the established system measurement model; step three: and carrying out recursive estimation on the motion state and the pneumatic parameters of the target aircraft based on the state equation set of the system, the measurement equation of the system and the measurement noise. According to the method, the dynamic tracking model set is constructed based on the dynamic characteristics of the target aircraft, the description precision of target motion is improved, and the target tracking precision is improved by adopting an improved variable-structure multi-model tracking algorithm.

Description

Strong maneuvering target tracking method based on variable structure multi-model
Technical Field
The invention relates to the field of target tracking, in particular to a strong maneuvering target tracking method based on variable structure multi-models.
Background
In the field of target tracking, a kalman filter is generally adopted for tracking, and an algorithm for correcting measured data by combining a target motion model and the measured data is adopted. Mainly solves the problems of three aspects: firstly, the measurement error of the observer comprises constant deviation and random deviation, and the instability and precision of measured data are limited in a target tracking algorithm to obtain certain correction; secondly, maneuvering of the target, which is a maneuvering mode of the target which cannot be accurately obtained because the target and a tracking party belong to different mechanisms, has high randomness and uncertainty, and can be used for distinguishing whether the target maneuvers according to residual errors in the tracking process so as to provide a reference basis; and thirdly, the sensor can only detect the position data of the target usually, the speed and related parameter data of the target cannot be acquired, and in a target tracking algorithm, the state vector of the target can be subjected to dimension expansion, so that an estimated value of the related parameter is obtained, the understanding of the motion mode of the target is increased, and the accuracy of target tracking is also improved.
The near space field is an airspace 20-100 km away from the ground, the flight speed of the high-speed aircraft in the space can reach more than 5 Mach, and the near space contains rarefied atmosphere, so that the aircraft has certain maneuvering capability, and the parameters such as speed and acceleration change violently. The vehicle can flexibly maneuver, quickly respond and super-strengthen the penetration, has strategic deterrence and actual combat application capabilities, and has important strategic significance for deterring strong enemies, controlling crisis and winning wars. In the defense field, the traditional tracking algorithm cannot realize accurate tracking, which has great difficulty in tracking and predicting the ultra-high-speed target in the adjacent space. Therefore, the method has very important military significance and practical significance for developing the near space strong maneuvering target tracking algorithm research.
At present, for tracking a strong maneuvering target, common models comprise a current statistical model, a Jerk model and other kinematic models, and a multi-model combined algorithm is often adopted for tracking a near space to perform fusion output so as to match different maneuvering modes of an aircraft. In the variable structure tracking algorithm, the IMM algorithm has the best tracking precision, but has certain limitation on the set value of the tracking model; the variable structure multi-model algorithm (VSMM algorithm) based on directed graph switching can solve the problem, but the delay problem is serious in model switching; the adaptive variable structure algorithm (AGIMM algorithm) is flexible in reaction and high in tracking precision, but an overfitting phenomenon occurs in the tracking and fitting process, so that the fitting result is changed quickly and unstably, and the final tracking error is increased.
Disclosure of Invention
The purpose of the invention is: aiming at the problem of low target tracking accuracy in the process of tracking a high-speed strong maneuvering target in an adjacent space, the strong maneuvering target tracking method based on the variable structure multi-model is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a strong maneuvering target tracking method based on variable structure multiple models comprises the following steps:
the method comprises the following steps: constructing a dynamic tracking model set by using the dynamic characteristics of the target aircraft, and then acquiring a state equation set of a maneuvering target tracking system;
step two: establishing a system measurement model, and obtaining a measurement equation and measurement noise of the system according to the established system measurement model;
step three: and carrying out recursive estimation on the motion state and the pneumatic parameters of the target aircraft based on the state equation set of the system, the measurement equation of the system and the measurement noise.
Further, the specific steps of the first step are as follows:
the method comprises the following steps: selecting the pneumatic parameters of the tracking model according to the maneuvering characteristics of the target,
the tracking model pneumatic parameters are as follows:
Figure BDA0002604484020000021
wherein, CL(. alpha.) and CD(α) is the pneumatic parameter, CL(α) is the coefficient of lift, CD(α) is the drag coefficient, S is the characteristic area of the target aircraft, m is the mass of the target aircraft, αD，αLResistance parameters and lift parameters;
the first step is: modeling the change characteristic of the pneumatic parameters by using Gaussian white noise to obtain a state equation of the maneuvering target tracking system, wherein the state equation of the maneuvering target tracking system is as follows:
Figure BDA0002604484020000022
wherein, ω iseIs the angular velocity vector of the earth rotation, g is the gravity acceleration of the earth, r is the position vector of the target under the detection system, v is the velocity of the target under the detection system,
Figure BDA0002604484020000023
is a transfer matrix from a ballistic coordinate system to a detection system, theta is a velocity inclination angle, sigma is an azimuth angle, and gamma isvIs the angle of inclination of the speed, omegaγWhite gaussian noise, omega, at the roll angleD，ωLWhite Gaussian noise as an aerodynamic parameter, R is aerodynamic force, wherein
Figure BDA0002604484020000024
S is the characteristic area of the target aircraft:
Figure BDA0002604484020000025
step one is three: the roll angle gamma of the speed in the first step and the second stepvAs model variables, different speed roll angles γ are selectedvAnd constructing a state equation set of the maneuvering target tracking system.
