均方意义下三维雷达无偏转换测量误差协方差阵的推导

在以前的研究中,无偏转测量误差协方差阵是基于当前测量值得到的.为了能利用所有历史数据以得到更精确的转换测量误差协方差阵估计,文中在均方意义下,推导了三维雷达的最优无偏转换测量误差协方差阵.     

Sequential nonlinear tracking using UKF and raw range-rate measurements

The three-dimensional (3D) converted measurements filtering (CMF) with both converted position and raw range-rate measurement is proposed to solve the Doppler radar target tracking, where the error between radar-target range and range rate are correlated. Firstly, not using pseudomeasurement constructed by product of range and range rate to reduce the high nonlinearity, the raw range-rate measurements are utilized by unscented Kalman filter (UKF), where the converted errors of the position and the range rate are decorrelated, then linear part (position measurements) and nonlinear part (range-rate measurement) are sequentially processed by Kalman filter (KF) and UKF. Secondly, based on the assumption of small measurement error, the mean and covariance of converted measurement errors are derived by second-order Taylor series expansion. Finally, the influence of the correlated coefficient rho between the range and range rate, and the range-rate noise deviation sigma_r are taken into account and extreme values of rho and sigma_r are used in Monte Carlo simulations. The results show that the proposed method is, in a sense, effective and practical     

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.     

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     

非线性系统中多传感器目标跟踪融合算法研究

 研究了在非线性系统中 ,基于转换坐标卡尔曼滤波器的多传感器目标跟踪融合算法。通过分析得出 :在非线性系统的多传感器目标跟踪中 ,基于转换坐标卡尔曼滤波器 ( CMKF)的分布融合估计基本可以重构中心融合估计。仿真实验也证明了此结论。由此可见分布的 CMKFA是非线性系统中较优的分布融合算法     

Automatic detection and tracking of a small surface watercraft in shallow water using a high-frequency active sonar

A high-frequency (HF) active sonar can be used to detect and track a small fast surface watercraft in shallow water based on the evolution of the watercraft wake observed in the sonar image sequence. An automatic detection and tracking (ADT) algorithm is described for this novel application. For each ping, the measurement of the target's polar position consists of 2 steps. First, the target bearing is estimated by finding the direction of arrival of the cavitation noise emitted by the watercraft. Then range measurements are extracted from the range profile (constant-angle cut of the sonar image) at the estimated target bearing. Range normalization and clutter map processing are used to reduce the number of false measurements. Estimates of the target's Cartesian position and velocity are updated at the sonar pulse repetition rate using the Kalman filter with debiased consistent converted measurements and nearest neighbour data association. The proposed algorithm is demonstrated using real data.     

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.     

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)     

Multiradar Tracking System Using Radial Velocity Measurements

Multiradar tracking using both position and radial velocity measurements is discussed. The measurement of two or more different radial velocity components allows the calculation of rectangular velocity components. The measurement noise of the velocity components is filtered using a Kalman filter in the same way as the Cartesian position components. Before the conversion of velocity components from radial to Cartesian coordinates, the radial velocities are aligned on a time scale to account for the time shift of the radar measurements. In order to compare multiradar tracking system performance with and without radial velocity, some simulation tests have been performed for typical paths. The simulation results show a significant improvement when radial velocity is used for tracking.     

False alarm effects on estimation in multitarget trackers

An analysis of false alarm effects on tracking filter performance in multitarget track-while-scan radars, using variable correlation gates, is presented. The false alarms considered originate from noise, clutter, and crossing targets. The dimensions of the correlation gates are determined by filter prediction and measurement error variances. Track association is implanted either by means of a distance weighted average of the observations or by the nearest neighbor rule. State estimation is performed by means of a second-order discrete Kalman filter, taking into consideration random target maneuvers. Measurements are made in polar coordinates, while target dynamics are estimated in Cartesian coordinates, resulting in coupled linear filter equations. the effect of false alarms on the observation noise covariance matrix, and hence on state estimation errors, is analyzed. A computer simulation example, implementing radar target tracking with a variable correlation gate in the presence of false alarms, is discussed     

