CN111239722B - Tracking algorithm for maneuvering mutation of near space high-speed maneuvering target - Google Patents

Tracking algorithm for maneuvering mutation of near space high-speed maneuvering target Download PDF

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CN111239722B
CN111239722B CN202010089368.5A CN202010089368A CN111239722B CN 111239722 B CN111239722 B CN 111239722B CN 202010089368 A CN202010089368 A CN 202010089368A CN 111239722 B CN111239722 B CN 111239722B
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CN111239722A (en
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邹昕光
周荻
李君龙
蔡明春
陈晓波
曹颖
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
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Abstract

The invention discloses a tracking algorithm of maneuvering mutation of a high-speed maneuvering target in a near space, belongs to the technical field of tracking of the high-speed maneuvering target in the near space, and aims to solve the problem that the tracking algorithm of the movement of the target is unreasonable in the prior art. The specific process of the tracking algorithm of the invention is as follows: establishing a coordinate system and establishing a coordinate transformation matrix; establishing a motion equation of a high-speed maneuvering target in the near space; establishing a nonlinear maneuver model of a near space high-speed maneuver target; and constructing an IMM tracking filter, and realizing the tracking filtering of the IMM tracking filter on the near space high-speed maneuvering target. The method and the device are used for estimating the motion state of the target.

Description

Tracking algorithm for maneuvering mutation of near space high-speed maneuvering target
Technical Field
The invention relates to a tracking algorithm for maneuvering mutation of a high-speed maneuvering target in a near space, and belongs to the technical field of tracking of the high-speed maneuvering target in the near space.
Background
An observer fixed on the ground needs to estimate the motion state of the target, including position, velocity, acceleration, and the like. The traditional method comprises the following steps: firstly, a target adopts a certain known motion mode, such as a uniform motion mode, a uniform acceleration motion mode or a turning motion mode; secondly, modeling the target motion on the basis of the assumption; then, a Kalman filter is used to estimate the motion state of the target.
However, the motion pattern of the near-space high-speed maneuvering target does not conform to the above-mentioned common pattern, and it is difficult to model the target motion using the conventional motion pattern.
Zhang Bolun, zhou Di and Wu Shikai are published in "System engineering and electronics, 2019,41 (09): 2072-2079." hypersonic in near spaceIn the maneuvering model and trajectory prediction of the aircraft, a new modeling method is adopted, and three state variables Z related to aerodynamic force are introduced x ,Z y ,Z z To describe a motion model of a high-speed maneuvering target in near space, assuming Z x ,Z y ,Z z On the basis of slower change, a corresponding motion model is deduced, and finally an extended Kalman filter is designed to track the target motion.
However, in some scenarios, the near space high speed maneuver target may maneuver with a fast rolling motion, thus assuming Z z It is not reasonable to change slowly.
On the other hand, when the target makes a rolling maneuver, the movement pattern of the target is changed. The conventional Kalman filter may have a reduced estimation accuracy in case of mismatch between its own model and actual mode.
Disclosure of Invention
The invention aims to solve the problem that the tracking algorithm of the target motion is unreasonable in the prior art, and provides a tracking algorithm of the maneuvering mutation of a near-space high-speed maneuvering target.
The invention relates to a tracking algorithm of a maneuvering mutation of a near space high-speed maneuvering target, which comprises the following specific processes:
s1, establishing a coordinate system and establishing a coordinate transformation matrix;
s2, establishing a motion equation of a high-speed maneuvering target in the near space;
s3, establishing a nonlinear maneuver model of the near space high-speed maneuver target;
s4, constructing an IMM tracking filter, and realizing the tracking filtering of the IMM tracking filter on the near space high-speed maneuvering target.
Preferably, the specific method for establishing the coordinate system in S1 is as follows:
establishing a geocentric inertial coordinate system O I x I y I z I : with the earth's center as the origin O I The direction of the origin point towards the observation point is O I y I Shaft, O I x I Shaft and O I y I The axis is vertical, and O I x I The axis being in the shooting plane of the target, O I x I The direction of the point on the axis pointing to the target is positive, and O is obtained according to the right hand rule I z I A shaft;
establishing an observer inertial coordinate system O o0 x o0 y o0 z o0 : with the position of the observer as the origin O o0 In the upward direction of plumb is O o0 y o0 Shaft, and O o0 y o0 With O I y I Overlap, O o0 x o0 Shaft and O I x I Parallel and in the same direction, and then according to the right hand rule, O is obtained o0 z o0 A shaft;
establishing an inertial coordinate system O of a transmitting point of a high-speed maneuvering target in a near space 0 x 0 y 0 z 0 : with the emission point of the target as the origin O 0 ，O 0 y 0 Shaft and O o0 y o0 The axial directions are the same, O 0 x 0 Shaft and O o0 x o0 The axial directions are opposite, and O is obtained according to the right hand rule 0 z 0 A shaft;
establishing a coordinate system Ox of a high-speed maneuvering target projectile body in a near space 1 y 1 z 1 : with the centroid of the target as the origin O and the direction of the projectile longitudinal axis as Ox 1 Axis, the direction of the projectile head of the target being the positive direction Oy 1 Axis and Ox 1 The axis is vertical and in the plane of longitudinal symmetry of the projectile, the upward direction is Oy 1 The positive direction of the axis is then determined by right hand rule to obtain Oz 1 A shaft;
establishing a trajectory coordinate system Ox of a high-speed maneuvering target in a near space 2 y 2 z 2 : with the centroid of the target as the origin O, ox 2 The positive direction of the axis is the direction of the target velocity vector v, oy 2 Axis and Ox 2 The axis is vertical, and the upward direction is Oy 2 Positive direction of axis, oy 2 The axis is in the vertical plane containing v, and Oz is obtained according to the right hand rule 2 A shaft;
establishing a near space high-speed maneuvering target speed coordinate system Ox 3 y 3 z 3 : with the centroid of the target as the origin O, ox 3 The positive direction of the axis is the direction of the target velocity vector v, oy 3 Axis and Ox 3 The axis is vertical, and the upward direction is Oy 3 Positive direction of axis, oy 3 The axis being in the plane of longitudinal symmetry of the projectile of the target, oz being obtained according to the right-hand rule 3 A shaft.