Further, the step of obtaining the measurement equation and the measurement noise of the system in the step two specifically includes:
step two, firstly: establishing a detection coordinate system according to the requirement of the tracking task, and determining position vectors of the detector and the target under the detection coordinate system;
step two: acquiring a three-dimensional position coordinate of a target aircraft in a detector body system according to an infrared detection principle;
step two and step three: and (3) performing expansion analysis on the mean square error of positioning by using the three-dimensional position coordinates of the target aircraft in the system of the detector, and determining a measurement equation and measurement noise of the tracking system.
Further, in the second step, the position vectors of the detector and the target in the detection coordinate system are as follows:
position vector of the target under the detection coordinate system: r ═ x, y, z;
position vector of the detector under the detection coordinate system: sl＝(xl,yl,zl) And l represents the l-th detector.
Further, the second step specifically comprises the following steps:
first, the vector of the probe pointing to the target is:
Figure BDA0002604484020000031
detector detection angle alphalAnd betalExpressed as:
Figure BDA0002604484020000032
the conversion obtains:
Figure BDA0002604484020000033
Figure BDA0002604484020000034
Figure BDA0002604484020000035
Figure BDA0002604484020000036
obtaining the three-dimensional position coordinate X ═ (X, y, z) of the target aircraft under the detector by using a least square method
The least squares are expressed as:
Figure BDA0002604484020000037
where M is the measurement matrix, X is the state quantity, and Y is the quantity measurement.
Further, the specific steps of determining the measurement equation and the measurement noise of the tracking system in the second step and the third step are as follows:
firstly, determining the relative position and angle relationship between the target and the detector according to the geometric principle:
Figure BDA0002604484020000041
in the formula,
Figure BDA0002604484020000042
x1，y1，z1the position components of the first detector in the x direction, the y direction and the z direction under a detection system are obtained; x is the number of2，y2，z2The position components of the second detector in the x direction, the y direction and the z direction under the detection system are obtained; Δ κ ═ κ2-κ1，
Figure BDA0002604484020000043
Then, obtaining noise R through a measurement noise formula, wherein the measurement noise formula is as follows:
Figure BDA0002604484020000044
wherein,
Figure BDA0002604484020000045
Figure BDA0002604484020000046
Figure BDA0002604484020000047
in the above formula, c1＝κ2(x2-x1)-(y2-y1)，c2＝-κ1(x2-x1)+(y2-y1)；
Figure BDA0002604484020000048
Figure BDA0002604484020000051
And
Figure BDA0002604484020000052
respectively the mean square error of the position coordinates of the detector itself,
Figure BDA0002604484020000053
the mean square error is located for the target,
Figure BDA0002604484020000054
the mean square error of the detector detection angle alpha 1,
Figure BDA0002604484020000055
the mean square error of the detector detection angle alpha 2,
Figure BDA0002604484020000056
mean square error of detecting angle beta 1 for a detector，
Figure BDA0002604484020000057
The mean square error of the angle β 2 is detected for the detector.
Further, in the third step, an improved variable structure multi-model algorithm is utilized to carry out recursive estimation on the motion state and the pneumatic parameters of the target aircraft; the improved variable structure multi-model algorithm comprises the following specific steps:
first, input interaction:
Figure BDA0002604484020000058
m is the set of the model totality, i, j represents the ith, j model,
Figure BDA0002604484020000059
wherein p isijIs the transition probability, μ, of model i transitioning to ji,j(k-1/k-1) is a mixed probability
Figure BDA00026044840200000510
Figure BDA00026044840200000511
Second step, filtering
For model Mj(k) To be provided with
Figure BDA00026044840200000512
Performing Kalman filtering, phijFor the state transition matrix, the prediction is:
Figure BDA00026044840200000513
the prediction error covariance is:
Figure BDA00026044840200000514
the filtering is:
Figure BDA00026044840200000515
Figure BDA00026044840200000516
the filtering covariance is:
Figure BDA00026044840200000517
and (4) estimating an observation equation, wherein the Kalman gain is as follows:
Figure BDA0002604484020000061
Figure BDA0002604484020000062
third, model probability updating
Figure BDA0002604484020000063
Wherein, Λj(k)＝N(rj(k),0,Sj(k) K) likelihood function of the pattern j at time k, defining a variable rj(k) Mean 0 and variance Sj(k) Of Gaussian distribution ofj(k) Comprises the following steps:
Figure BDA0002604484020000064
step four, outputting interaction:
Figure BDA0002604484020000065
Figure BDA0002604484020000066
fifthly, updating the model set:
calculating the maximum model probability:
umax＝max{u1,u2,u3}
and the corresponding model is set as a model j, the distance function is as follows:
Figure BDA0002604484020000067
tracking model adjustment, which is performed by analogy with the principle of directed graph switching,
when u1maxWhen, if D1(k) Not less than M, then
Figure BDA0002604484020000068
Wherein G is0Is the minimum grid spacing, k1，k2In order to be able to adjust the parameters,
if D is1(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000069
When u2maxWhen, if D2(k) Not less than M, then
Figure BDA0002604484020000071
If D is2(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000072
When u3maxWhen, if D3(k) Not less than M, then
Figure BDA0002604484020000073
If D is3(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000074
For the initialization of the state vector and covariance of the newly activated model, the probability weighted combination of each model at the previous moment is adopted for initialization, that is:
Figure BDA0002604484020000075
Figure BDA0002604484020000076
the invention has the beneficial effects that:
the method constructs a dynamic tracking model set based on the dynamic characteristics of the target aircraft, improves the description precision of target motion, further improves the target tracking precision by adopting an improved variable-structure multi-model tracking algorithm, and improves the robustness of target maneuvering by updating the model and the corresponding probability by detecting the target maneuvering.
