Interacting acceleration compensation algorithm for trackingmaneuvering targets

The two-stage Kalman estimator has been studied for state estimation in the presence of random bias and applied to the tracking of maneuvering targets by treating the target acceleration as a bias vector. Since the target acceleration is considered a bias, the first stage contains a constant velocity motion model and estimates the target position and velocity, while the second stage estimates the target acceleration when a maneuver is detected, the acceleration estimate is used to correct the estimates of the first stage. The interacting acceleration compensation (IAC) algorithm is proposed to overcome the requirement of explicit maneuver detection of the two-stage estimator. The IAC algorithm is viewed as a two-stage estimator having two acceleration models: the zero acceleration of the constant velocity model and a constant acceleration model. The interacting multiple model (IMM) algorithm is used to compute the acceleration estimates that compensate the estimate of the constant velocity filter. Simulation results indicate the tracking performance of the IAC algorithm approaches that of a comparative IMM algorithm while requiring approximately 50% of the computations     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

Tracking Accuracies with Position and Rate Measurements

Tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target These results will be of interest to persons developing trackers for pulse Doppler surveillance radars. The normalized accuracies, computed for a two state Kalman tracking filter with white noise maneuver capability, are shown to depend upon two parameters, r = 4?0/?aT2 and s = ?dT/?0. The symbols ?0 and ?d are the position and rate measurement accuracies, respectively, ?a is the standard deviation of the white noise maneuver process and T is the antenna scan time. The scalar tracking filter equations are derived and numerical results are presented. Lower steady state tracking errors plus the earlier attainment of steady state accuracies are the direct consequence of incorporating the rate measurements into the tracking filter.     

A Kalman Tracker with a Simple Input Estimator

Two Kalman filter based schemes are proposed for tracking maneuvering targets. Both schemes use least squares to estimate a target's acceleration input vector and to update the tracker by this estimate. The first scheme is simpler and by an approximation to its input estimator the computation can be considerably reduced with insignificant performance degradation. The second scheme requires two Kalman filters and hence is more complex. However, since one of its two filters assumes input noise, it may outperform the first scheme when input noise is indeed present. A detector that compares the weighted norm of the estimated input vector to a threshold is used in each scheme. Its function is to guard against false updating of the trackers and to keep the error covariance small during constant velocity tracks. Simulation results for various target profiles are included. They show that in terms of tracking performance, both schemes are comparable. However, because of its computation simplicity, the first scheme is far superior.     

Maneuvering target tracking using IMM method at high measurementfrequency

The problem of tracking a maneuvering target with a high measurement frequency is considered. The measurement noise is significantly correlated when the measurement frequency is high. A simple decorrelation process is proposed to enhance the interacting multiple model (IMM) algorithm to track a maneuvering target with correlated measurement noise. It is found that the decorrelation process may improve system performance significantly, especially in velocity and acceleration estimations     

机动目标“当前”统计模型与自适应跟踪算法

本文提出机动目标“当前”统计模型的概念并建议用修正的瑞利-马尔科夫过程描述目标随机加速机动的统计特性。文中指出了在机动目标运动模型中状态（机动加速度）估值与状态噪声之间的内在联系。在此基础上提出了具有机动加速度均值及方差自适应的卡尔曼滤波算法。对一维和三维的情形进行了计算机模拟。计算结果表明,在仅对目标位置进行观测的情况下,这类自适应估值算法无论对高度机动或无机动的目标均可绘出较好的位置、速度及加速度估值。     

Optimal and Suboptimal Guidance for a Short-Range Homing Missile

Optimal and suboptimal guidance laws for short-range homing missiles are developed and compared to the commonly mechanized quidance law of proportional navigation. The optimal controller is derived as an optimal feedback regulator; the suboptimal controller is an approximation of the optimal regulator and consists of timevarying proportional navigation plus a time-varying gain term times a calculated target acceleration. Monte Carlo studies of the three controllers show that the optimal and suboptimal controllers are much superior to proportional navigation for the case of combined constant target acceleration, line-of-sight rate noise, and missile acceleration saturation.     

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation     

一种二维耦合模型机动目标跟踪算法

针对雷达跟踪固定翼飞机的单目标跟踪问题,提出了一种新的二维耦合运动模型。该方法把切向加速度和法向加速度作为状态变量,给出了切向加速度和法向加速度为常值时解析计算状态转移的方法。该模型可以较好地一步预测目标加速度的变化,而且法向和切向加速度的过程噪声可以分别设置。利用该耦合模型的滤波方法,显著地改善了滤波效果,尤其是对加速度的估计。     

Enhancements to a multiple model adaptive estimator/image-tracker

Three major enhancements to a previously devised multiple model adaptive estimator (MMAE) for target image tracking are developed and analyzed. These are: allowing some of the elemental filters to have rectangular fields of view and to be tuned for target dynamics that are harsher in one direction than others; considering both Gauss-Markov acceleration models and constant turn-rate models for target dynamics; and devising an initial target acquisition algorithm to remove important biases in the estimated target template to be used in a correlator within the tracker. Particularly good adaptation responsiveness is demonstrated in the multiple model algorithm's ability to handle harsh maneuver onset, yielding performance essentially equivalent to that of the best artificially informed tracking algorithm     