The invention has the advantages that:
1. the assumption is relaxed and the aerodynamic related state variable Z is no longer assumed z Is slowly varying;
2. the novel operation model is provided, the IMM (interactive multi-model) tracking algorithm is adopted to realize tracking filtering on the motion model, the problem of target motion mode jump can be well processed, and better filtering performance is achieved.
Drawings
FIG. 1 is a schematic diagram of a geocentric inertial coordinate system and an observer inertial coordinate system according to the present invention;
FIG. 2 is a roll angle from gamma c Jump to gamma=45 deg c Target flight trajectory schematic at=0 deg;
FIGS. 3-5 are schematic diagrams of target acceleration estimates for the X-axis, Y-axis, and Z-axis, respectively, for the case of FIG. 2;
FIGS. 6-8 are schematic diagrams of target speed estimation for the X-axis, Y-axis, and Z-axis, respectively, of the case of FIG. 2;
FIGS. 9-11 are schematic diagrams of target position estimation for the X-axis, Y-axis and Z-axis, respectively, of the case of FIG. 2;
FIGS. 12-14 are, respectively, parameter Z in the case of FIG. 2 x ，Z y and Zz Is an estimated schematic of (1);
FIG. 15 is a schematic diagram of probability of IMM model in the case of FIG. 2;
FIG. 16 is a roll angle from γ c Jump to gamma=45 deg c Target flight trajectory diagram at = -45 deg;
FIGS. 17-19 are schematic diagrams of target acceleration estimates for the X-axis, Y-axis, and Z-axis, respectively, for the case of FIG. 16;
FIGS. 20-22 are schematic diagrams of target speed estimation for the X-axis, Y-axis, and Z-axis, respectively, of the case of FIG. 16;
FIGS. 23-25 are schematic diagrams of target position estimation for the X-axis, Y-axis and Z-axis, respectively, of the case of FIG. 16;
FIGS. 26-28 are, respectively, parameter Z in the case of FIG. 16 x ，Z y and Zz Is an estimated schematic of (1);
fig. 29 is a schematic diagram of IMM model probabilities in the case of fig. 16.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The first embodiment is as follows: the following describes, with reference to fig. 1, a tracking algorithm for maneuver mutation of a high-speed maneuver target in the near space according to the present embodiment, where the specific process of the tracking algorithm is as follows:
s1, establishing a coordinate system and establishing a coordinate transformation matrix;
s2, establishing a motion equation of a high-speed maneuvering target in the near space;
s3, establishing a nonlinear maneuver model of the near space high-speed maneuver target;
s4, constructing an IMM tracking filter, and realizing the tracking filtering of the IMM tracking filter on the near space high-speed maneuvering target.
Further, the specific method for establishing the coordinate system in S1 is as follows:
establishing a geocentric inertial coordinate system O I x I y I z I : with the earth's center as the origin O I The direction of the origin point towards the observation point is O I y I Shaft, O I x I Shaft and O I y I The axis is vertical, and O I x I The axis being in the shooting plane of the target, O I x I The direction of the point on the axis pointing to the target is positive, and O is obtained according to the right hand rule I z I A shaft;
establishing an observer inertial coordinate system O o0 x o0 y o0 z o0 : with the position of the observer as the origin O o0 In the upward direction of plumb is O o0 y o0 Shaft, and O o0 y o0 With O I y I Overlap, O o0 x o0 Shaft and O I x I Parallel and in the same direction, and then according to the right hand rule, O is obtained o0 z o0 A shaft;
establishing an inertial coordinate system O of a transmitting point of a high-speed maneuvering target in a near space 0 x 0 y 0 z 0 : with the emission point of the target as the origin O 0 ，O 0 y 0 Shaft and O o0 y o0 The axial directions are the same, O 0 x 0 Shaft and O o0 x o0 The axial directions are opposite, and O is obtained according to the right hand rule 0 z 0 A shaft;
establishing a coordinate system Ox of a high-speed maneuvering target projectile body in a near space 1 y 1 z 1 : with the centroid of the target as the origin O and the direction of the projectile longitudinal axis as Ox 1 Axis, the direction of the projectile head of the target being the positive direction Oy 1 Axis and Ox 1 The axis is vertical and in the plane of longitudinal symmetry of the projectile, the upward direction is Oy 1 The positive direction of the axis is then determined by right hand rule to obtain Oz 1 A shaft;
establishing a trajectory coordinate system Ox of a high-speed maneuvering target in a near space 2 y 2 z 2 : with the centroid of the target as the origin O, ox 2 The positive direction of the axis is the direction of the target velocity vector v, oy 2 Axis and Ox 2 The axis is vertical, and the upward direction is Oy 2 Positive direction of axis, oy 2 The axis is in the vertical plane containing v, and Oz is obtained according to the right hand rule 2 A shaft;
establishing a near space high-speed maneuvering target speed coordinate system Ox 3 y 3 z 3 : order ofThe centroid of the target is the origin O, ox 3 The positive direction of the axis is the direction of the target velocity vector v, oy 3 Axis and Ox 3 The axis is vertical, and the upward direction is Oy 3 Positive direction of axis, oy 3 The axis being in the plane of longitudinal symmetry of the projectile of the target, oz being obtained according to the right-hand rule 3 A shaft.
