Analytical Steady State Solution for a Kalman Tracking Filter

Analytical expressions are given for the steady state solution to a Kalman tracking filter used in a track-while-scan radar system. The radar sensor measures range and range rate, and both these measurements are utilized in the filter. The solution for range measurements only is obtained as a special case. Graphs are also given which show how the solution depends on different parameters.     

Mean Power Estimation with a Recursive Filter

Power estimates from smoothed detector outputs of stationary signals are analyzed for linear, square law, and logarithmic receiverdetectors. Smoothing is accomplished with a first-order recursive digital filter. lnput amplitude is assumed to be Rayleigh distributed and detector output samples independent. Expansion of results to other distributions is indicated.     

The Closed-Form Solution of True Proportional Navigation

The closed-form solution of the equations of motion of an ideal missile pursuing a nonmaneuvering target according to the true propotional navigation law is obtained. An analysis of the solution is performed, and the conditions necessary for the missile to reach the target are determined.     

Compensating a Recursive MTI Filter for Missing Pulses

Four methods of compensating a recursive, double-delay movingtarget indictor (MTI) cltter-cancellation filter for missing pulses were simulated and compared. One technique involving feedback from the delay outputs gave an average frequency response closely approximating that of the unperturbed filter.     

Mean-Level Detection Utilizing a Digital First-Order Recursive Filter

The use of a simple digital first-order recursive filter for mean-level detection is described. Performance characteristics are derived for the case where the background noise is stationary, and detection results are given for Swerling Case 2 fluctuating signals. Equations are derived for computing false-alarm performance in nonstationary backgrounds, and results are given for some special cases. Comparisons are made with performance of a conventional mean-level circuit in stationary and nonstationary noise.     

一个有理递归序列解的性质

文中分析了方程xn＋1=a＋bxn^2/1＋xn-2^2（其中a,6∈[0,∞）,a＋b〉0）的解的性质．并得山①当a=0,0〈b〈2时,方程的每一个解最终严格递减到0;②当b=0,0〈a时,方程的每一个非平凡解关于方程的平衡解振动。特别,当b=0、0〈a≤2时,方程的每一个正解收敛到平衡解x^-上.     

Noise-Free Analysis of a Tracking Filter FM Demodulator

The genesis and development of tracking filter structure arising out of a phase-plane study of the forced behavior of a general nonlinear second-order differential equation describing narrowband filters is discussed. By appropriately choosing the functional form of the feedback coefficients, two feasible filter structures for FM demodulation are obtained and their performance is compared in terms of tracking range, demodulation linearity, and steady state amplitude and phase response. Simulation study further supplements these results.     

多目标跟踪的概率假设密度粒子滤波

在多目标跟踪中,当目标数很大时,目标状态的联合分布的计算量会非常大。如果目标独立运动,可用各目标分别滤波来代替,但这要求考虑数据互联问题。文章介绍一种可以解决计算量问题的方法,只需计算联合分布的一阶矩——概率假设密度(PHD),PHD在任意区域S上的积分是S内目标数的期望值。因未记录目标身份,避免了数据互联问题。仿真中,传感器为被动雷达,目标观测值为距离、角度及速度时,对上述的PHD滤波进行了粒子实现,并对观测值是否相关的不同情况进行比较。PHD粒子滤波应用在非线性模型的多目标跟踪,实验结果表明,滤波可以稳健跟踪目标数为变数的情况,得到了接近真实情况的结果。     

不完全量测下一类非线性光电跟踪系统滤波器设计

 随着不完全量测条件下探测概率的下降,传统光电跟踪系统的跟踪性能显著降低。为此,本文考虑将俯仰和偏航两个方向的角速度量测引入传统光电跟踪系统,并设计了不完全量测下基于置信度融合的目标跟踪滤波器。首先针对这类新型的光电跟踪系统建立了系统的量测模型,利用嵌套条件方法推导了转换量测误差前两阶矩的一致性估计;然后针对位置探测通道与角速度探测通道的4种数据探测情形设计了4个子滤波器,并根据探测通道的探测情况计算出各子滤波器的置信度,进而对各子滤波器的输出按置信度进行加权融合,得到了跟踪滤波器的全局输出;最后给出了非线性跟踪系统统计意义下的Cramer-Rao下界(CRLB)。Monte-Carlo仿真表明：在不完全量测下,相比传统光电跟踪系统,附加角速度量测的光电跟踪系统的跟踪性能有了显著提高,并且滤波器估计误差均方差(RMSE)已逼近非线性跟踪系统统计意义下的CRLB。     

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.     