Drawings
FIG. 1 is a schematic block diagram of a variable structure multi-model algorithm tracking;
FIG. 2 is a diagram of the actual motion trajectory of a simulation example target;
FIG. 3 is a diagram illustrating a variation of an actual movement velocity and a roll angle of a target in a simulation example;
FIG. 4 is a tracking error diagram of a variable structure tracking algorithm in a weak maneuvering state;
FIG. 5 is a diagram of the error of the fit of each algorithm to the target roll angle under weak maneuvering conditions;
FIG. 6 is a tracking error diagram of a variable structure tracking algorithm under a strong maneuvering condition;
FIG. 7 is a diagram of the error of the fit of each algorithm to the target roll angle under a strong maneuver condition.
Detailed Description
The first embodiment is as follows:
the embodiment is specifically described by referring to fig. 1, and the invention aims to improve the tracking and positioning accuracy of a high-speed maneuvering target in an adjacent space and predict the pneumatic characteristic parameters of the target and detect the maneuvering target by combining the tracking principle. Expanding the pneumatic characteristic parameters of the target into a target tracking state quantity by establishing an aircraft dynamics model, and carrying out filtering tracking; and simultaneously, tracking data of the target is obtained by combining a variable structure multi-model algorithm based on maneuvering detection. The above object is achieved by the following technical scheme:
in step 1, a dynamic tracking model set is constructed according to the dynamic characteristics of the target aircraft, and a state equation set of a maneuvering target tracking system is obtained.
In step 2 of the invention, a system measurement model is established according to the principle and distribution of the detection devices; a measurement equation and measurement noise for the system are obtained. The infrared observed quantity is the azimuth angle of the target, belongs to passive direction finding positioning, and the target is positioned through two or more infrared detectors.
In step 3, based on a state equation of the system, a measurement equation of the system and measurement noise, the motion state and the control parameters of the target aircraft are recursively estimated by using an improved variable structure multi-model algorithm based on target maneuver detection.
In the invention, the specific method for constructing the dynamics tracking model set according to the dynamics characteristics of the target aircraft and acquiring the state equation set of the maneuvering target tracking system in the step 1 comprises the following steps:
step 1-1, analyzing target maneuvering characteristics, selecting tracking model pneumatic parameters:
the maneuvering of the aircraft in the free glide section mainly comes from aerodynamic force in a mode that aerodynamic acceleration can be divided into resistance acceleration, turning acceleration and climbing acceleration along three directions of a ballistic system through pairs, namely:
Figure BDA0002604484020000081
from this equation, the aerodynamic parameter CL(alpha) with pneumatic parameters
Figure BDA0002604484020000082
The relationship (2) of (c). The frequent and great adjustment of range of flight angle of attack alpha can lead to that pneumatic parameter changes complicacy, aircraft acutely vibrate, is difficult to control, and the rate of change of alpha is very little in the process of gliding usually, and pneumatic parameter changes comparatively gently along with the angle of attack, and the parameter variation is less in the short time promptly, can estimate as the quantity of state, and the pneumatic parameter setting in the tracking model of event here is:
Figure BDA0002604484020000091
wherein S is the characteristic area of the target aircraft, and m is the mass of the target aircraft. Alpha is alphaD，αLAre a drag parameter and a lift parameter. Modeling the change characteristic of the pneumatic parameters by using Gaussian white noise to obtain a state equation of the maneuvering target tracking system:
Figure BDA0002604484020000092
wherein gamma isvIs the angle of inclination of the speed, omegaγWhite gaussian noise, omega, at the roll angleD，ωLThe Gaussian white noise is an aerodynamic parameter, R is aerodynamic force, and the expression is as follows:
Figure BDA0002604484020000093
the invention inclines the speed by the angle gammavAs model variables, different γ's were selectedvTo construct a set of mobile target tracking models. Further, in the present invention, the specific method for obtaining the measurement equation and the measurement noise of the system in step 2 is as follows:
step 2-1, establishing a detection system according to the tracking task requirement, and determining position vectors of a detector and a target under a detection coordinate system;
2-2, acquiring a three-dimensional position coordinate of the target aircraft under a detector according to an infrared detection principle to realize positioning of the target aircraft;
and 2-3, carrying out expansion analysis on the positioning mean square error according to the three-dimensional position coordinates of the target aircraft under the detector, and determining a measurement equation and measurement noise of the tracking system.