Still further, the specific method for performing coordinate transformation in S1 is as follows:
from observer inertial coordinate system O o0 x o0 y o0 z o0 Inertial coordinate system O of high-speed maneuvering target emission point in near space 0 x 0 y 0 z 0 The conversion matrix between them is:
Figure BDA0002383208070000041
inertial coordinate system O of emission point of high-speed maneuvering target from near space 0 x 0 y 0 z 0 To the near space high speed maneuvering target projectile coordinate system Ox 1 y 1 z 1 The conversion matrix between them is:
Figure BDA0002383208070000051
namely:
Figure BDA0002383208070000052
wherein ,
Figure BDA0002383208070000053
pitch angle of Ox representing high-speed maneuvering target in near space 1 Shaft and O 0 x 0 z 0 Included angle between planes Ox 1 Axis direction O 0 x 0 z 0 The angle is positive when the plane is above;
psi denotes the yaw angle of the near space high speed maneuver target, ox 1 Axis at O 0 x 0 z 0 In-plane projections Ox' and O 0 x 0 The included angle between the axes facing O 0 x 0 Shaft, when O 0 x 0 When the shaft rotates to Ox', the psi is positive when the shaft rotates anticlockwise;
gamma denotes the roll angle of the high-speed maneuvering target in the near space, which is Oy 1 Shaft and contain Ox 1 The included angle between the vertical planes of the axes is seen from the tail of the projectile body along the longitudinal axis, when Oy 1 When the shaft is positioned on the right side of the vertical plane, gamma is positive;
inertial coordinate system O of emission point of high-speed maneuvering target from near space 0 x 0 y 0 z 0 To the near space high speed maneuvering target trajectory coordinate system Ox 2 y 2 z 2 The conversion matrix between them is:
Figure BDA0002383208070000054
namely:
Figure BDA0002383208070000055
wherein θ represents the ballistic inclination of the high-speed maneuvering target in the near space, which is Ox 2 Shaft and O 0 x 0 z 0 Included angle between planes, ox 2 Axis direction O 0 x 0 z 0 When the plane is above, θ is positive;
ψ v a ballistic deflection angle of Ox representing a high-speed maneuvering target in the near space 2 Axis at O 0 x 0 z 0 Projection Ox 'on plane' 2 With O 0 x 0 The angle of the axes facing O 0 x 0 Shaft, when O 0 x 0 Pivoting to Ox' 2 Rotated anticlockwise, ψ v Is positive.
Still further, the specific method for establishing the motion equation of the high-speed maneuvering target in the near space in S2 is as follows:
establishing a motion equation of a high-speed maneuvering target in the near space:
Figure BDA0002383208070000061
/>
wherein ,xI 、y I and zI Representing the position information of the near space high speed maneuvering target in the geocentric inertial coordinate system,
Figure BDA0002383208070000062
Figure BDA0002383208070000063
and />
Figure BDA0002383208070000064
Respectively represent x I 、y I and zI Second derivative of>
Figure BDA0002383208070000065
Representing the distance between the high-speed maneuvering target in the near space and the earth center, wherein the unit is meter; a, a xI 、a yI and azI Representing components of acceleration information in a geocentric inertial coordinate system;
μ＝3.98199×10 14 ；
the flight height h is:
Figure BDA0002383208070000066
wherein ,Re Representing the average radius of the earth.
In the present embodiment, a xI 、a yI and azI Refers to the component of the acceleration in the geocentric inertial coordinate system that is generated by aerodynamic forces.
Still further, a xI 、a yI and azI The acquisition method of (1) comprises the following steps:
the projection of the stress of the high-speed maneuvering target in the near space in the projectile body coordinate system is as follows:
R x1 ＝-C x qS
R y1 ＝C y sign(α)qS；
R z1 ＝0
where α is the angle of attack of the near space high speed maneuver target, q=ρv 2 2 is dynamic pressure head, ρ is air density;
C x and Cy Respectively representing components of aerodynamic coefficients in an x axis and a y axis of a target trajectory coordinate system;
s represents the equivalent reference area of the target,
Figure BDA0002383208070000071
representing the target speed magnitude;
in the geocentric inertial coordinate system, the projection of the flying speed of the near-space high-speed maneuvering target on the geocentric inertial coordinate system is as follows:
Figure BDA0002383208070000072
Figure BDA0002383208070000073
Figure BDA0002383208070000074
respectively represent x I 、y I and zI Is the first derivative of (a);
projecting a vector of the flying speed of the near-space high-speed maneuvering target on an inertial coordinate system of a transmitting point of the near-space high-speed maneuvering target:
Figure BDA0002383208070000075
C I→0 a conversion matrix for representing the geocentric inertial coordinate system to a near space high-speed maneuvering target inertial coordinate system;
C I→0 ＝C I→o0 C o0→0 ＝C o0→0 ；
wherein ,
Figure BDA0002383208070000076
/>
the ballistic inclination and ballistic deflection of the near space high speed maneuver target is:
Figure BDA0002383208070000077
the attitude angle of the near space high speed maneuver target is:
Figure BDA0002383208070000078
wherein ,γc Is a roll angle command;
then a xI 、a yI and azI The method comprises the following steps:
Figure BDA0002383208070000081
m represents the target mass in Kg.
