Real-Time Tracking Filter Evaluation and Selection for Tactical Applications

Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-? filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.     

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.     

Efficient Approximation of Kalman Filter for Target Tracking

A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.     

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bi?s is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.     

基于改进容积卡尔曼滤波的惯性/光流组合自主测速方法

针对容积卡尔曼滤波算法在惯性/光流组合测速数据融合时出现由于各系统输出数据频率不一致导致融合精度有限的问题,提出了一种基于多速率残差校正的改进容积卡尔曼滤波算法.通过当前时刻误差估算组合导航系统残差,再使用估算后的残差对速度估计值进行补偿,最终实现惯性/光流组合系统速度测量值的数据融合.实验结果表明,通过提出的改进容积...     

一种基于组合导航系统的新融合滤波算法

本文设计了一种可用于地面用户的低成本组合导航系统，提出了基于该系统的新信息融合方法，即模糊卡尔曼滤波算法和地图匹配技术联合起来。仿真结果表明模糊卡尔曼滤波算法相当于一数据平滑处理窗口，具有比常规卡尔曼滤波算法更高的精度。     

飞行数据相容性检验技术

飞行试验测量数据中存在过程噪声和测量噪声,导致飞行数据之间不相容,国内目前常用的输出误差法不适用于耦合严重的直升机飞行数据相容性检验。采用增广卡尔曼滤波方法进行状态估计,大幅度地消除测量值中的误差;再用输出误差法对增广卡尔曼滤波估计的结果进行相容性检验,并将其应用于直升机四阶纵向等效模型辨识中。结果表明:提出的这种方法既解决了单独使用增广卡尔曼滤波进行数据相容性分析时由于初期收敛过程造成的滤波误差问题,又克服了单独使用输入误差法进行数据相容性时需手动修改时间延迟问题和测量值中误差过大时输出误差法无法收敛问题,使得检验效果与计算效率大幅提升。     

基于置信度加权的组合导航数据融合算法

 针对联邦滤波融合算法中由于模型量测噪声统计特性未能被准确描述导致其子滤波器误差变大，进而导致联邦滤波估计出现偏差的问题，为了改进联邦滤波融合方法，将模糊自适应卡尔曼滤波方法和置信度加权方法与联邦滤波融合方法相结合，应用于组合导航系统。该方法首先将模糊自适应卡尔曼滤波方法应用于各子滤波器，使其能够跟踪真实量测噪声统计特性。然后通过模糊方法计算得到各子滤波器的置信度，进而得到联邦滤波器的置信度，再由得到的置信度对各子滤波器及联邦滤波器输出进行加权，得到最终的全局输出。对车载组合导航系统的仿真结果表明，这种算法对量测噪声具有较强的自适应性，能够抑制置信度低的子滤波器在融合系统中所占的权重，提高联邦滤波融合算法的精度，是一种可行的车载组合导航数据融合算法。     

自适应扩展增量 Kalman 滤波方法

基于扩展增量Kalman滤波方法(EIKF)和自适应增量Kalman滤波(AIKF),建立自适应扩展增量Kalman(AEIKF)模型及其分析方法,给出递推算法.在许多实际情况(如深空探测),由于环境因素的影响、测量设备的不稳定性等原因,量测方程往往存在未知的系统误差,并且模型参数也具有不确定性,结果导致较大的Kalman滤波误差,影响滤波的收敛性.提出的AEIKF方法能够成功消除这种未知的系统误差,并能够实时估计变化的噪声统计量,提高Kalman滤波精度.该方法计算简单,便于工程应用.      

基于正反Kalman滤波的动基座重力仪数据处理方法

重力数据处理是动基座重力仪的核心技术,采用了一种基于正反Kalman滤波的数据处理方法提取重力异常值.以动基座重力仪(Sea and Air Gravity,SAG)为研究对象,根据系统参数推导了Kalman滤波方程,并运用正反Kalman滤波方法处理了SAG某飞行架次的数据.将提取的重力异常值与同机搭载飞行的俄罗斯高精度重力仪GT-1A的结果进行比对,试验结果表明,两者滤波结果差值的均方根误差要小于1 mGal.     