Further, in the invention, a detection coordinate system is established according to the position of the detector in the step 2-1, and the position vectors of the base point of the detector and the target in the detection coordinate system are determined;
position vector of the target under the detection system: r ═ x, y, z;
position vector of the base point of the detector under the detection system: sl＝(xl,yl,zl) And l represents the l-th detector;
the vector pointed to the target by the detector is: rl＝r-Sl＝(x-xl,y-yl,z-zl)。
Further, in the present invention, the step 2-2 of obtaining the three-dimensional position coordinates of the target aircraft under the detector according to the infrared detection principle includes the specific steps of:
let the target aircraft be at a distance from the probe:
Figure BDA0002604484020000094
due to the angle of detection alpha of the detectorlAnd betalComprises the following steps:
Figure BDA0002604484020000101
the conversion obtains:
Figure BDA0002604484020000102
Figure BDA0002604484020000103
Figure BDA0002604484020000104
Figure BDA0002604484020000105
the least square method is used as follows:
Figure BDA00026044840200001011
and obtaining the three-dimensional position coordinate X of the target aircraft under the detector as (X, y, z).
Further, in the present invention, the specific method for determining the noise measured by the tracking system in step 2-3 is as follows:
determining according to geometric principles:
Figure BDA0002604484020000106
in the formula,
Figure BDA0002604484020000107
wherein x is1，y1，z1The position components of the first detector in the x direction, the y direction and the z direction under a detection system are obtained; x is the number of2，y2，z2The position components of the second detector in the x direction, the y direction and the z direction under the detection system are obtained; Δ κ ═ κ2-κ1，
Figure BDA0002604484020000108
By measuring the noise formula:
Figure BDA0002604484020000109
the noise R is obtained, wherein,
Figure BDA00026044840200001010
Figure BDA0002604484020000111
Figure BDA0002604484020000112
in the above formula, c1＝κ2(x2-x1)-(y2-y1)，c2＝-κ1(x2-x1)+(y2-y1)；
Figure BDA0002604484020000113
Figure BDA0002604484020000114
And
Figure BDA0002604484020000115
respectively the mean square error of the position coordinates of the detector itself,
Figure BDA0002604484020000116
the mean square error is located for the target,
Figure BDA0002604484020000117
the mean square error of the detector detection angle alpha 1,
Figure BDA0002604484020000118
the mean square error of the detector detection angle alpha 2,
Figure BDA0002604484020000119
the mean square error of the angle beta 1 is detected for the detector,
Figure BDA00026044840200001110
the mean square error of the angle β 2 is detected for the detector.
Further, in step 3 of the invention, the motion state and the pneumatic parameters of the target aircraft are recursively estimated by using an improved variable structure multi-model algorithm based on target maneuver detection:
determining initial state quantity and initial covariance of the filter:
Figure BDA00026044840200001111
wherein,
Figure BDA00026044840200001112
as initial state quantity of the filter, E (x)0) The mean value of the initial state quantities of the target aircraft is obtained; taking the mean value
Figure BDA00026044840200001113
Is an initial covariance, x0Is the initial state quantity of the target aircraft;
the mathematical expectation of the matrix of random variables is defined as the matrix of the mathematical expectation of their individual elements, e (x) ═ μ. The covariance matrix of the multidimensional random variables is a symmetric matrix and plays a role of one-dimensional random variable variance in a certain sense. The covariance matrix C of X can be expressed as:
C＝E((X-μ)T(X-μ))
is provided with
Figure BDA0002604484020000121
Then:
Figure BDA0002604484020000122
Cov(X1,X2)＝ρσ1σ1
then (X)1,X2) Has a covariance matrix of
Figure BDA0002604484020000123
The probability density is:
Figure BDA0002604484020000124
c has a determinant of
Figure BDA0002604484020000125
Inverse matrix of
Figure BDA0002604484020000126
Let x ═ x1,x2)，
Then there are:
Figure BDA0002604484020000127
thus (X)1,X2) The probability density of (d) can be expressed as:
Figure BDA0002604484020000128
if n-dimensional random variable X ═ X (X)1,X2,…Xn) The probability density of (a) is:
Figure BDA0002604484020000129
let njFor events where model j is correct, with a prior probability
Figure BDA00026044840200001210
If j is 1,2 … r, then under the premise of model j, the likelihood function of the measured data at time k is:
Figure BDA00026044840200001211
wherein
Figure BDA00026044840200001212
Innovation residual calculated for filter j
Figure BDA00026044840200001213
The probability density of (a) is as follows:
Figure BDA0002604484020000131
under the guidance of Bayes theory, the posterior probability density of the model j at the moment k is as follows:
Figure BDA0002604484020000132
1. variable structure multi-model algorithm
First, input interaction:
Figure BDA0002604484020000133
Figure BDA0002604484020000134
wherein p isijIs the transition probability of model i transitioning to j. Mu.si,j(k-1/k-1) Mixed probability
Figure BDA0002604484020000135
Figure BDA0002604484020000136
Second step, filtering
Corresponding model Mj(k) To be provided with
Figure BDA0002604484020000137
Performing Kalman filtering
And (3) prediction:
Figure BDA0002604484020000138
prediction error covariance:
Figure BDA0002604484020000139
filtering:
Figure BDA00026044840200001310
Figure BDA00026044840200001311
filtering covariance:
Figure BDA00026044840200001312
and (3) estimating an observation equation:
kalman gain:
Figure BDA0002604484020000141
Figure BDA0002604484020000142
third, model probability updating
Figure BDA0002604484020000143
Λj(k)＝N(rj(k),0,Sj(k) K) the likelihood function of the pattern j at time k, defines a variable rj(k) Mean 0 and variance Sj(k) Gaussian distribution (also called normal distribution).