In the present embodiment, the high-speed maneuvering target in the near space adopts BTT mode, and the sideslip angle thereof is kept to be β=0 during the movement, so that the force applied to the target is easily known to be R z1 ＝0。
Still further, the specific method for establishing the nonlinear maneuver model of the near space high-speed maneuver target in S3 is as follows:
s3-1, acquiring state variables Z related to aerodynamic drag, lift force and lateral force x 、Z y 、Z z ：
Figure BDA0002383208070000082
wherein ,mT Representing the target mass, C x 、C y 、C z Respectively representing components of aerodynamic coefficients in the x-axis, y-axis and z-axis of a target trajectory coordinate system, and S tableShowing the target equivalent reference area;
s3-2, establishing a nine-order motion model of a near space high-speed maneuvering target:
Figure BDA0002383208070000083
wherein [ x, y, z] T For the position vector of the high-speed maneuvering target in the near space, [ v ] x ,v y ,v z ] T For the velocity vector of a high-speed maneuvering target in the near space, [ a ] x ,a y ,a z ] T For the acceleration vector of the near space high-speed maneuvering target caused by aerodynamic force, [ g ] x ,g y ,g z ] T Is a gravitational acceleration vector acting on a high-speed maneuvering target in near space;
Z x 、Z y and Zz Representing components of aerodynamic related state variables in the x-axis, y-axis and z-axis of the target ballistic coordinate system, respectively;
Figure BDA0002383208070000091
and />
Figure BDA0002383208070000092
Respectively x, y, z, v x 、v y 、v z 、Z x 、Z y and Zz Is the first derivative of (a);
Figure BDA0002383208070000093
Figure BDA0002383208070000094
wherein ρ is the air density;
Figure BDA0002383208070000095
is the target speed size; μ= 3.98199 ×10 14 ；
Figure BDA0002383208070000096
Is the distance between the high-speed maneuvering target in the near space and the earth center;
C o0→2 the system comprises a conversion matrix from an observer inertia coordinate system to a trajectory coordinate system of a high-speed maneuvering target in the near space;
Figure BDA0002383208070000097
s3-3 due to
Figure BDA0002383208070000098
The force of the aerodynamic force of the high-speed maneuvering target in the near space under the bullet system of the high-speed maneuvering target in the near space is shown, and +.>
Figure BDA0002383208070000099
The acceleration generated by the forces of the aerodynamic forces of the high-speed maneuvering target in the near space under the inertial coordinate system of the observer is represented, so that:
Figure BDA00023832080700000910
will be
Figure BDA0002383208070000101
Substituted into->
Figure BDA0002383208070000102
The method can obtain:
Figure BDA0002383208070000103
then the following is obtained:
Figure BDA0002383208070000104
the measurement matrix is:
Figure BDA0002383208070000105
still further, the specific method for constructing the IMM tracking filter in S3 is as follows:
the model set of the IMM tracking filter is: m= { M 1 ,…,M n }；
wherein ,Mj Represents the j-th model with a priori probability of
Figure BDA0002383208070000106
Figure BDA0002383208070000107
An event indicating that the jth model at the initial time is matched with the real mode;
Figure BDA0002383208070000108
converting probabilities for a known model;
Figure BDA0002383208070000109
events representing the j-th model at time k and true pattern matching, < >>
Figure BDA00023832080700001010
An event representing the matching of the ith model at time k-1 with the true pattern;
M j the corresponding state equation and measurement equation are respectively:
Figure BDA00023832080700001011
wherein ,fj (k,x k-1 ) Represents M j State transition function, h j (k,x k ) Represents M j Is used as a measurement function of the (c),
Figure BDA00023832080700001012
represents M j Process noise of->
Figure BDA00023832080700001013
Represents M j Is a measurement noise of (a);
s7-1, calculating a current initial state and a covariance matrix by the element filter according to the estimated state and the covariance matrix of the last iteration:
Figure BDA0002383208070000111
wherein ,
Figure BDA0002383208070000112
representing the model M at time k-1 j Under the condition of matching with the real mode, the kth moment model M i Probability of matching with real pattern, +.>
Figure BDA0002383208070000113
For model M i Probability of matching with real pattern at time k, +.>
Figure BDA0002383208070000114
Is a normalization factor;
the mixed input calculation formula is:
Figure BDA0002383208070000115
wherein ,
Figure BDA0002383208070000116
and />
Figure BDA0002383208070000117
Representing a hybrid input and a hybrid covariance matrix, respectively;
Figure BDA0002383208070000118
the i-th model representing the moment k-1 corresponds to the state input of the Kalman filter;
Figure BDA0002383208070000119
representing a state covariance matrix of a Kalman filter corresponding to an ith model at the moment k-1;
s7-2, adopting a UKF filter as a meta-filter of the IMM tracking filter, and adopting S7-1 to obtain
Figure BDA00023832080700001110
And
Figure BDA00023832080700001111
as input, each UKF filter performs one filtering iteration;
the filtering includes two sub-steps, state prediction and state update, respectively:
Figure BDA00023832080700001112
wherein ,UKFp (. Cndot.) is the state prediction function, UKF u (. Cndot.) is a status update function;
Figure BDA00023832080700001113
