CN104833967A - Radar target tracking method based on moving horizon estimation - Google Patents
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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
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Abstract
The invention discloses a radar target tracking method based on moving horizon estimation, comprising the following steps: acquiring a motion model of target tracking, and obtaining a state equation and an observation equation; introducing constraint conditions for state estimation; calculating an arrival cost function according to a moving horizon estimation algorithm, and estimating the position of a tracked target; and calculating the error mean and standard deviation of position tracking and evaluating the tracking effect. According to the method, the influence of physical constraints is taken into full consideration in the process of target tracking. State estimation is converted into a problem of optimization with constraints. Linear moving horizon estimation is adopted for a linear model in radar tracking. The constraints of a system are taken into consideration, and the effect of estimation is improved greatly. The estimation problem is converted into a constrained and limited-size quadratic optimization problem by an approximate arrival cost method, which reduces the calculation difficulty. An effective on-line state estimation method is provided.
Description
Technical Field
The invention belongs to the field of target tracking, and relates to a radar target tracking method based on rolling time domain estimation.
Background
The target tracking means that a computer or other instrument equipment tracks and positions a target according to a certain algorithm and takes corresponding measures according to the position and the movement of the target. The target tracking technology occupies an extremely important position in the field of national defense, and can be used for defense of anti-ballistic missiles, air early warning, ground-to-air, ship-to-ship, and air-to-air beyond-visual-range target detection, tracking and attack, battlefield monitoring, accurate guidance and striking, low-altitude penetration and the like. For example, the VIGIL system developed by Liebe et al, a target tracking system based on GPS, equipped on a helicopter, can track remotely flying targets such as cruise missiles in real time; the ATDT system designed by the cdc (computing devices canada) can be used to observe and track ground targets. Target tracking has also been widely used in the civilian field, and can be used for air traffic control, collision avoidance, navigation, robot vision and the like. The computer vision laboratory and MIT artificial intelligence laboratory of the university of Maryland and the like have successively carried out the research of human body tracking and the application research thereof in the fields of monitoring and the like.
In many military and civilian applications, detection and tracking of a wide variety of moving targets is required to maintain an estimate of the current state of the target. The state estimation problem of the system is to estimate the state of the system according to the selected estimation criteria and the obtained measurement signals. The purpose of state estimation is to smooth the past motion state of the target, filter the present motion state of the target, and predict the future motion state of the target. These motion states include target position, velocity, acceleration, and the like.
The common estimation methods have a common drawback in that they cannot effectively handle constraints. The existence of a constraint (constraint condition) means that the physical state of an actual system often changes only in a certain area. Common constraints are physical constraints and process constraints. Physical constraints are also called hard constraints, such as speed limits of moving objects, non-negative concentration of substances, non-negative leakage of liquid, non-negative certain parameters, etc.; process constraints are information about the operation of the system, such as the upper and lower bounds of the state, the form, magnitude, range, statistical distribution characteristics, etc. of the disturbance. When the actual system has constraints, the method of using unconstrained state estimation inevitably reduces the estimation accuracy, even if the situation does not conform to the physical limit. In addition, in the tracking problem, the amount of the collected ambient environment information is larger and larger as time goes on, which not only may overflow the memory capacity, but also the processing time of the ambient information is longer and longer, which is difficult to meet the requirement of real-time performance, so the ambient information must be optimized.
Compared with a classical state estimation method such as a Kalman filtering method, the MHE (moving horizon estimation) method is more effective because on one hand, constraint conditions of a system are considered, the estimation effect is greatly improved, and on the other hand, the estimation problem is converted into a constrained quadratic optimization problem with limited size by using an approximate arrival cost method, which provides possibility for online state estimation in terms of a solved method and the computing power of a computer.
Therefore, the rolling time domain estimation algorithm is researched and applied to the linear filtering and nonlinear filtering problems in radar target tracking, the performance of the system is further improved, and the method has important engineering significance.