Linear Regression Filtering and Prediction for Tracking Maneuvering Aircraft Targets

A Cartesian coordinate linear regression filter is utilized for tracking maneuvering aircraft targets. Measurements of target position are made in a line-of-sight coordinate frame, but filtering is performed in Cartesian coordinates. Numerical results are given for optimizing the truncation time constant such that a good balance is obtained between the dynamic errors and the standard deviations. Lower bounds on the dynamic errors are established for the Cartesian coordinate linear regression filter and compared with a line-of-sight coordinate Kalman filter.     

Limits in tracking with extended Kalman filters

The classical linearized conversion of measurements from polar or spherical coordinates to Cartesian ones generates a bias restricting the use of this conversion to cases where the bias can be neglected. In this work, the validity limits for the classical 2D transformation from polar to Cartesian coordinates, as derived in previous work, are shown to be too restrictive and the limits for the 3D transformation from spherical to Cartesian coordinates are introduced. Furthermore, quantitative measures for the performance degradation of the commonly used extended Kalman filter (EKF) in comparison with the best linear unbiased estimation (BLUE) filter are obtained by simulating typical tracking scenarios.     

Best linear unbiased filtering with nonlinear measurements for target tracking

In tracking applications, target dynamics are usually modeled in the Cartesian coordinates, while target measurements are directly available in the original sensor coordinates. Measurement conversion is widely used such that the Kalman filter can be applied in the Cartesian coordinates. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation, as pointed out in a recent survey conducted by the authors. A filter is proposed here that is theoretically optimal in the sense of minimizing the mean-square error among all linear unbiased filters in the Cartesian coordinates. The proposed filter is free of the fundamental limitations of the measurement-conversion approach. Results of an approximate, recursive implementation are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.     

A three-state Kalman tracker using position and rate measurements

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs pulsed Doppler processing, such as the moving target detector providing unambiguous Doppler data. The steady-state filter parameters have been analytically obtained under the assumption of white noise maneuver capability. The numerical computations of these parameters are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. The solution for the case when only the range measurements are available is obtained as a special case of this model. Graphs of normalized covariances and gains are presented to illustrate how the solution depends on different parameters     

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...     

Analytical Results for the x, y Kalman Tracking Filter

A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing (r, ?) at uniform sampling intervals T seconds apart. This development explicitly considers the coupling between the quantities measured by the sensor (r, ?) and the Cartesian x, y coordinate system selected for the tracking operation. The steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions. These results are verified by computer calculation of the Kalman filter matrix equations.     

Tracking a Maneuvering Target Using Input Estimation

The conventional Kalman tracking filter incurs mean tracking errors in the presence of a pilot-induced target maneuver. Chan,Hu, and Plant proposed a solution to this problem which used themean deviations of the residual innovation sequence to make corrections to the Kalman filter. This algorithm is further developedhere for the case of a one-dimensional Kalman filter, for which an Implementable closed-form recursive relation exists. Simulation results show that the Chan, Hu, and Plant method can accurately detect and correct an acceleration discontinuity under a variety of maneuver models and radar parameters. Also, the inclusion of thislogic into a multiple hypothesis tracking system is briefly outlined.     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

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。     

无源定位跟踪滤波算法研究及仿真分析

首先介绍了几种无源定位跟踪滤波算法原理,包括扩展卡尔曼滤波（EKF）,无迹卡尔曼滤波器（EKF）,交互多模型滤波器（IMM）;然后通过建立几种不同模型来对每一种滤波算法进行仿真,依据仿真图形和误差结果对滤波算法进行分析,从而实现不同滤波模型根据目标运动状态进行监视和切换,这对无源定位跟踪算法精度的提高和实际应用有很大的...