a state transfer function representing the j-th model at time k-1;
Figure BDA00023832080700001114
a noise matrix representing the j-th model at time k-1; />
Figure BDA00023832080700001115
A state forecast covariance matrix of a j-th model at the moment k-1;
z k representing the measured value;
Figure BDA0002383208070000121
a measurement matrix representing a j-th model at time k;
Figure BDA0002383208070000122
a measurement noise matrix representing a j-th model at time k;
model M j At time t k Likelihood functions of (2) are:
Figure BDA0002383208070000128
wherein ,
Figure BDA0002383208070000123
for model M j At time t k Information of->
Figure BDA0002383208070000124
As a new covariance matrix, N (·) is a normal distribution probability density function;
Figure BDA0002383208070000125
for model M j Model probability at time k:
Figure BDA0002383208070000126
s7-3, the state estimation and covariance matrix is as follows:
Figure BDA0002383208070000127
in this embodiment, the IMM filter has the ability to estimate the state of the variable structure system, and is one of the most commonly used multimode filters. Unlike a fixed-structure multi-model filter, the input of the meta-filter is mixed in each filtering iteration process, which is also the origin of the term "interactive". Like other multi-model filters, the IMM filter has a set of models that contains all possible motion models of the tracked object. Each motion model corresponds to a filter (e.g., KF, EKF, UKF, etc.), referred to as a meta-filter. The model set of filters thus corresponds to a set of component filters. The estimate of the IMM filter is a model probability weighted sum of its meta-filter estimates. The model probability characterizes the matching degree of each model and the actual motion model of the target.
In this embodiment, the UKF (Unscented Kalman Filter, lossless Kalman filter) filter is a combination of a lossless transform (UT) and a standard Kalman filter system, and the nonlinear system equation is adapted to the standard Kalman filter under the linear assumption by the lossless transform.
In this embodiment, the models in the IMM filter model set are all near space high speed maneuver target motion models. Presuming parameter Z in the model Z Knowing the parameters Z corresponding to different models Z Different from each other. For example, in our simulations, it is assumed that the IMM filter contains three models, one corresponding to the near space high speed maneuver target roll angle γ c =45 deg, corresponding parameter Z z ＝1.4×10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Corresponding to the rolling angle gamma of a high-speed maneuvering target in the near space c = -45deg, corresponding parameter Z z ＝-1.4×10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Another corresponds to the roll angle gamma of the high-speed maneuvering target in the near space c =0deg.C, corresponding parameter Z z ＝0。
Due to the assumed parameter Z Z As known, the near space high-speed maneuvering target motion model can be reduced to an 8-dimensional motion model, which is expressed as follows:
Figure BDA0002383208070000131
the following simulation is carried out on a tracking algorithm of the maneuvering mutation of the near space high-speed maneuvering target, which is provided by the invention:
1. the roll angle is maintained at gamma c Fly =45 deg, then maneuver to hold γ c Estimate and predict of =0deg flight:
the position of the near space high-speed maneuvering target in the inertial coordinate system of the observer at the initial moment of simulation is set as [1161, -35.5,0] T km; the initial speed vector of the near space high-speed maneuvering target is [ -4426,811,0] T m/S, the target flying speed is V approximately 15Mach, the target mass m= 907.2k, and the target characteristic reference area is S= 0.4837m 2 . After the target enters the gliding stage, the thrust force P received in the longitudinal axis direction of the projectile coordinate system is set to zero. It is assumed that the near space high speed maneuver target takes a motion pattern with equal angle of attack α=10°, and the sideslip angle remains β=0 at all times. At t 0 =82s as initial time of simulation. A 100s tracking estimation is performed on the near space high speed maneuver target, followed by a 100s prediction.
The high-speed maneuvering target in the near space controls the self-flight by using the banked turning technology and controls the roll angle gamma c =45° and hold the roll angle for 100 seconds, and then control the roll angle to jump to γ c =0°, and the roll angle is kept flying for 100 seconds. Observers performed 200 seconds tracking and 100 predictions of near space high speed maneuver targets. Taking one simulation as an example, the trajectory of a high-speed maneuvering target in the near space is shown in fig. 2, the acceleration estimation results are shown in fig. 3-5, the speed estimation results are shown in fig. 6-8, the position estimation is shown in fig. 9-11, and the parameter Z is shown in the following formula x ，Z y and Zz The estimation is as in fig. 12-14. The IMM model probabilities are shown in fig. 15. It can be seen that at roll angle gamma c After the jump, the Kalman filter takes a period of time to converge to near the true value, so the error is large. Compared with the IMM filter, the convergence speed is faster, and most of time is closer to the true value. The IMM filter is therefore advantageous over the Kalman filter.