Figure BDA0002604484020000144
Fourth, output interaction
Figure BDA0002604484020000145
Figure BDA0002604484020000146
Fifthly, updating the model set
And further obtaining a corresponding model decision according to the model probability updating, wherein the model decision is a model self-adaptive process depending on a set model transformation algorithm and is used for filtering at the next moment. For the initialization of the state vector and covariance of the newly activated model, the probability weighted combination of each model at the previous moment is adopted for initialization, that is:
Figure BDA0002604484020000147
Figure BDA0002604484020000148
2. improved variable structure multi-model method
The variable structure tracking algorithm has a good tracking effect on the problem of strong maneuvering, and mainly comprises the steps of working a plurality of tracking filters simultaneously, calculating the output probability of each filter according to the residual error and the covariance of each filter, and finally combining the interactive output result of each filter to serve as tracking data. The specific flow is shown in fig. 1.
Aiming at the tracking of the strong maneuvering flying target, whether the target has strong maneuvering or not is detected in the tracking process, and the filtering innovation and the covariance thereof in the target tracking process are utilized to carry out discrimination detection by combining a variable structure multi-model algorithm. Past information should be forgotten much at the maneuvering time; the past information is used for a large amount of non-maneuvering time, and the model is adjusted in a self-adaptive mode by using the past information, so that the model parameters are closer to a real model, and the tracking precision of the target non-maneuvering time is improved. The tracking result of the improved multi-model algorithm (GIMM algorithm) is between the IMM algorithm and the AGIMM algorithm, but compared with the IMM algorithm, the improved multi-model algorithm is not limited by a preset model, and compared with the AGIMM algorithm, the improved multi-model algorithm is relatively stable without the phenomenon of overfitting.
The specific method comprises the following steps:
during the filtering process, the innovation rk+1|kSum innovation covariance Sk+1|kAnd the error of the one-step prediction is shown, when the one-step prediction has a large error, the target is most likely to have strong maneuvering, and the tracking system does not detect and make corresponding adjustment at the moment. Therefore, after the filtering is finished at each moment, the following are calculated: u _ max ═ max (u)L,uC,uR) The model with the highest posterior probability represents the model most suitable at this moment, if the innovation of the corresponding model is still large, the aircraft is considered to have strong maneuver, at this moment, whether the aircraft has the strong maneuver needs to be judged, and D (k) ═ r (k) is calculatedTS(k)-1r (k), r (k) representing the innovation of the maximum probability model at time k; s (k) represents the innovation covariance of the maximum probability model at time k. And reasonably setting a threshold value M, and if D (k) is greater than M, considering that the target has strong maneuvering.
The specific content of the method is as follows:
and after k filtering is finished at a certain moment, obtaining innovation corresponding to the maximum probability model and covariance of the innovation.
Calculating the maximum model probability:
umax＝max{u1,u2,u3}
the corresponding model is set as model j, then the distance function
Figure BDA0002604484020000151
Adjusting a tracking model:
the model adjustment is performed by analogy to the principle of directed graph switching.
When u1maxWhen, if D1(k) Not less than M, then
Figure BDA0002604484020000152
Wherein G is0Is the minimum grid spacing, k1，k2Is an adjustable parameter.
If D is1(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000153
When u2maxWhen, if D2(k) Not less than M, then
Figure BDA0002604484020000161
If D is2(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000162
When u3maxWhen, if D3(k) Not less than M, then
Figure BDA0002604484020000163
If D is3(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure BDA0002604484020000164
Example (b):
the computer adopted by the simulation of the embodiment of the invention is configured as follows: the CPU is i7-8550U, the main frequency is 1.80GHz, and the memory is 8 GB.
Simulation scene: the target does maneuvering motion in the adjacent space, the motion trail is shown in fig. 2, the attack angle of the target changes slowly in the process, the maneuvering condition of the target is mainly realized according to the change of the roll angle of the moving speed of the target, and the change of the roll angle is shown in fig. 3.
The method is characterized in that multiple multi-model algorithms are combined with a target tracking dynamic model to realize the tracking of a strong maneuvering target in an adjacent space, Monte Carlo simulation is carried out for multiple times, and the precision, the convergence speed and the stability of each algorithm are mainly analyzed and compared.
The target tracking state quantity is X ═ X yz vxvyvzαDαL]TAngle of inclination gammavThe angular velocity in the circular turning model is used as a multi-model discrimination value, filter tracking is performed by adopting an ckf filter method, and the velocity roll angle used by each model is output alternately as an estimated value of the roll angle, and is used as one of judgment and tracking accuracy.
The measurement adopts double infrared detection, the height of the original point of the infrared detection system is 5000m from the ground, the infrared detection system is coincident with the local geographic coordinate system, the north-sky-east coordinate system is adopted, the distance between the two infrared detectors is 900km, the detection distance of each infrared detector is 1100km, and the detection angle error is 6 multiplied by 10-4rad。
The algorithm tracking performance index is expressed by Normalized Position Error (NPE), which is the ratio of Root Mean Square Error (RMSE) of position filtering to RMSE of position measurement, and is specifically expressed as follows:
Figure BDA0002604484020000171
wherein M is the simulation times of the Monte Carlo.
