Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem     

UKF方法及其在方位跟踪问题中的应用

采用UKF(Unscented Kalman Filter)方法处理了平面内地面站对目标的方位跟踪的估计问题。目标的位置和速度由选定的高斯分布采样点来近似，在每个更新过程中，采样点随着状态方程传播并随着非线性测量方程变换，由此不但得到目标位置和速度的均值及较高的计算精度，而且避免了对非线性方程的线性化过程。仿真结果表明，UKF方法比传统的扩展卡尔曼滤波(EKF)算法有更高的估计精度，并能有效地克服非线性严重时，方位跟踪问题中很容易出现的滤波发散问题。     

Tracking a ballistic target: comparison of several nonlinear filters

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.     

Discrete-time min-max tracking

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.     

Waveform selective probabilistic data association

An adaptive, waveform selective probabilistic data association (WSPDA) algorithm for tracking a single target in clutter is presented. The assumption of an optimal receiver allows the inclusion of transmitted waveform specification parameters in the tracking subsystem equations, leading to a waveform selection scheme where the next transmitted waveform parameters are selected so as to minimize the average total mean-square tracking error at the next time step. Semiclosed form solutions are given to the local (one-step-ahead) adaptive waveform selection problem for the case of one-dimensional target motion. A simple simulation example is given to compare the performance of a tracking system using a WSFDA based tracking filter with that of a conventional system with a fixed waveform shape and probabilistic data association (PDA) tracking filter.     

一种分散化多站联合目标跟踪算法

 本文基于分散估计理论的基本原理,考虑各子站基于不同坐标系这个一般情形,给出了一种新的分散化多站联合目标跟踪算法。并针对子站间四种不同的通讯方式,对算法进行了仿真。结果表明,本文的最优合成算法即使在各个子站由于缺少足够的信息而得到错误估计的情况下,也能快速地给出正确的估计。     

星载红外探测阵列对导弹跟踪定位的研究

通过分析研究建立了前视红外探测阵列 (FL IR)对导弹进行精确跟踪、定位的数学模型 ,其中包括导弹的运动模型、大气干扰模型和探测阵列的观测模型。根据探测阵列的原始观测数据 ,利用扩展卡尔曼滤波器 (EKF)精确跟踪导弹目标。由于导弹与探测器的距离较远 ,故可视为点目标。导弹在探测阵列上投影的位置由两部分组成 :导弹真实运动位置和由于大气干扰造成的偏移。滤波器分别估计了这两种位移在探测阵列上的变化。最后用蒙特卡罗方法分析了滤波器的性能。     

The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance

This note deals with the effect of the common process noise on the fusion (combination) of the state estimates of a target based on measurements obtained by two different sensors. This problem arises in a multisensor environment where each sensor has its information processing (tracking) subsystem. In the case of an ?-? tracking filter the effect of the process noise is that, over a wide range of its variance, the uncertainty area corresponding to the fused estimates is about 70 percent of the single-sensor uncertainty area as opposed to 50 percent obtained if the dependence is ignored.     

Quadratic extended Kalman filter approach for GPS/INS integration

GPS/INS integration system has been widely applied for navigation due to their complementary characteristics. And the tightly coupled integration approach has the advantage over the loosely coupled approach by using the raw GPS measurements, but hence introduces the nonlinearity into the measurement equation of the Kalman filter. So the typical method for navigation using measurements of range or pseudorange is by linearizing the measurements in an extended Kalman filter (EKF). However, the modeling errors of the EKF will cause the bias and divergence problems especially under the situation that the low quality inertial devices are included. To solve this problem, a quadratic EKF approach by adding the second-order derivative information to retain some nonlinearities is proposed in this paper. Simulation results indicate that the nonlinear terms included in the filtering process have the great influence on the performance of integration, especially in the case that the low quality INS is used in the integrated system. Furthermore, a two-stage cascaded estimation method is used, which circumvents the difficulty of solving nonlinear equations and greatly decreases the computational complexity of the proposed approach, so the quadratic EKF approach proposed in this paper is of great value in practice.     

Rao-blackwellised particle filtering in random set multitarget tracking

This article introduces a Rao-Blackwellised particle filtering (RBPF) approach in the finite set statistics (FISST) multitarget tracking framework. The RBPF approach is proposed in such a case, where each sensor is assumed to produce a sequence of detection reports each containing either one single-target measurement, or a "no detection" report. The tests cover two different measurement models: a linear-Gaussian measurement model, and a nonlinear model linearised in the extended Kalman filter (EKF) scheme. In the tests, Rao-Blackwellisation resulted in a significant reduction of the errors of the FISST estimators when compared with a previously proposed direct particle implementation. In addition, the RBPF approach was shown to be applicable in nonlinear bearings-only multitarget tracking.     