2. The roll angle is maintained at gamma c Fly =45 deg, then maneuver to hold γ c Estimation and prediction of = -45deg flight:
near space high speed maneuvering target controlRolling angle gamma c =45° and hold the roll angle for 100 seconds, and then control the roll angle to jump to γ c -45 °, and maintaining the roll angle for 100 seconds. Observers performed 200 seconds tracking and 100 predictions of near space high speed maneuver targets. Taking one simulation as an example, the trajectory of a high-speed maneuvering target in the near space is shown in fig. 16, the acceleration estimation results are shown in fig. 17-19, the speed estimation results are shown in fig. 20-22, the position estimation is shown in fig. 23-25, and the parameter Z is shown in the following formula x ，Z y and Zz The estimation is as in fig. 26-28. The IMM model probabilities are shown in FIG. 29. It can be seen that at roll angle gamma c After the jump, the Kalman filter takes a period of time to converge to near the true value, so the error is large. Compared with the IMM filter, the convergence speed is faster, and most of time is closer to the true value. The IMM filter is therefore advantageous over the Kalman filter.
When the roll angle gamma c When jump occurs, the near space high speed maneuvering target tracking Kalman filter needs a period of time to converge to a true value after jump, so that the error is larger. In comparison, the near space high speed maneuver object tracking IMM filter has a faster convergence speed, most of the time being closer to the true value than the Kalman filter. The IMM filter is therefore of significant advantage when the roll angle jumps.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.

Claims (6)

1. The tracking algorithm of the maneuvering mutation of the near space high-speed maneuvering target is characterized by comprising the following specific processes:
s1, establishing a coordinate system and establishing a coordinate transformation matrix;
s2, establishing a motion equation of a high-speed maneuvering target in the near space;
s3, establishing a nonlinear maneuver model of the near space high-speed maneuver target;
s4, constructing an IMM tracking filter, and realizing the tracking filtering of the IMM tracking filter on the near space high-speed maneuvering target;
s3, the specific method for establishing the nonlinear maneuver model of the near space high-speed maneuver target comprises the following steps:
s3-1, acquiring state variables Z related to aerodynamic drag, lift force and lateral force x 、Z y 、Z z ：
Figure FDA0004052186380000011
wherein ,mT Representing the target mass, C x 、C y 、C z Respectively representing components of aerodynamic coefficients in an x-axis, a y-axis and a z-axis of a target trajectory coordinate system, wherein S represents an equivalent reference area of a target;
s3-2, establishing a nine-order motion model of a near space high-speed maneuvering target:
Figure FDA0004052186380000012
wherein [ x, y, z] T For the position vector of the high-speed maneuvering target in the near space, [ v ] x ,v y ,v z ] T For the velocity vector of a high-speed maneuvering target in the near space, [ a ] x ,a y ,a z ] T For the acceleration vector of the near space high-speed maneuvering target caused by aerodynamic force, [ g ] x ,g y ,g z ] T Is a gravitational acceleration vector acting on a high-speed maneuvering target in near space;
Z x 、Z y and Zz Respectively represent and aerodynamic forceComponents of the associated state variables in the x-axis, y-axis, and z-axis of the target ballistic coordinate system;
Figure FDA0004052186380000021
and />
Figure FDA0004052186380000022
Respectively x, y, z, v x 、v y 、v z 、Z x 、Z y and Zz Is the first derivative of (a);
Figure FDA0004052186380000023
/>
Figure FDA0004052186380000024
wherein ρ is the air density;
Figure FDA0004052186380000025
is the target speed size; μ= 3.98199 ×10 14 ；
Figure FDA0004052186380000026
Is the distance between the high-speed maneuvering target in the near space and the earth center;
C o0→2 the system comprises a conversion matrix from an observer inertia coordinate system to a trajectory coordinate system of a high-speed maneuvering target in the near space;
Figure FDA0004052186380000027
s3-3 due to
Figure FDA0004052186380000028
Representing near space high speedForce of aerodynamic force of maneuvering target under high-speed maneuvering target bullet system in near space, and +.>
Figure FDA0004052186380000029
The acceleration generated by the forces of the aerodynamic forces of the high-speed maneuvering target in the near space under the inertial coordinate system of the observer is represented, so that:
Figure FDA00040521863800000210
will be
Figure FDA0004052186380000031
Substituted into->
Figure FDA0004052186380000032
The method can obtain:
Figure FDA0004052186380000033
then the following is obtained:
Figure FDA0004052186380000034
/>
the measurement matrix is:
Figure FDA0004052186380000035
2. the algorithm for tracking motor mutation of a high-speed maneuvering target in the near space according to claim 1, wherein the specific method for establishing the coordinate system in S1 is as follows:
establishing a geocentric inertial coordinate system O I x I y I z I : with the earth's center as the origin O I The direction of the origin point towards the observation point is O I y I Shaft, O I x I Shaft and O I y I The axis is vertical, and O I x I The axis being in the shooting plane of the target, O I x I The direction of the point on the axis pointing to the target is positive, and O is obtained according to the right hand rule I z I A shaft;