Simulation one: the period of 590s and 640s for tracking the target is in the weak maneuvering state, the tracking result is shown in fig. 4, and the tilt angle fitting error is shown in fig. 5. The following are NEP error cases:
table 1 comparison of simulation results
Figure BDA0002604484020000172
Simulation II: the period of time that the target 540 and 590s are tracked, the target is in a strong maneuvering state, the tracking result is shown in fig. 6, and the tilt angle fitting error is shown in fig. 7. The following are simulation results of the NEP error case:
TABLE 1 tracking result comparison
Figure BDA0002604484020000173
From the above simulation images and data, it can be seen that:
1) in the aspect of tracking precision: when the target maneuverability is not strong, the tracking errors of the four variable structure multi-model tracking methods reach within one hundred meters, and the tracking precision is kept about one hundred meters when strong maneuverability occurs; and comprehensively comparing, the GIMM algorithm has the best comprehensive tracking precision in the aspects of weak maneuver and strong maneuver.
2) In the convergence rate aspect: the AGIMM algorithm reacts fastest under the condition of strong maneuvering and can keep up with maneuvering change of a target, and the GIMM algorithm is adopted secondly, but the methods have no great difference in data processing time.
3) Stability aspect: the four methods can be adjusted at any time according to the target maneuvering condition in the filtering process, can ensure that the tracking error is stable in a certain range, and has no dispersion condition.
The method is used for discussing the tracking problem of the near space strong maneuvering aircraft, and a target dynamic model and a variable structure multi-model method are combined to position and track the target. The tracking accuracy is improved, the pneumatic characteristic and the maneuvering state of the target are obtained, and the method is greatly helpful for recognizing the target and forecasting the track.
From the above, the embodiment of the invention realizes the problem of strong maneuvering aircraft tracking in the near space. The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and the present invention is also applicable to other related tracking problems. Any modification, equivalent replacement, and improvement made within the spirit and scope of the present invention shall be included in the protection scope of the present invention.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (7)

1. A strong maneuvering target tracking method based on variable structure multiple models is characterized by comprising the following steps:
the method comprises the following steps: constructing a dynamic tracking model set by using the dynamic characteristics of the target aircraft, and then acquiring a state equation set of a maneuvering target tracking system;
step two: establishing a system measurement model, and obtaining a measurement equation and measurement noise of the system according to the established system measurement model;
step three: and carrying out recursive estimation on the motion state and the pneumatic parameters of the target aircraft based on the state equation set of the system, the measurement equation of the system and the measurement noise.
2. The method for tracking the strong maneuvering target based on the variable structure multiple models as claimed in claim 1, characterized in that the specific steps of the first step are as follows:
the method comprises the following steps: selecting the pneumatic parameters of the tracking model according to the maneuvering characteristics of the target,
the tracking model pneumatic parameters are as follows:
Figure FDA0002604484010000011
wherein, CL(. alpha.) and CD(α) is the pneumatic parameter, CL(α) is the coefficient of lift, CD(α) is the drag coefficient, S is the characteristic area of the target aircraft, m is the mass of the target aircraft, αD，αLResistance parameters and lift parameters;
the first step is: modeling the change characteristic of the pneumatic parameters by using Gaussian white noise to obtain a state equation of the maneuvering target tracking system, wherein the state equation of the maneuvering target tracking system is as follows:
Figure FDA0002604484010000012
wherein, ω iseIs the angular velocity vector of the earth rotation, g is the gravity acceleration of the earth, r is the position vector of the target under the detection system, and v is the target under the detection systemThe speed of the object under the system is detected,
Figure FDA0002604484010000013
is a transfer matrix from a ballistic coordinate system to a detection system, theta is a velocity inclination angle, sigma is an azimuth angle, and gamma isvIs the angle of inclination of the speed, omegaγWhite gaussian noise, omega, at the roll angleD，ωLWhite Gaussian noise as an aerodynamic parameter, R is aerodynamic force, wherein
Figure FDA0002604484010000014
S is the characteristic area of the target aircraft:
Figure FDA0002604484010000015
step one is three: the roll angle gamma of the speed in the first step and the second stepvAs model variables, different speed roll angles γ are selectedvAnd constructing a state equation set of the maneuvering target tracking system.
3. The variable structure multi-model-based strong maneuvering target tracking method according to claim 2, characterized in that the step of obtaining the measurement equation and the measurement noise of the system in the step two specifically comprises:
step two, firstly: establishing a detection coordinate system according to the requirement of the tracking task, and determining position vectors of the detector and the target under the detection coordinate system;
step two: acquiring a three-dimensional position coordinate of a target aircraft in a detector body system according to an infrared detection principle;
step two and step three: and (3) performing expansion analysis on the mean square error of positioning by using the three-dimensional position coordinates of the target aircraft in the system of the detector, and determining a measurement equation and measurement noise of the tracking system.
