CN111896946A - Continuous time target tracking method based on track fitting - Google Patents

Continuous time target tracking method based on track fitting Download PDF

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CN111896946A
CN111896946A CN202010602081.8A CN202010602081A CN111896946A CN 111896946 A CN111896946 A CN 111896946A CN 202010602081 A CN202010602081 A CN 202010602081A CN 111896946 A CN111896946 A CN 111896946A
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李天成
周金阳
王小旭
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Northwestern Polytechnical University
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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
    • 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/883—Radar or analogous systems specially adapted for specific applications for missile homing, autodirectors

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Abstract

The invention relates to a new continuous time target tracking method based on track fitting, which skillfully uses time sequence measurement data, models system external information into system constraint, further provides a constraint least square method to fit the measurement data, and predicts and estimates the state of a target through a target curve function obtained through fitting. The method has simple design and high calculation efficiency and tracking precision.

Description

Continuous time target tracking method based on track fitting
Technical Field
The invention relates to the field of radar signal processing, in particular to a continuous time target tracking method based on track fitting. The invention is suitable for the targets of smoothly changing missiles, passenger planes and spacecrafts.
Background
As an indispensable technology, researchers in various countries have conducted intensive research on target tracking, and put forward a large number of tracking theories and methods. At present, the target tracking method is almost completely based on a state space model, namely a dynamic model of motion needs to be established, a complex filter needs to be designed, and the whole process needs a large amount of prior information which is usually unknown.
The document "Joint smoothing and tracking based on continuous-time targeting function setting" discloses a target tracking method based on a continuous time trajectory function. The method is completely different from the traditional filtering target tracking algorithm, and the motion trail of the target is represented by using a continuous function, so that the target tracking precision is improved, and the calculation time is reduced. However, the method described in the literature does not consider the regularization term problem, and only a single least square fitting is performed, so that the result is not accurate enough in the calculation process. Meanwhile, in the target tracking process, the target is subjected to certain constraints, and the documents do not consider the constraint conditions, so that the target tracking precision is to be further improved.
Disclosure of Invention
Technical problem to be solved
In order to solve the problem that the target model is difficult to establish by the existing method, the invention provides a continuous time target tracking method based on track fitting.
Technical scheme
A continuous time target tracking method based on flight path fitting is characterized by comprising the following steps:
step 1: modeling a target track, namely modeling a target motion equation into a continuous time function curve:
xt＝F(t；λ)+et(1)
the sensor measurement model is built as:
yt＝h(xt)+vt(2)
in the formula, xtRepresenting the state of the target at time t, λ representing the coefficient of the continuous-time function curve, F (t; λ) representing the continuous-time function curve, etRepresents the process error, ytRepresenting the measured value of the target at time t, h (-) representing the measurement function, vtRepresenting the measurement noise;
step 2: the continuous-time trajectory function order determination is as follows for typical constant-speed models and uniform acceleration models:
Figure BDA0002559331900000021
according to the formula (1), the polynomial order of the constant velocity model is 1, the polynomial order of the constant acceleration model is 2, and so on; considering constraint information, when the target moves at a constant speed, selecting a polynomial order of 1, and when the target moves in a turning motion or a uniform acceleration motion, selecting a polynomial order of 2, so as to realize the online switching of the fitting function order;
and step 3: continuous time trajectory function parameter estimation, estimating coefficient parameter lambda by minimizing fitting residual, and setting fitting data length, i.e. fitting time window as [ k ]1k2](ii) a Obtaining an optimal fitting function by fitting the sensor observation data with continuous time; error is measured using the measured and estimated minimum distances:
Figure BDA0002559331900000022
in the formula (I), the compound is shown in the specification,
Figure BDA0002559331900000023
| λ | is a regularization term, ρ is a regularization parameter;
through the determination of the continuous time trajectory function order and the coefficient, a continuous time trajectory function curve is obtained, and then the state of any point on the trajectory curve, that is, any time can be obtained, that is, the following steps are performed:
Figure BDA0002559331900000024
wherein, the interval [ K1K2]Includes fitting a time window interval [ k ]1k2]I.e. K1≤k1，k2≤K2。
Advantageous effects
The invention provides a novel continuous time target tracking method based on track fitting, which aims to find an optimal continuous time track function from time sequence measurement so as to obtain a target state in real time. The method can realize high-precision real-time tracking on the smoothly-changing target without prior model information, overcomes the difficulty of complex system dynamics modeling of the traditional filtering method, and realizes tracking on the target through track fitting under constraint. The method skillfully uses time sequence measurement data, models system external information into system constraint, further provides a constraint least square method to fit the measurement data, and predicts and estimates the state of a target through a target curve function obtained through fitting. The method has simple design and high calculation efficiency and tracking precision.
Drawings
FIG. 1 is a flow chart of the structure of the method of the present invention.
Figure 2 is a structural framework of the method of the invention.
FIG. 3 is a simulation scenario of the method of the present invention.
FIG. 4 is a simulation accuracy result of the method of the present invention.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
a continuous time target tracking method based on flight path fitting adopts the following steps:
step one, modeling a target track, namely modeling a target motion equation into a continuous time function curve (such as a multi-style curve and a spline curve):
xt＝F(t；λ)+et(1)
the sensor measurement model is built as:
yt＝h(xt)+vt(2)
in the formula, xtRepresenting the state of the target at time t, λ representing the coefficient of the continuous-time function curve, F (t; λ) representing the continuous-time function curve, etRepresents the process error, ytRepresenting the measured value of the target at time t, h (-) representing the measurement function, vtRepresenting the measurement noise.
And step two, determining the order of the continuous time track function. To find the most suitable continuous-time trajectory function, preventing over-fitting and under-fitting, the order of the function polynomial needs to be determined, assuming that the parameters are independent of each other in each dimension, for typical constant-speed and constant-acceleration models, there are:
Figure BDA0002559331900000041
according to the formula (1), the polynomial order of the constant velocity model is 1, the polynomial order of the constant acceleration model is 2, and so on. And considering constraint information, selecting the polynomial order to be 1 when the target moves at a constant speed, and selecting the polynomial order to be 2 when the target moves at a turning speed or at a uniform acceleration speed, so as to realize the online switching of the fitting function order.
And step three, continuous time trajectory function parameter estimation, in order to obtain the most suitable time trajectory function, the coefficient parameter lambda can be estimated by minimizing the fitting residual error, and the fitting data length is set, namely the fitting time window is [ k ]1k2]. The best fit function is then obtained by fitting the time-continuous sensor observations. Error is measured using the measured and estimated minimum distances:
Figure BDA0002559331900000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002559331900000043
| λ | is a regularization term and ρ is a regularization parameter.
The above is the determination of the order and coefficients of the continuous-time trajectory function. Theoretically, a continuous time function trajectory curve is obtained, and then any point on the trajectory curve, that is, the state at any time can be obtained, that is:
Figure BDA0002559331900000044
wherein, the interval [ K1K2]Includes fitting a time window interval [ k ]1k2]I.e. K1≤k1，k2≤K2。
The embodiment is shown in figures 1-4, and the specific steps are as follows:
step 1, setting a simulation scene.
The simulation scene is set to be a two-dimensional coordinate system, the target starts to do uniform linear motion at the first time, at a certain moment in the middle, the target starts to do turning motion after maneuvering, and continues to do uniform linear motion after maneuvering. The target motion model consists of two parts, namely a linear motion model and a turning motion model, and the motion models are respectively as follows:
Figure BDA0002559331900000051
Figure BDA0002559331900000052
in the formula, T represents a sampling time interval of a sensor, and omega represents a target rotating speed;
Figure BDA0002559331900000053
and
Figure BDA0002559331900000054
representing the process noise of model one and model two, respectively.
The measuring model expressions of the fighter are respectively as follows:
Figure BDA0002559331900000055
Figure BDA0002559331900000056
in the formula (I), the compound is shown in the specification,
Figure BDA0002559331900000057
and
Figure BDA0002559331900000058
respectively representing the measurement noise of the model one and the model two.
The flight speed of the fighter moving at high speed is high, the simulation time length is set to be 20s reasonably in the simulation scene, and the measurement time interval of the sensor is set to be 0.1 s.
Setting the process noise and the observation noise of the linear motion model as follows:
q1＝0.01(km/s2)2(10)
r1＝0.2(km)2(11)
then discretizing to obtain:
Figure BDA0002559331900000061
Figure BDA0002559331900000062
for the cornering model, let the rotational speed process error be 0.01(rad/s)2And if the observation noise is not changed, then:
Figure BDA0002559331900000063
Figure BDA0002559331900000064
the state vector in the target estimation is:
Figure BDA0002559331900000065
the initial state and covariance are:
Figure BDA0002559331900000066
Figure BDA0002559331900000067
in the first 4s, the fighter moving at high speed moves according to a linear model, maneuvers in the 8 th s, starts to turn at the rotating speed of 0.785rad/s, and continues to move linearly in the 12 th s.
And 2, determining the order of the continuous time track function.
In order to find the most suitable continuous-time trajectory function, the order of the function polynomial needs to be determined, assuming that the parameters are independent of each other in each dimension, for a typical constant velocity model, the function polynomial order is 1, and for a constant acceleration model and a cornering model the polynomial order is 2. In the stage of uniform motion of the target and the stage of maneuvering of the target, setting continuous time functions as follows:
Figure BDA0002559331900000071
Figure BDA0002559331900000072
in the formula, PxAnd PyRespectively representing the positions of the moving objects in the X-axis direction and the Y-axis direction under a two-dimensional coordinate system. A continuous time function. And considering constraint information, selecting a formula (19) for fitting when the target moves at a constant speed, and selecting a formula (20) for fitting when the target moves at a turning motion or a uniform acceleration motion, so as to realize the online switching of the order of the fitting function.
And 3, estimating parameters of the continuous time track function.
To obtain the most suitable time trajectory function, the coefficient parameter λ may be estimated by minimizing the fitted residualtAnd setting a reasonable fitting data length, and obtaining an optimal continuous time function through fitting continuous-time sensor observation data. The sensor type is a position measurement sensor, namely, the position of the current target in the X-axis and Y-axis directions is obtained at each sampling moment.
And 4, estimating a target state.
And substituting the current time or the next time according to the obtained time track function to estimate and predict the target state.
And 5, comparing the performance indexes.
To illustrate the superiority of the method, the position root mean square error and the position average root mean square error were selected as comparison indicators. The comparison method is the conventional target tracking algorithm, such as extended Kalman filtering, unscented Kalman filtering, extended Kalman smoothing, unscented Kalman smoothing and interactive multi-model traditional methods. The Root Mean Square Error (RMSE) is used as a comparison index, and the target position RMSE at the moment t is defined as follows:
Figure BDA0002559331900000081
in the formula, xtAnd ytIs a position of the sensor to measure the position,
Figure BDA0002559331900000082
and
Figure BDA0002559331900000083
is a continuous time function to estimate the position.
From FIG. 4, it can be seen that: the traditional extended Kalman filtering and unscented Kalman filtering algorithms have large position errors, and particularly when a target is maneuvered, the target cannot be effectively tracked; when a target turns, the interactive multi-model algorithm cannot realize high-precision tracking of the target; the extended Kalman smoothing algorithm and the unscented Kalman smoothing algorithm improve the tracking precision of the maneuvering target, but cannot improve the tracking precision of the non-maneuvering target; the method provided by the invention is superior to the traditional method, and the position error is obviously reduced regardless of the maneuvering of the target.