establishing an observer inertial coordinate system O o0 x o0 y o0 z o0 : with the position of the observer as the origin O o0 In the upward direction of plumb is O o0 y o0 Shaft, and O o0 y o0 With O I y I Overlap, O o0 x o0 Shaft and O I x I Parallel and in the same direction, and then according to the right hand rule, O is obtained o0 z o0 A shaft;
establishing an inertial coordinate system O of a transmitting point of a high-speed maneuvering target in a near space 0 x 0 y 0 z 0 : with the emission point of the target as the origin O 0 ，O 0 y 0 Shaft and O o0 y o0 The axial directions are the same, O 0 x 0 Shaft and O o0 x o0 The axial directions are opposite, and O is obtained according to the right hand rule 0 z 0 A shaft;
establishing a coordinate system Ox of a high-speed maneuvering target projectile body in a near space 1 y 1 z 1 : with the centroid of the target as the origin O and the direction of the projectile longitudinal axis as Ox 1 Axis, the direction of the projectile head of the target being the positive direction Oy 1 Axis and Ox 1 The axis is vertical and in the plane of longitudinal symmetry of the projectile, the upward direction is Oy 1 The positive direction of the axis is then determined by right hand rule to obtain Oz 1 A shaft;
establishing a trajectory coordinate system Ox of a high-speed maneuvering target in a near space 2 y 2 z 2 : with the centroid of the target as the origin O, ox 2 The positive direction of the axis is the direction of the target velocity vector v, oy 2 Axis and Ox 2 The axis is vertical, and the upward direction is Oy 2 Positive direction of axis, oy 2 The axis is in the vertical plane containing v, and Oz is obtained according to the right hand rule 2 A shaft;
establishing a near space high speed maneuver target speedCoordinate system Ox 3 y 3 z 3 : with the centroid of the target as the origin O, ox 3 The positive direction of the axis is the direction of the target velocity vector v, oy 3 Axis and Ox 3 The axis is vertical, and the upward direction is Oy 3 Positive direction of axis, oy 3 The axis being in the plane of longitudinal symmetry of the projectile of the target, oz being obtained according to the right-hand rule 3 A shaft.
3. The algorithm for tracking motor mutation of a high-speed maneuvering target in the near space according to claim 2, wherein the specific method for performing coordinate transformation in S1 is as follows:
from observer inertial coordinate system O o0 x o0 y o0 z o0 Inertial coordinate system O of high-speed maneuvering target emission point in near space 0 x 0 y 0 z 0 The conversion matrix between them is:
Figure FDA0004052186380000041
inertial coordinate system O of emission point of high-speed maneuvering target from near space 0 x 0 y 0 z 0 To the near space high speed maneuvering target projectile coordinate system Ox 1 y 1 z 1 The conversion matrix between them is:
Figure FDA0004052186380000042
namely:
Figure FDA0004052186380000043
wherein θ represents the pitch angle of the high-speed maneuvering target in the near space, which is Ox 1 Shaft and O 0 x 0 z 0 Included angle between planes Ox 1 Axis direction O 0 x 0 z 0 The angle is positive when the plane is above;
psi denotes the yaw angle of the near space high speed maneuver target, ox 1 Axis at O 0 x 0 z 0 In-plane projections Ox' and O 0 x 0 The included angle between the axes facing O 0 x 0 Shaft, when O 0 x 0 When the shaft rotates to Ox', the psi is positive when the shaft rotates anticlockwise;
gamma denotes the roll angle of the high-speed maneuvering target in the near space, which is Oy 1 Shaft and contain Ox 1 The included angle between the vertical planes of the axes is seen from the tail of the projectile body along the longitudinal axis, when Oy 1 When the shaft is positioned on the right side of the vertical plane, gamma is positive;
inertial coordinate system O of emission point of high-speed maneuvering target from near space 0 x 0 y 0 z 0 To the near space high speed maneuvering target trajectory coordinate system Ox 2 y 2 z 2 The conversion matrix between them is:
Figure FDA0004052186380000051
namely:
Figure FDA0004052186380000052
wherein θ represents the ballistic inclination of the high-speed maneuvering target in the near space, which is Ox 2 Shaft and O 0 x 0 z 0 Included angle between planes, ox 2 Axis direction O 0 x 0 z 0 When the plane is above, θ is positive;
ψ v a ballistic deflection angle of Ox representing a high-speed maneuvering target in the near space 2 Axis at O 0 x 0 z 0 Projection Ox 'on plane' 2 With O 0 x 0 The angle of the axes facing O 0 x 0 Shaft, when O 0 x 0 Pivoting to Ox' 2 Rotated anticlockwise, ψ v Is positive.
4. The algorithm for tracking motor mutation of a high-speed motor target in the near space according to claim 3, wherein the specific method for establishing the motion equation of the high-speed motor target in the near space in S2 is as follows:
establishing a motion equation of a high-speed maneuvering target in the near space:
Figure FDA0004052186380000053
wherein ,xI 、y I and zI Representing the position information of the near space high speed maneuvering target in the geocentric inertial coordinate system,
Figure FDA0004052186380000054
and
Figure FDA0004052186380000061
respectively represent x I 、y I and zI Second derivative of>
Figure FDA0004052186380000062
Representing the distance between the high-speed maneuvering target in the near space and the earth center, wherein the unit is meter; a, a xI 、a yI and azI Representing components of acceleration information in a geocentric inertial coordinate system;
μ＝3.98199×10 14 ；
the flight height h is:
Figure FDA0004052186380000063
wherein ,Re Representing the average radius of the earth.