4. The method for tracking the strongly maneuvering target based on the variable structure multi-model as recited in claim 3, characterized in that in the first step, the position vectors of the detector and the target under the detection coordinate system are:
position vector of the target under the detection coordinate system: r ═ x, y, z;
position vector of the detector under the detection coordinate system: sl＝(xl，yl，zl) And l represents the l-th detector.
5. The method for tracking the strong maneuvering target based on the variable structure multiple models as claimed in claim 4, characterized in that the specific steps of the second step are:
first, the vector of the probe pointing to the target is:
Figure FDA0002604484010000021
detector detection angle alphalAnd betalExpressed as:
Figure FDA0002604484010000022
the conversion obtains:
Figure FDA0002604484010000023
Figure FDA0002604484010000024
Figure FDA0002604484010000025
Figure FDA0002604484010000026
obtaining the three-dimensional position coordinate X ═ (X, y, z) of the target aircraft under the detector by using a least square method
The least squares are expressed as:
Figure FDA0002604484010000027
where M is the measurement matrix, X is the state quantity, and Y is the quantity measurement.
6. The variable structure multi-model-based strong maneuvering target tracking method according to claim 5, characterized in that the specific steps of determining the measurement equation and the measurement noise of the tracking system in the second and third steps are as follows:
firstly, determining the relative position and angle relationship between the target and the detector according to the geometric principle:
Figure FDA0002604484010000031
in the formula,
Figure FDA0002604484010000032
x1，y1，z1the position components of the first detector in the x direction, the y direction and the z direction under a detection system are obtained; x is the number of2，y2，z2The position components of the second detector in the x direction, the y direction and the z direction under the detection system are obtained; Δ κ ═ κ2-κ1，
Figure FDA0002604484010000033
Then, obtaining noise R through a measurement noise formula, wherein the measurement noise formula is as follows:
Figure FDA0002604484010000034
wherein,
Figure FDA0002604484010000035
Figure FDA0002604484010000036
Figure FDA0002604484010000041
in the above formula, c1＝κ2(x2-x1)-(y2-y1)，c2＝-κ1(x2-x1)+(y2-y1)；
Figure FDA0002604484010000042
Figure FDA0002604484010000043
Figure FDA0002604484010000044
And
Figure FDA0002604484010000045
respectively the mean square error of the position coordinates of the detector itself,
Figure FDA0002604484010000046
the mean square error is located for the target,
Figure FDA0002604484010000047
the mean square error of the detector detection angle alpha 1,
Figure FDA0002604484010000048
the mean square error of the detector detection angle alpha 2,
Figure FDA0002604484010000049
the mean square error of the angle beta 1 is detected for the detector,
Figure FDA00026044840100000410
the mean square error of the angle β 2 is detected for the detector.
7. The variable structure multi-model-based strong maneuvering target tracking method is characterized in that in the third step, the motion state and the pneumatic parameters of the target aircraft are estimated recursively by using an improved variable structure multi-model algorithm; the improved variable structure multi-model algorithm comprises the following specific steps:
first, input interaction:
Figure FDA00026044840100000411
m is the set of the model totality, i, j represents the ith, j model,
Figure FDA00026044840100000412
wherein p isijIs the transition probability, μ, of model i transitioning to ji，j(k-1/k-1) is a mixed probability
Figure FDA00026044840100000413
Figure FDA00026044840100000414
And step two, filtering:
for model Mj(k) To be provided with
Figure FDA0002604484010000051
Performing Kalman filtering, phijFor the state transition matrix, the prediction is:
Figure FDA0002604484010000052
the prediction error covariance is:
Figure FDA0002604484010000053
the filtering is:
Figure FDA0002604484010000054
Figure FDA0002604484010000055
the filtering covariance is:
Figure FDA0002604484010000056
and (4) estimating an observation equation, wherein the Kalman gain is as follows:
Figure FDA0002604484010000057
Figure FDA0002604484010000058
thirdly, updating model probability:
Figure FDA0002604484010000059
Λj(k)＝N(rj(k)，0，Sj(k) k) the likelihood function of the pattern j at time k, defines a variable rj(k) Mean 0 and variance Sj(k) Gaussian distribution (also called normal distribution).