A Kalman Filter Based Tracking Scheme with Input Estimation

Beginning with the derivation of a least squares estimator that yields an estimate of the acceleration input vector, this paper first develops a detector for sensing target maneuvers and then develops the combination of the estimator, detector, and a "simple" Kalman filter to form a tracker for maneuvering targets. Finally, some simulation results are presented. A relationship between the actual residuals, assuming target maneuvers, and the theoretical residuals of the "simple" Kalman filter that assumes no maneuvers, is first formulated. The estimator then computes a constant acceleration input vector that best fits that relationship. The result is a least squares estimator of the input vector which can be used to update the "simple" Kalman filter. Since typical targets spend considerable periods of time in the constant course and speed mode, a detector is used to guard against automatic updating of the "simple" Kalman filter. A maneuver is declared, and updating performed, only if the norm of the estimated input vector exceeds a threshold. The tracking sclheme is easy to implement and its capability is illustrated in three tracking examples.     

Covariance Matrix for ?-?-? Filtering

Closed-form expressions are derived for the output noise response of an ?-?-? filter in steady-state operation with constant measurement noise statistics. To the author's knowledge such expressions have been unavailable until now. These formulas are useful for target tracking applications.     

Use of measurements from an imaging sensor for precision targettracking

The extraction of measurements for precision tracking of the centroid of a target from a forward-looking infrared imaging sensor is presented. The size of the image of the target is assumed to be small, i.e. around 10 pixels. The statistical characterization of the centroid of the target is obtained. Similarly, the statistical properties of the image correlation of two frames, which measures the target offset, are derived. Explicit expressions that map the video noise statistics into measurement noise statistics are obtained. The offset measurement noise is shown to be autocorrelated. State variable models for tracking the target centroid with these measurements are then presented. Simulation results and quantitative conclusions about achievable subpixel tracking accuracy are given. It is shown that the filter that models the autocorrelated measurement noise provides the best performance     

机动目标的模型与跟踪算法

 <正> 在机动目标的“当前”统计模型中,目标的加速度被描述为修正的瑞利—马尔科夫过程,对应的自适应跟踪算法呈现出较好的跟踪特性。文献[2]研究了该模型及其自适应算法在实际的机载雷达跟踪系统的应用;文献[3]进一步推广了基于“当前”模型的MPDAF算法。本文提出一个新的机动目标模型,即假定目标加速度为一高斯—马尔     

机载跟踪雷达的次最优控制

 本文把机载跟踪雷达的目标视为匀速直线运动叠加一阶马尔柯夫过程,在视线坐标系内建立状态方程和观测方程。采用二次型性能指标,用E-coupling法求得次最优控制律。模拟计算表明,采用该控制律的系统具有很高的跟踪精度,比经典比例控制大约提高一个数量级,和最优控制相当。     

Optimum Steady-State Position and Velocity Estimation Using Noisy Sampled Position Data

The Kalman filtering technique is used to obtain analytical expressions for the optimum position and velocity accuracy that can be achieved in a navigation system that measures position at uniform sampling intervals of T seconds through random noise with an rms value of ?x. A one-dimensional dynamic model, with piecewise-constant acceleration assumed, is used in the analysis, in which analytic expressions for position and velocity accuracy (mean square), before and after observations, are obtained. The errors are maximum immediately before position measurements are made. The maximum position error, however, can be bounded by the inherent sensor error by use of a sufficiently high sampling rate, which depends on the sensor accuracy and acceleration level. The steady-state Kalman filter for realizing the optimum estimates consists of a double integrator, the initial conditions of which are reset at each observation.     

机动目标的多项式预测模型及其跟踪算法

根据匀变速运动的多项式描述形式,利用多项式预测滤波器对目标状态建模,提出了一种全新机动目标运动的动态模型——多项式预测模型,并针对这个全新的模型给出了相应的最优滤波算法。分析表明：该模型可以精确描述任意可以由多项式描述的目标运动,而不需要已知运动的具体参数,因此相应的最优滤波算法适用于任何可以用多项式描述的机动目标状态估计问题。一个机动目标跟踪问题的计算机仿真证明了本文方法的有效性和实用性。     

Canonical transform for tracking with kinematic models

A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.     

Navigation Accuracy Category-Position Models and Estimate Position Uncertainty Calculations for TIS-B System

Navigation accuracy category-position (NACp) is an important parameter for system accuracy of traffic information service-broadcast (TIS-B), which is determined by estimate position uncertainty (EPU). Centered about the problems that the existing EPU calculation based on noise measurement is low in accuracy and unfit for describing uncorrected biases in target reports, this article analyses the traditional NACp model, and uses the least square estimation (LSE) in EPU calculation. Furthermore, it proposes an extended NACp model, which considers both noise and biases and acquires EPU estimation with the help of approximate multiplex Taylor expression. Analysis and simulation show that the proposed method not only leads to significant improvement of the accuracy of EPU calculation, but is fit for EPU calculation with tracking biases in TIS-B system as well. As such it can find application in practice to depict different kinds of error models in TIS-B system.     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.