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.     

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.     

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.     

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.     

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.     

涡轴发动机健康管理跟踪滤波器技术

以反映部件健康状态的变几何涡轴发动机部件级数学模型为基础,利用线性化方法建立了反映航空发动机健康状态的线性状态空间数学模型;利用Kalman滤波器原理,构建了涡轴发动机健康状态跟踪滤波器。对线性状态空间模型和健康状态跟踪滤波器进行了仿真,结果表明：线性状态数学模型准确、实时;健康状态跟踪滤波器可准确地估计出涡轴发动机健康状态的变化。     

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.     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.     

小波分析在外测数据滤波中的应用研究

为提高弹道估计精度,提出了一种基于小波分析的滤波方法,滤除外测数据中AR（自回归）模型的随机误差。分析讨论了滤波过程中的几个关键问题,提出了利用基于偏自相关系数截尾检验的方法来确定分解层数,然后采用GCV（广义交叉确认）准则来确定均方差意义下最优阈值的方法。本文提出的外测数据滤波方法计算简单,不需要估计噪声的方差。仿真结果表明,该方法能有效滤除外测数据中的AR噪声。     

Comments on "Analytical Steady-State Solution for a Continuous Time Kalman Filter"

The analytical expression for the steady-state solution to acontinuous-time Kalman filter with two state variables consideredby Ekstrand is found by directly solving the continuous-timealgebraic Ricatti equation.     

一种基于二级变维Kalman滤波的跟踪算法

Kalman滤波器是一种高速的目标跟踪器.针对不同阶数的Kalman滤波器具有不同的跟踪能力与跟踪效率之间存在的矛盾,设计了一种自适应Kalman滤波算法.该算法使用两级滤波器,根据目标机动性的变化,适当的调整滤波器的阶数,使跟踪结果快速收敛,很好地解决了矛盾.通过对仿真结果分析表明,算法具有可靠、计算简便、快速等特点,模型滤波精度较高,并可实现实时跟踪预测,具有一定的理论价值和实用价值.     

基于概率假设密度滤波器的多目标跟踪方法

在总结分析现有多目标跟踪方法的基础上,重点阐述了一种新的基于概率假设密度的多目标滤波跟踪方法,利用带有新生目标检测功能的概率假设密度滤波方法,通过仿真算例,与传统的MHT方法和GM-PHD方法进行了跟踪性能对比,说明了概率假设密度滤波器在强杂波和新生目标未知情况下的优越性。     

Tracking of a Ballistic Missile with A-Priori Information

The paper addresses the problem of estimating the launch and impact points of a ballistic target from radar measurements. The problem has been faced under different hypotheses on the available prior knowledge. The proposed approach combines a nonlinear batch estimator with a recursive MM (multiple model) particle filter in order to attain the estimation goal. Extensive simulations assess the achievable estimation performance.     

Tracking a 3D maneuvering target with passive sensors

A novel application of the interacting multiple models (IMM) algorithm in which passive infrared sensors are fused for tracking a target maneuvering in three dimensions is discussed. More accurate models of target motion are proposed to improve performance. When the general models are used to describe the maneuvering periods, it is shown that the IMM behaviour is not satisfactory, in that the innovations associated with the different models do not discriminate between the corresponding target maneuvering regimes. The turning of the Markov chain transition matrix, i.e., a priori information, is then crucial to obtaining the correct ordering of the a posteriori regime probabilities. On the contrary, a more satisfactory behavior of the IMM algorithm is obtained by carefully selecting the target motion models in the different regimes     

Stability of Gyro in a Vehicle Spinning with Uncertain Angular Velocity

The analysis of a single-axis rate gyroscope mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using circle criterion, it is shown that the gimbal motion is globally asymptotically stable if Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. A simple analytical relation for the selection of gyro parameters for stability is derived.     

Precise Decoupling Tracking of Airspeed and Altitude for UAV Based on Causal Solution of Stable Inversion

Use stable inversion to accomplish precise decoupling tracking of airspeed and altitude for conventional takeoff and landing of unmanned aerial vehicles (UAVs) is in essence a non-minimum phase output tracking problem. The main contribution of this article is that a new method to calculate the causal solution of stable inversion is proposed by introducing a well defined perturbed signal to the system's unstable internal dynamics. It is helpful to overcome the pitfalls resulting from non-causality in existing methods. Different from the mathematically accurate offline non-causal solution, the causal solution is an approximation with asymptotically convergent errors. The important merits are: It obviates the needs for the output trajectory to be pre-known time parameterized functions, hence broadening the application of stable inversion; The low computational workload is much more suitable for and beneficial to real-time applications than any existing method based on stable inversion. The output tracking problem is then converted into a state tracking problem based on the causal solution of stable inversion. Precise decoupling tracking of airspeed and altitude is realized by using a feedback controller. Simulations are carried out to verify the viability and low computational workload of the method.