Application of Recursive Estimation and Kalman Filtering to Doppler Tracking

The techniques of recursive estimation and Kalman filtering are applied to the problem of estimation of space vehicle orbits and trajectories using only measurements of the Doppler shifts in radio signals transmitted by or reflected from the target. Two approaches are described. One is a global fit technique in which the parameters of an assumed trajectory model are estimated. The second is a pointwise mapping technique in which the trajectory estimate is extrapolated as the target tracking data is received. The paper provides a tutorial illustration of the direct application of recursive optimization techniques to a class of engineering problems.     

Steady-State Covariance Matrix Determination for a Three-Dimensional Kalman Tracking Filter

The steady-state components of the covariance matrix of estimation errors after processing an observation have been analytically determined ined for a tree-dimensional Kalman tracking filter.     

Analytical Steady-State Solution for a Continuous Time Kalman Filter

Analytical expressions are given for the steady-state solution to a continuous time Kalman filter for a two-state model where both states are measured. The solution is obtained by a limiting operation on the known solution for the corresponding discrete time case. The solution is visualized in two graphs. The filter transfer function is also given.     

Biased Estimation Properties of the Pseudolinear Tracking Filter

Estimation bias in the pseudolinear filter applied to bearings-only target tracking is discussed. Approximate expressions for the pertinent error terms are developed and subsequently used to predict tracking performance under realistic operating conditions. It is shown that once own-ship executes a maneuver, only the estimated range vector remains biased; the corresponding velocity vector becomes asymptotically unbiased. Further investigation reveals that this range bias is highly dependent upon geometry and can be altered by additional own-ship maneuvers. Experimental data are presented to support these findings.     

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.     

多坐标系下目标跟踪的联合滤波

针对雷达目标观测和处理在不同的坐标系下完成，本文提出了联合滤波算法来跟踪机动目标。该算法以卡尔曼滤波器为基础，直角坐标系下和极坐标系下的算法相联合，不仅克服了两种坐标系下滤波算法的不足，而且对机动目标有很好的跟踪效果。仿真实验结果表明了该算法的有效性。     

基于均值漂移无味粒子滤波的地面运动目标变结构交互多模型跟踪(英文)

为了跟踪地面运动目标,本文提出在变结构交互多模型基础上使用均值漂移无味粒子滤波的算法。模型滤波中,通过均值漂移将无味粒子滤波产生的采样粒子向目标状态最大后验密度估计方向移动。"停止"模型基础上,提出了"遮蔽"模型:出现地形遮蔽时,使用上一时刻的预测代替下一时刻的测量,且保持道路模型与遮蔽前一致。仿真实验采用地面运动目标指示雷达,考虑地面运动目标的三种常见场景:进入或离开道路、经过道路交叉点以及无测量值。使用了RMSE和ANEES两种评价指标,实验结果表明本文算法有效地提高了目标改变行驶道路时的跟踪精度;且目标速度过低或被遮蔽时,可以避免轨迹中断。     

Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements

Using two separate algorithms, called Kalman's recursive and Vaughan's nonrecursive, exact closed-form solutions of the steady-state two-state exponentially correlated velocity (ECV) and three-state exponentially correlated acceleration (ECA) target-tracking filters are derived for discrete position measurements. For this particular application, the superiority of Vaughan's nonrecursive over Kalman's recursive algorithm is observed.     

基于强跟踪EKF的组合导航系统故障检测方法

针对大方位失准角的机载SINS/GPS组合导航系统,为保证在高动态环境下实现高精度、高可靠的导航,利用强跟踪EKF滤波残差设计了一种基于残差统计特性的坏值检测算法,对导航信息进行估计和跟踪.仿真结果表明,该算法能够实时检测出GPS量测信息中的坏值信息,隔离后可显著提高组合导航精度,具有较高的可靠性、出色的容错能力和重要的工程应用价值.