Disclosure of Invention
In order to overcome the defects of the traditional estimation method in radar target tracking, the invention aims to provide a radar target tracking method based on rolling time domain estimation. The algorithm aims at a linear model in radar tracking, adopts linear rolling time domain estimation, approximately calculates the arrival cost function of a constrained system by Kalman filtering, and greatly improves the estimation precision compared with the traditional Kalman filtering algorithm. The method not only considers the constraint condition of the system and greatly improves the estimation effect, but also converts the estimation problem into a quadratic optimization problem with constraint and limited size by using a method of approximate arrival cost, and provides possibility for online state estimation no matter from the solved method or the computing power of a computer.
In order to achieve the purpose, the invention provides the following technical scheme:
a radar target tracking method based on rolling time domain estimation comprises the following steps:
the method comprises the following steps: obtaining a motion model of target tracking to obtain a state equation and an observation equation;
step two: introducing a constraint condition of an estimation state;
step three: according to a rolling time domain estimation algorithm, calculating an arrival cost function, and further estimating the position of a tracking target;
step four: and calculating the error mean value and standard deviation of position tracking, and evaluating the tracking effect.
The invention has the beneficial technical effects that: compared with other classical state estimation methods such as a Kalman filtering method, on one hand, constraint conditions of a system are considered, the estimation effect is greatly improved, on the other hand, the estimation problem is converted into a quadratic optimization problem with constraint and limited size by using an approximate arrival cost method, and possibility is provided for online state estimation no matter a solved method or the computing power of a computer; and an approximate arrival cost function is adopted in the estimation process, the optimization problem is solved in a finite time domain, the solving time of the optimization problem is shortened, the estimation of the state can be completed in the radar scanning period, and the requirement of tracking instantaneity is met.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a block diagram of the basic principle of target tracking according to the present invention
FIG. 2 is a schematic diagram of an approximate rolling time domain estimation strategy
FIG. 3 is a rolling time domain estimation algorithm for unconstrained system
FIG. 4 is a graph of position tracking in the x-direction of a target
FIG. 5 is a position tracking curve in the y-direction of the target
FIG. 6 is a graph of the mean error value in the x direction during target tracking
FIG. 7 is a graph of the mean error in the y-direction during target tracking
FIG. 8 is a plot of standard deviation of error in the x-direction during target tracking
FIG. 9 shows the error standard deviation curves in the y-direction
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
In the method, a radar target tracking method based on rolling time domain estimation is adopted, an approximate arrival cost function is adopted in the estimation process, the optimization problem is solved in a limited time domain, the solving time of the optimization problem is shortened, the estimation of the state can be completed in a radar scanning period, and the requirement of tracking instantaneity is met
FIG. 1 is a block diagram of the basic principle of target tracking according to the present invention. As shown, the target dynamics are represented by state vectors including position, velocity, and acceleration, the observed quantities are assumed to be linear combinations of state vectors containing measurement noise, and the residual vectors are the differences between the measured and predicted states. Generally, maneuvering target tracking is a self-adaptive filtering process, firstly, observed quantity, state and measurement form a residual vector, then maneuvering detection or maneuvering identification is carried out according to the change of the residual vector, secondly, filtering gain and a covariance matrix are adjusted according to a certain criterion or logic, or target maneuvering characteristics are identified in real time, and finally, a state estimation value and a predicted value of a target are obtained through a filtering algorithm, so that maneuvering target tracking is completed.
Because the invention adopts the radar target tracking method based on the rolling time domain estimation, and adopts the approximate arrival cost function in the estimation process, the optimization problem is solved in the limited time domain, and the solving time of the optimization problem is shortened. According to the rolling optimization principle, the latest measurement data at the current sampling moment is used for refreshing the measurement output sequenceThe optimization problem is then solved again on-line. The rolling time domain estimation algorithm of all the measurement data is adopted, the algorithm adopted by the invention only utilizes the latest N data at the current moment, and the influence of the rest measurement data on the estimation can be used by the arrival cost function thetaT-N(xT-N) To approximate the description. The "rolling temporal estimation" comes from an analysis of the rolling temporal window, as shown in FIG. 2.