5. The near space high speed maneuver target maneuver mutation tracking algorithm as claimed in claim 4 wherein a xI 、a yI and azI The acquisition method of (1) comprises the following steps:
the projection of the stress of the high-speed maneuvering target in the near space in the projectile body coordinate system is as follows:
Figure FDA0004052186380000064
where α is the angle of attack of the near space high speed maneuver target, q=ρv 2 2 is dynamic pressure head, ρ is air density;
C x and Cy Respectively representing components of aerodynamic coefficients in an x axis and a y axis of a target trajectory coordinate system;
s represents the equivalent reference area of the target,
Figure FDA0004052186380000065
representing the target speed magnitude;
in the geocentric inertial coordinate system, the projection of the flying speed of the near-space high-speed maneuvering target on the geocentric inertial coordinate system is as follows:
Figure FDA0004052186380000066
Figure FDA0004052186380000067
Figure FDA0004052186380000068
respectively represent x I 、y I and zI Is the first derivative of (a);
projecting a vector of the flying speed of the near-space high-speed maneuvering target on an inertial coordinate system of a transmitting point of the near-space high-speed maneuvering target:
Figure FDA0004052186380000069
C I→0 representing the geocentric inertial coordinate system to the vicinityA transformation matrix of a space high-speed maneuvering target inertial coordinate system;
C I→0 ＝C I→o0 C o0→0 ＝C o0→0 ；
wherein ,
Figure FDA0004052186380000071
the ballistic inclination and ballistic deflection of the near space high speed maneuver target is:
Figure FDA0004052186380000072
the attitude angle of the near space high speed maneuver target is:
Figure FDA0004052186380000073
wherein ,γc Is a roll angle command;
then a xI 、a yI and azI The method comprises the following steps:
Figure FDA0004052186380000074
m represents the target mass in Kg.
6. The algorithm for tracking abrupt transitions of high-speed maneuvering targets in near space according to claim 5, wherein the specific method for constructing the IMM tracking filter in S3 is as follows:
the model set of the IMM tracking filter is: m= { M 1 ,…,M n }；
wherein ,Mj Represents the j-th model with a priori probability of
Figure FDA0004052186380000075
Figure FDA0004052186380000076
An event indicating that the jth model at the initial time is matched with the real mode;
Figure FDA0004052186380000077
converting probabilities for a known model;
Figure FDA0004052186380000078
events representing the j-th model at time k and true pattern matching, < >>
Figure FDA0004052186380000079
An event representing the matching of the ith model at time k-1 with the true pattern;
M j the corresponding state equation and measurement equation are respectively:
Figure FDA0004052186380000081
wherein fj (k, x k-1 ) Represents M j State transition function, h j (k,x k ) Represents M j Is used as a measurement function of the (c),
Figure FDA0004052186380000082
represents M j Process noise of->
Figure FDA0004052186380000083
Represents M j Is a measurement noise of (a);
s7-1, calculating a current initial state and a covariance matrix by the element filter according to the estimated state and the covariance matrix of the last iteration:
Figure FDA0004052186380000084
wherein ,
Figure FDA0004052186380000085
representing the model M at time k-1 j Under the condition of matching with the real mode, the kth moment model M i Probability of matching with real pattern, +.>
Figure FDA0004052186380000086
For model M i Probability of matching with real pattern at time k, +.>
Figure FDA0004052186380000087
Is a normalization factor;
the mixed input calculation formula is:
Figure FDA0004052186380000088
wherein ,
Figure FDA0004052186380000089
and />
Figure FDA00040521863800000810
Representing a hybrid input and a hybrid covariance matrix, respectively;
Figure FDA00040521863800000811
the i-th model representing the moment k-1 corresponds to the state input of the Kalman filter;
Figure FDA00040521863800000812
representing a state covariance matrix of a Kalman filter corresponding to an ith model at the moment k-1;
s7-2, adopting a UKF filter as a meta-filter of the IMM tracking filter, and adopting S7-1 to obtain
Figure FDA00040521863800000813
and />
Figure FDA00040521863800000814
As input, each UKF filter performs one filtering iteration;
the filtering includes two sub-steps, state prediction and state update, respectively:
Figure FDA00040521863800000815
wherein ,UKFp (. Cndot.) is the state prediction function, UKF u (. Cndot.) is a status update function;
Figure FDA0004052186380000091
a state transfer function representing the j-th model at time k-1;
Figure FDA0004052186380000092
a noise matrix representing the j-th model at time k-1;
Figure FDA0004052186380000093
a state forecast covariance matrix of a j-th model at the moment k-1;
z k representing the measured value;
Figure FDA0004052186380000094
a measurement matrix representing a j-th model at time k;
Figure FDA0004052186380000095
measurement of the jth model representing the moment kA quantity noise matrix;
model M j At time t k Likelihood functions of (2) are:
Figure FDA0004052186380000096
wherein ,
Figure FDA0004052186380000097
for model M j At time t k Information of->
Figure FDA0004052186380000098
For the new covariance matrix, +.>
Figure FDA0004052186380000099
Is a normal distribution probability density function;
Figure FDA00040521863800000910
for model M j Model probability at time k:
Figure FDA00040521863800000911
s7-3, the state estimation and covariance matrix is as follows:
Figure FDA00040521863800000912
/>
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