FDEKF在反辐射无人机抗目标雷达关机中的应用

基于捷联惯导/反辐射导引头组合抗目标雷达关机制导方案,研究了有限差分卡尔曼滤波(FDEKF)方法在对目标雷达被动定位中的应用。考虑反辐射导引头测角存在非线性特性,提出了一种基于扩展状态变量维数的方法实现了目标状态估计和导引头非线性特性补偿。仿真结果表明,FDEKF是一种具有良好性能的非线性滤波方法,可以代替传统的EKF解决反辐射无人机对目标雷达的被动定位问题。     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

Adaptive Nonlinear Optimal Compensation Control for Electro-hydraulic Load Simulator

 Directing to the strong position coupling problem of electro-hydraulic load simulator (EHLS), this article presents an adap-tive nonlinear optimal compensation control strategy based on two estimated nonlinear parameters, viz. the flow gain coeffi-cient of servo valve and total factors of flow-pressure coefficient. Taking trace error of torque control system to zero as control object, this article designs the adaptive nonlinear optimal compensation control strategy, which regards torque control output of closed-loop controller converging to zero as the control target, to optimize torque tracking performance. Electro-hydraulic load simulator is a typical case of the torque system which is strongly coupled with a hydraulic positioning system. This article firstly builds and analyzes the mathematical models of hydraulic torque and positioning system, then designs an adaptive nonlinear optimal compensation controller, proves the validity of parameters estimation, and shows the comparison data among three control structures with various typical operating conditions, including proportion-integral-derivative (PID) controller only, the velocity synchronizing controller plus PID controller and the proposed adaptive nonlinear optimal compensation controller plus PID controller. Experimental results show that systems’ nonlinear parameters are estimated exactly using the proposed method, and the trace accuracy of the torque system is greatly enhanced by adaptive nonlinear optimal compensation control, and the torque servo system capability against sudden disturbance can be greatly improved.     

Reduced spatio-temporal complexity MMPP and image-based tracking filters for maneuvering targets

We present reduced-complexity nonlinear filtering algorithms for image-based tracking of maneuvering targets. In image-based target tracking, the mode of the target is observed as a Markov modulated Poisson process (MMPP) and the aim is to compute optimal estimates of the target's state. We present a reduced complexity algorithm in two steps. First, a gauge transformation is used to reexpress the filtering equations in a form that is computationally more efficient for time discretization than naive discretization of the filtering equations. Second, a spatial aggregation algorithm with guaranteed performance bounds is presented for the time-discretized filters. A numerical example illustrating the performance of the resulting reduced-complexity filtering algorithms for a switching turn-rate model is presented.     

Bearings-only and Doppler-bearing tracking using instrumentalvariables

In bearings-only tracking (BOT) or Doppler and bearing tracking (DBT), both common passive sonar problems, the measurement equations are nonlinear. To apply the Kalman filter, it is necessary either to linearize the equations or to embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence, while the latter produces biased estimates. A formulation of BOT and DBT which has a constant state vector and simplifies the tracking problem to one of constant parameter estimation is given. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive unbiased estimator. The theoretical developments are verified by simulation, which also shows that the formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB)     

基于变分贝叶斯的星载雷达非线性滤波

星载雷达由于其探测范围广、距离远、全天候等优点,在预警防御系统中占有十分重要的地位。然而,由于观测平台的高速运动以及摄动干扰、传感器观测非线性等问题,使得星载雷达目标高精度跟踪带来严峻挑战。针对星载雷达非线性状态估计问题,采用一种基于变分贝叶斯的非线性滤波方法,该方法通过将非线性状态估计问题转化为优化问题,通过迭代优化获得了闭环解析解。此外,针对坐标变换中俯仰角量测缺失问题,提出了一种基于先验目标高度的俯仰角估计方法。通过数值仿真,验证了所提方法较传统非线性滤波方法,如扩展卡尔曼滤波、不敏卡尔曼滤波、转换量测卡尔曼滤波,具有更好的估计精度。     

Optimal Cooperative Sensing using a Team of UAVs

The authors investigates the joint optimal estimation of both the position and velocity of a ground moving target (GMT) using pulse Doppler radars on-board unmanned aerial vehicles (UAVs). The problem of cooperative estimation using a UAV team and the optimization of the team's configuration to achieve optimal GMT position and velocity estimates are addressed. Based on the Cramer-Rao bound, the minimum achievable error variance of the GMT position and velocity estimates is derived. The expression of the minimum achievable estimation error variance for unbiased estimation provided by the Cramer-Rao bound is minimized yielding the optimal configuration of the UAV team. Our solution is complete in that it addresses various GMT tracking scenarios and an arbitrary number of UAVs. Optimal sensor geometries for typical applications are illustrated