自由段弹道目标跟踪算法在工程中的应用

在对弹道目标跟踪预警的工程实践中,雷达系统对目标运动的信息处理速度尤为重要,因而,文章选取自适应跟踪模型与卡尔曼滤波相结合的方法解决自由段弹道目标的跟踪问题,并与扩展卡尔曼跟踪算法做了对比分析。仿真显示,2种滤波方式分别与自适应跟踪模型相结合后,卡尔曼滤波和扩展卡尔曼滤波跟踪性能相差不大,但其算法简单、运算时间短,可以较好满足自由段弹道目标跟踪的工程需求。     

基于联邦滤波结构的INS／GPS组合导航系统数据融合研究

为了研究平台式惯导INS（interial navigation system）和全球定位系统GPS（globe position system）组合导航联邦滤波器的实现,使用速度局部滤波器和位置局部滤波器,分别对INS／GPS组合导航系统的向东速度、向北速度,以及对经度和纬度进行卡尔曼滤波,然后将位置数据和速度数据输入主滤波进行数据融合。以无人机的向东匀速水平飞行为背景,运用联邦卡尔曼滤波器算法,使用matelab进行仿真分析。可以证明联邦滤波器算法简单,易于实现,并且可以提高导航系统精度．实际应用中此方法可行。     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

An alternate algorithm for discrete-time filtering

The discrete-time Kalman filter is an optimal estimator for the states of a linear, stochastic system. It assumes that measurements are linear combinations of the states, and all disturbances are Gaussian. The influence diagram, a decision analysis tool that provides an algorithm for discrete-time filtering equivalent to the Kalman filter when the influence diagram represents Gaussian random variables, is discussed. The influence diagram algorithm is a factored form of the Kalman filter, similar to other factored forms such as the U-D filter. Compared with the Kalman filter, it offers improved numerical properties. Compared with other factored forms, it offers a reduced computational load     

Kalman Filter Applications in Airborne Radar Tracking

This paper studies the application of Kalman filtering to single-target track systems in airborne radar. An angle channel Kalman filter is configured which incorporates measures of range, range rate, and on-board dynamics. Theoretical performance results are given and a discussion of methods for reducing the complexity of the Kalman gain computation is presented. A suboptimal antenna controller which operates on the outputs of the angle Kalman filter is also described. In addition, methodological improvements are shown to exist in the design of range and range-rate trackers using the Kalman filter configuration.     

Passive Position Location Estimation Using the Extended Kalman Filter

Several papers have been published recently using the method ofleast squares for passive position location estimation. While the Kalman filter is mentioned as an alternative approach in most ofthese papers, none of the papers actually compare the performanceof the Kalman filter with the method of least squares. In this paper,the performances of the extended Kalman filter and the iteratedextended Kalman filter are compared with the method of leastsquares. Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the extended Kalmanfilter.     

低成本的多普勒-捷联惯性组合导航系统

本文研究了一种采用低精度的惯性器件,应用卡尔曼滤波技术的多普勒捷联惯性组合导航系统。讨论了组合方案,推导了系统的动态方程,设计了一种最优和四种次优卡尔曼滤波器。对系统进行了协方差分析。分析结果表明,采用随机漂移为0.1°/h的陀螺仪,零位误差为10^-4g的加速度计,应用卡尔曼滤波技术可以实现1nmile/h的导航精度,成为一种低成本、中等精度的导航系统。     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

An Adaptive Two-Dimensional Kalman Tracking Filter

A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.     

一种基于可观测度分析的SINS/GPS自适应-反馈校正滤波新方法

 针对机载捷联惯导系统(SINS)/全球定位系统（GPS）组合导航系统不完全可观测导致滤波器精度下降甚至发散的问题,提出了一种基于系统状态可观测度分析的自适应反馈校正滤波新方法。该滤波方法改进了系统可观测度的归一化处理方法,将归一化处理后的系统状态可观测度作为反馈因子,对SINS系统进行自适应反馈校正。最后,将该方法应用于机载合成孔径雷达(SAR)运动补偿用SINS/GPS组合导航系统中,飞行试验结果表明该方法在系统不完全可观测的情况下有效地提高了导航精度。