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     

Analytical solution for continuous-time Kalman tracking filterswith colored measurement noise in frequency domain

New expressions are given for analytical solutions to the steady-state Kalman gains of the two-state exponentially correlated velocity (ECV) and the three-state exponentially correlated acceleration (ECA) tracking filters with position measurements by using spectral factorization method. The measurement colored noise model is characterized by a correlation time 1/λ. The vehicle oscillations such as wind-induced-bending is also considered in the modeling of the system which leads to the most generalized state transition matrix     

Self-Tuning Multisensor Weighted Measurement Fusion Kalman Filter

For the multisensor systems with unknown noise variances, based on the solution of the matrix equations for the correlation function, the on-line estimators of the noise variance matrices are obtained, whose consistency is proved using the ergodicity of sampled correlation function. Further, two self-tuning weighted measurement fusion Kalman filters are presented for the multisensor systems with identical and different measurement matrices, respectively. Based on the stability of the dynamic error system, a new convergence analysis tool is presented for a self-tuning fuser, which is called the dynamic error system analysis (DESA) method. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is rigorously proved that the proposed self-tuning Kalman fusers converge to the steady-state optimal Kalman fusers in a realization or with probability one, so that they have asymptotic global optimality. A simulation example for a target tracking system with 3 sensors shows their effectiveness.     

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.     

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.     

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.     

Analytical Results for a Kalman Tracker Using Position and Rate Measurements

Analytical results are presented for determining the steady-state components of the gain and error covariance matrices of the two-state Kalman tracking filter with white noise maneuver capability.     

Track-to-track fusion with dissimilar sensors

An analysis is described of a kinematic state vector fusion algorithm when tracks are obtained from dissimilar sensors. For the sake of simplicity, it is assumed that two dissimilar sensors are equipped with nonidentical two-dimensional optimal linear Kalman filters. It is shown that the performance of such a track-to-track fusion algorithm can be improved if the cross-correlation matrix between candidate tracks is positive. This cross-correlation is introduced by noise associated with target maneuver that is common to the tracking filters in both sensors and is often neglected. An expression for the steady state cross-correlation matrix in closed form is derived and conditions for positivity of the cross-correlation matrix are obtained. The effect of positivity on performance of kinematic track-to-track fusion is also discussed     

Kalman Filter Design for Target Tracking

The problem of solving the matrix Riccati differential equation in the design of Kalman filters for the target tracking problem is considered. An algebraic transformation method is used to reduce the order of the Riccati differential equation and to obtain explicit expressions for the filter gains (in terms of the interceptor /target separation range) which results in a substantial reduction of the computer burden involved in estimating the target states. The applicability of the transform technique is demonstrated for the receiver thermal noise and the target glint noise cases.     

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     

包含乘性噪声自适应修正的非合作目标相对导航算法

无人机（UAV）态势感知的任务是利用机载传感器对未知环境进行目标识别和引导,针对无人机与非合作目标间中远距离的相对导航问题,提出了一种基于角度和距离量测的相对状态估计算法。在现有滤波算法的基础上,为了提高精度和稳定性,本文利用了列文伯格-马夸尔特（LM）优化的思想对迭代卡尔曼滤波（IEKF）算法进行改进,提出了一种LM-IEKF算法,并推导该算法在迭代过程中的状态更新方程及协方差阵的递推公式。在此基础上,考虑到距离传感器由于信号相关特性而引入的乘性噪声,现有的加性噪声模型难以适应,因此,进一步提出了基于量测噪声自适应修正的Modified LM-IEKF方法,通过在线实时更新噪声阵提高滤波的精度,并设置渐消记忆指数平滑估计结果。算法验证结果表明,与现有的EKF、IEKF算法相比,在仅含加性噪声的情况下,LM-IEKF算法具有更好的性能;在包含乘性噪声的情况下,Modified LM-IEKF可以有效地估计量测噪声,与目前广泛使用的EKF算法相比,在综合相对位置和相对速度精度上分别提高了10%和23%。     

Digital tracking filters with high order correlated measurement noise

The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.     