In this embodiment, assuming that the radar observes a target on a plane, if the acceleration is used as a disturbance, the motion model of the target can be described as the following equation of state:
X(k+1)＝AX(k)+GW(k) (1)
wherein k is more than or equal to 0,is a state variable, where x and y are the position of the object in a cartesian coordinate system,andthe speed of the target in the x and y directions; a is a state transition matrix, G is an input matrix, respectively denoted as
Wherein W ═ Wx,wy]ΤFor system noise, independent of the measured noise and the initial state, the system noise sequence is assumed to be zero-mean Gaussian white noise with a covariance matrix of Q, i.e., E [ W ]k]＝0，E[WkWj]＝0(If k is j, thenk,j0, otherwisek,jNot equal to 1); t is radar observation period.
In the embodiment, the radar is assumed to be located at the origin of coordinates of a cartesian coordinate system, the observed value has a distance r and an azimuth angle θ, and the observed value is composed of a state value and measurement noise. Converting the radar observations to a Cartesian coordinate system: the abscissa d is rcos θ and the ordinate h is rsin θ, then the observation model of the target is:
Y(k)＝CX(k)+V(k) (2)
wherein, Y ═ d, h]ΤIs an observation vector; is an observation matrix; v is observation noise, independent of process noise and initial state, and is zero-mean white Gaussian noise with a covariance matrix of R, i.e., E [ V ]k]＝0，E[VkVj]＝0(If k is j, thenk,j0, otherwisek,j≠1)。
As shown in fig. 3, in this embodiment, the specific steps of the rolling time domain estimation algorithm are as follows:
1) initial state estimation assuming a known systemInitial covariance of state error is P0Covariance of process noise and measurement noise, Q and R, respectively, and P0Q, R is reversible, the rolling time domain length is N;
2) when T is less than or equal to N, the optimization problem defined by the rolling time domain estimation is as follows:
if there is a unique optimal solution to optimize the above equation at time TThen the estimated value of the system state at time k (k ═ 1, …, T) is:
3) when T > N, the optimization problem defined by MHE is:
at this time, if the matrix PT-NReversible, then the cost Θ is reachedT-N(z) can be expressed as:
wherein,for the a priori estimated state at time T-N,represents the optimal cost, P, of the T-N instantT-NRepresenting the error covariance at time T-N,and PT-NIt can be obtained by the recursive formula of Riccati:
if there is a unique optimal solution to the problem described by equations (7) and (8) at time TThe optimal estimate of the system state at time k (k-T-N +1, …, T) is:
in the present embodiment, toThe radar located at the origin of coordinates observes a target moving on a plane, and the initial position of the target is (2000,10000) m. The target does uniform linear motion along the y direction at the t-0-400 s, and the motion speed is-15 m/s; making a 90-degree slow turn along the x direction at t 400-600s and the acceleration ax＝ay＝0.075m/s2After the slow turning is finished, the acceleration is reduced to 0; making a 90-degree fast turn from t to 610s with acceleration ax＝ay＝0.3m/s2(ii) a The turn is ended 660s and the acceleration is reduced to zero. The radar scanning period T is 1s, the target is observed independently in the x and y directions, and the standard deviation of the observation noise is 10 m.
In the present embodiment, the position limit of the target in the x direction is taken as a constraint condition of the state estimation problem. And establishing initial values of the state estimation and error covariance matrix by adopting a two-point method. The rolling time domain length N is chosen to be 10, and the sample points are compared 50 times by Monte Carlo simulation of MHE and kf (kalman filter) in MATLAB environment. Fig. 4 and 5 are position tracking curves in the x-direction and y-direction of the target, respectively.
In this embodiment, the mean value and the standard deviation of the position filtering error of the tracking target are selected as the performance index meter for evaluating the tracking method of the present invention, and the specific method is as follows:
where M is the Monte Carlo simulation number, k is 1,2, …, n (n is the sampling number). Fig. 6 and 7 show the error mean curves in the x and y directions, respectively, during target tracking, and fig. 8 and 9 show the error standard deviation curves in the x and y directions, respectively, during target tracking.
Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, although the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (7)
1. A radar target tracking method based on rolling time domain estimation is characterized by comprising the following steps:
the method comprises the following steps: obtaining a motion model of target tracking to obtain a state equation and an observation equation;
step two: introducing a constraint condition of an estimation state;
step three: according to a rolling time domain estimation algorithm, calculating an arrival cost function, and further estimating the position of a tracking target;
step four: and calculating the error mean value and standard deviation of position tracking, and evaluating the tracking effect.