Claims (1)

1. A continuous time target tracking method based on flight path fitting is characterized by comprising the following steps:
step 1: modeling a target track, namely modeling a target motion equation into a continuous time function curve:
xt＝F(t；λ)+et(1)
the sensor measurement model is built as:
yt＝h(xt)+vt(2)
in the formula, xtRepresenting the state of the target at time t, λ representing the coefficient of the continuous-time function curve, F (t; λ) representing the continuous-time function curve, etRepresents the process error, ytRepresenting the measured value of the target at time t, h (-) representing the measurement function, vtRepresenting the measurement noise;
step 2: the continuous-time trajectory function order determination is as follows for typical constant-speed models and uniform acceleration models:
Figure FDA0002559331890000011
according to the formula (1), the polynomial order of the constant velocity model is 1, the polynomial order of the constant acceleration model is 2, and so on; considering constraint information, when the target moves at a constant speed, selecting a polynomial order of 1, and when the target moves in a turning motion or a uniform acceleration motion, selecting a polynomial order of 2, so as to realize the online switching of the fitting function order;
and step 3: continuous time trajectory function parameter estimation, estimating coefficient parameter lambda by minimizing fitting residual, and setting fitting data length, i.e. fitting time window as [ k ]1k2](ii) a Obtaining an optimal fitting function by fitting the sensor observation data with continuous time; error is measured using the measured and estimated minimum distances:
Figure FDA0002559331890000012
in the formula (I), the compound is shown in the specification,
Figure FDA0002559331890000013
| λ | is a regularization term, ρ is a regularization parameter;
through the determination of the continuous time trajectory function order and the coefficient, a continuous time trajectory function curve is obtained, and then the state of any point on the trajectory curve, that is, any time can be obtained, that is, the following steps are performed:
Figure FDA0002559331890000021
wherein, the interval [ K1K2]Includes fitting a time window interval [ k ]1k2]I.e. K1≤k1，k2≤K2。
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113008222A (en) * 2021-02-20 2021-06-22 西北工业大学 Track constraint target tracking method based on continuous time track function
CN114510676A (en) * 2022-02-17 2022-05-17 西北工业大学 Measurement method for evaluating performance of continuous time track tracking algorithm

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7249730B1 (en) * 2004-09-23 2007-07-31 United States Of America As Represented By The Secretary Of The Army System and method for in-flight trajectory path synthesis using the time sampled output of onboard sensors
CN101718870A (en) * 2009-11-13 2010-06-02 西安电子科技大学 High-speed weak target flight path detection method of image field
CN106023244A (en) * 2016-04-13 2016-10-12 南京邮电大学 Pedestrian tracking method based on least square locus prediction and intelligent obstacle avoidance model

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7249730B1 (en) * 2004-09-23 2007-07-31 United States Of America As Represented By The Secretary Of The Army System and method for in-flight trajectory path synthesis using the time sampled output of onboard sensors
CN101718870A (en) * 2009-11-13 2010-06-02 西安电子科技大学 High-speed weak target flight path detection method of image field
CN106023244A (en) * 2016-04-13 2016-10-12 南京邮电大学 Pedestrian tracking method based on least square locus prediction and intelligent obstacle avoidance model

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
TIANCHENG LI: "Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting", 《IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING》 *
TIANCHENG LI: "Single-Road-Constrained Positioning Based on Deterministic Trajectory Geometry", 《IEEE COMMUNICATIONS LETTERS》 *
焦竹青等: "基于曲线拟合的无线传感器网络目标定位算法", 《东南大学学报(自然科学版)》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113008222A (en) * 2021-02-20 2021-06-22 西北工业大学 Track constraint target tracking method based on continuous time track function
CN114510676A (en) * 2022-02-17 2022-05-17 西北工业大学 Measurement method for evaluating performance of continuous time track tracking algorithm

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