Figure FDA00026044840100000510
Step four, outputting interaction:
Figure FDA00026044840100000511
Figure FDA00026044840100000512
fifthly, updating the model set:
calculating the maximum model probability:
umax＝max{u1，u2，u3}
and the corresponding model is set as a model j, the distance function is as follows:
Figure FDA00026044840100000513
tracking model adjustment, which is performed by analogy with the principle of directed graph switching,
when u1maxWhen, if D1(k) Not less than M, then
Figure FDA0002604484010000061
Wherein G is0Is the minimum grid spacing, k1，k2In order to be able to adjust the parameters,
if D is1(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure FDA0002604484010000062
When u2maxWhen, if D2(k) Not less than M, then
Figure FDA0002604484010000063
If D is2(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure FDA0002604484010000064
When u3maxWhen, if D3(k) Not less than M, then
Figure FDA0002604484010000065
If D is3(k) If < M, updating the model according to a method of switching a directed graph, namely
Figure FDA0002604484010000066
For the initialization of the state vector and covariance of the newly activated model, the probability weighted combination of each model at the previous moment is adopted for initialization, that is:
Figure FDA0002604484010000067
Figure FDA0002604484010000068
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111798491A (en) * 2020-07-13 2020-10-20 哈尔滨工业大学 Maneuvering target tracking method based on Elman neural network
CN112257259A (en) * 2020-10-21 2021-01-22 中国人民解放军战略支援部队信息工程大学 Ballistic missile whole-course ballistic estimation method and system based on improved autonomous multi-model
CN112577489A (en) * 2020-12-08 2021-03-30 北京电子工程总体研究所 Seeker sight rotation rate extraction method based on interactive multi-model filtering
CN112784506A (en) * 2021-01-29 2021-05-11 中国人民解放军空军工程大学 Reentry maneuvering trajectory target tracking algorithm based on variable structure multi-model
CN114019792A (en) * 2021-10-08 2022-02-08 北京控制工程研究所 Mars atmosphere entering process lift guidance error analysis method and system
CN115268487A (en) * 2022-07-13 2022-11-01 北京电子工程总体研究所 Aircraft altitude control method and system based on disturbance estimation compensation LOS guidance law
CN115390560A (en) * 2022-08-18 2022-11-25 哈尔滨工业大学 Ground target track tracking method based on mixed grid multi-model
CN118194609A (en) * 2024-05-17 2024-06-14 北京理工大学前沿技术研究院 Group target tracking method, device and storage medium based on generalization multivariable model

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104020466A (en) * 2014-06-17 2014-09-03 西安电子科技大学 Maneuvering target tracking method based on variable structure multiple models
CN104793201A (en) * 2015-05-04 2015-07-22 哈尔滨工业大学 Modified variable-structure grid interaction multi-model filtering method for tracking hypersonic-speed target of near space
CN107544067A (en) * 2017-07-06 2018-01-05 西北工业大学 One kind is based on the approximate Hypersonic Reentry Vehicles tracking of Gaussian Mixture

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104020466A (en) * 2014-06-17 2014-09-03 西安电子科技大学 Maneuvering target tracking method based on variable structure multiple models
CN104793201A (en) * 2015-05-04 2015-07-22 哈尔滨工业大学 Modified variable-structure grid interaction multi-model filtering method for tracking hypersonic-speed target of near space
CN107544067A (en) * 2017-07-06 2018-01-05 西北工业大学 One kind is based on the approximate Hypersonic Reentry Vehicles tracking of Gaussian Mixture

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
WEI H等: "Review of the algorithms for radar single target tracking", 《IOP CONFERENCE SERIES: EARTH AND ENVIRONMENTAL SCIENCE》 *
于红娟等: "基于变结构多模型的机动目标跟踪算法", 《火力与指挥控制》 *
刘德虎: "基于变结构多模型算法的高机动目标跟踪研究", 《中国优秀硕士学位论文全文数据库信息科技辑》 *
娄益茂: "变结构多模型机动目标跟踪算法研究", 《中国优秀硕士学位论文全文数据库信息科技辑》 *
陈志锋: "强机动目标自适应跟踪算法研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 *

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111798491A (en) * 2020-07-13 2020-10-20 哈尔滨工业大学 Maneuvering target tracking method based on Elman neural network
CN112257259B (en) * 2020-10-21 2023-08-22 中国人民解放军战略支援部队信息工程大学 Method and system for estimating whole-course trajectory of ballistic missile based on improved autonomous multiple models
CN112257259A (en) * 2020-10-21 2021-01-22 中国人民解放军战略支援部队信息工程大学 Ballistic missile whole-course ballistic estimation method and system based on improved autonomous multi-model
CN112577489A (en) * 2020-12-08 2021-03-30 北京电子工程总体研究所 Seeker sight rotation rate extraction method based on interactive multi-model filtering
CN112577489B (en) * 2020-12-08 2024-05-07 北京电子工程总体研究所 Seeker sight rotation rate extraction method based on interactive multi-model filtering
CN112784506A (en) * 2021-01-29 2021-05-11 中国人民解放军空军工程大学 Reentry maneuvering trajectory target tracking algorithm based on variable structure multi-model
CN112784506B (en) * 2021-01-29 2023-04-07 中国人民解放军空军工程大学 Reentry maneuvering trajectory target tracking algorithm based on variable structure multi-model
CN114019792B (en) * 2021-10-08 2023-08-01 北京控制工程研究所 Mars atmosphere entry process lift force guidance error analysis method and system
CN114019792A (en) * 2021-10-08 2022-02-08 北京控制工程研究所 Mars atmosphere entering process lift guidance error analysis method and system
CN115268487A (en) * 2022-07-13 2022-11-01 北京电子工程总体研究所 Aircraft altitude control method and system based on disturbance estimation compensation LOS guidance law
CN115268487B (en) * 2022-07-13 2024-05-28 北京电子工程总体研究所 Aircraft altitude control method and system based on disturbance estimation and compensation LOS guidance law
CN115390560A (en) * 2022-08-18 2022-11-25 哈尔滨工业大学 Ground target track tracking method based on mixed grid multi-model
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CN118194609A (en) * 2024-05-17 2024-06-14 北京理工大学前沿技术研究院 Group target tracking method, device and storage medium based on generalization multivariable model

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