2. The radar target tracking method based on rolling time domain estimation according to claim 1, wherein: the first step specifically includes that a radar is assumed to observe a target on a plane, and if acceleration is taken as disturbance, a motion model of the target can be described as the following equation of state: x (k +1) ═ AX (k) + GW (k), where k ≧ 0,is a state variable, where x and y are the position of the object in a cartesian coordinate system,andthe speed of the target in the x and y directions; a is a state transition matrix, G is an input matrix, and W ═ Wx,wy]ΤThe system noise is independent of the measurement noise and the initial state, the system noise sequence is assumed to be white Gaussian noise with zero mean, the covariance matrix is Q, and T is the radar observation period.
3. The radar target tracking method based on rolling time domain estimation according to claim 1, wherein: in the first step, the radar is assumed to be located at the origin of coordinates of a Cartesian coordinate system, the observed quantity has a distance r and an azimuth angle theta, and the observed value consists of a state value and measurement noise. Converting the radar observations to a Cartesian coordinate system: the abscissa d is rcos θ and the ordinate h is rsin θ, then the observation model of the target is: y (k) ═ cx (k) + v (k), where Y ═ d, h]ΤIs an observation vector; c is an observation matrix; v is observation noise, independent of process noise and initial state, and is zero mean Gaussian white noise, and its covariance matrix is R.
4. The radar target tracking method based on the rolling time domain estimation according to claim 1, wherein the second step specifically comprises: according to the dynamics principle of target motion in target tracking, the constraint condition of the estimation state is obtained, and the state variable in the system is estimated on the premise of meeting the constraint condition by using a rolling time domain estimation method through coordinate conversion based on system measurement information.
5. The radar target tracking method based on rolling time domain estimation according to claim 1, wherein the rolling time domain estimation algorithm of step three comprises the following specific steps:
1) initial state estimation assuming a known systemInitial covariance of state error is P0Covariance of process noise and measurement noise, Q and R, respectively, and P0Q, R is reversible, the rolling time domain length is N;
2) when T is less than or equal to N, the optimization problem defined by the rolling time domain estimation is as follows:
if there is a unique optimal solution to optimize the above equation at time TThen the estimated value of the system state at time k (k ═ 1, …, T) is:
3) when T > N, the optimization problem defined by MHE is:
at this time, if the matrix PT-NReversible, then the cost Θ is reachedT-N(z) can be expressed as:
if there is a unique optimal solution to the problem described by the above equation at time TThe optimal estimate of the system state at time k (k-T-N +1, …, T) is:
6. the method for tracking radar target based on rolling time domain estimation according to claim 1, wherein the step four of calculating the mean and standard deviation of the error of the position tracking specifically comprises:
where M is the Monte Carlo simulation number, k is 1,2, …, n (n is the sampling number).
7. A radar target tracking method based on rolling time domain estimation applying any one of claims 1 to 6.
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| CN105182283B (en) * | 2015-08-17 | 2017-08-25 | 周口师范学院 | A kind of passive radar fixes target time domain direction-finding method |
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| CN109000663A (en) * | 2018-08-07 | 2018-12-14 | 中国人民解放军海军航空大学 | Based on the self-adjusting moving horizon estimation arrival cost calculation method of time-varying |
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| CN114126944B (en) * | 2019-07-02 | 2024-03-05 | 三菱电机株式会社 | Rolling time domain state estimator |
| CN110490907A (en) * | 2019-08-21 | 2019-11-22 | 上海无线电设备研究所 | Motion target tracking method based on multiple target feature and improvement correlation filter |
| CN110490907B (en) * | 2019-08-21 | 2023-05-16 | 上海无线电设备研究所 | Moving target tracking method based on multi-target feature and improved correlation filter |
| CN118392190A (en) * | 2024-06-25 | 2024-07-26 | 齐鲁工业大学(山东省科学院) | Combined navigation data fusion method based on hypothesis constraint |
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Application publication date: 20150812 |
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