Simple Kalman gains for filtering position and velocitymeasurements

An alternate set of equations is given for the exact computation of the Kalman gains under the conditions of no maneuvering input noise and measurements in position and velocity. They are simpler than the standard recursive equations, and are useful in applications where implementation of the standard Kalman filter is not possible due to real-time restrictions. When there is maneuvering input noise, the same gains can still approximate the optimal gains with a very minor degradation in performance, even when some parameters, for example the measurement interval, change during a track. Simulation studies have indicated that there is negligible performance degradation with this method of gain approximation     

带异步相关噪声的战斗机蛇形机动跟踪算法

针对异步相关噪声背景下战斗机蛇形机动模式转弯角速度辨识问题,考虑到目标状态与转弯角速度之间相互耦合的特性,从联合优化的解决思路出发,基于期望最大化（EM）算法框架,提出了一种带异步相关噪声的联合估计与辨识算法。首先采用"去相关框架"解除过程噪声与量测噪声之间的相关性,从而将异步相关噪声背景下的转弯角速度辨识问题转换成具有一步状态延迟的转弯角速度辨识问题,其次通过解除目标状态与转弯角速度之间的非线性耦合关系,基于期望最大化算法实现了战斗机蛇形机动目标状态与转弯角速度的联合估计与辨识,从而获得转弯角速度闭环形式的解析解：在E-step,通过利用异步相关噪声背景下的高阶容积卡尔曼平滑器（HCKS）,获得目标状态的后验估计;在M-step,通过极大化条件似然函数,获得转弯角速度的解析解。最后通过仿真验证了所提算法的目标状态估计与角速度辨识的精度均优越于传统的扩维法。     

涡扇发动机变参数鲁棒H_∞滤波器设计

针对存在建模误差及测量噪声干扰条件下的涡扇发动机性能参数估计问题,标准卡尔曼滤波及其改进算法滤波估计误差收敛速度慢,滤波估计精度低,对不确定测量噪声及建模误差较为敏感,为此本文提出了一种变参数鲁棒H_∞滤波器设计方法。该方法采用仿射参数依赖Lyapunov函数设计满足H_∞性能指标要求的鲁棒滤波器,通过引入凸多胞技术,将参数依赖线性矩阵不等式(Linear Matrix Inequality,LMI)中变参数Lyapunov矩阵与系统系数矩阵之间耦合乘积导致的非凸优化问题,转化为常规LMI约束下的凸优化问题进行求解,降低了线性变参数(Linear Parameter Varying,LPV)鲁棒滤波器设计的保守性,得到了全局解。针对涡扇发动机的仿真结果表明:与扩展卡尔曼滤波器对比,采用该方法设计的滤波器具有较快的动态跟踪速度和较高的滤波精度,ΔFn的稳态估计误差不大于0.1%,ΔFn的相对估计误差不大于2.5%,同时对建模误差和测量噪声干扰具有较强的抑制能力。     

Incremental maneuver estimation model for target tracking

An incremental model for maneuver detection and estimation for use in target tracking with the Kalman filter is described. The approach is similar to the multiple Kalman filter bank, but with a memory for the maneuver status for the track under consideration. The advantage of this approach is that the target acceleration can be more accurately estimated. The maneuver-detection model has shown good maneuver-following capability. Moreover, it needs only a finite number of Kalman filters to handle all possible maneuver values and it responds quickly as maneuver occurs. When there is an abrupt maneuver change the model can still track the targets in short time     

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Mobile robots are often subject to multiplicative noise in the target tracking tasks, where the multiplicative measurement noise is correlated with additive measurement noise. In this paper,first, a correlation multiplicative measurement noise model is established. It is able to more accurately represent the measurement error caused by the distance sensor dependence state. Then, the estimated performance mismatch problem of Cubature Kalman Filter(CKF) under multiplicative noise is analyzed. An i...     

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.     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets

The majority of tactical weapons systems require that manned maneuverable vehicles, such as aircraft, ships, and submarines, be tracked accurately. An optimal Kalman filter has been derived for this purpose using a target model that is simple to implement and that represents closely the motions of maneuvering targets. Using this filter, parametric tracking accuracy data have been generated as a function of target maneuver characteristics, sensor observation noise, and data rate and that permits rapid a priori estimates of tracking performance to be made when maneuvering targets are to be tracked by sensors providing any combination of range, bearing, and elevation measurements.