Adaptive Tracking Filter for Maneuvering Targets

A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.     

Comments on `Tracking a maneuvering target using input estimation''

P.L. Boglar (see ibid., vol.AES-23, no.3, p.298-310, May 1987) developed a recursive formulation of the Chan, Hu, and Plant (CHP) algorithm, and the results of the simulation verified the performance improvements. The commenter claims that Bogler obtained an incorrect recursive formulation of input estimation because he incorrectly used the formulation of the Kalman filter. The commenter presents calculations that aim to demonstrate this claim     

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     

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.     

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.     

一种新的基于机动检测的机动目标跟踪算法

针对Kalman滤波跟踪机动目标发散和目前多数自适应Kalman滤波算法对运动模型适应性不强的问题,提出了一种新的基于机动检测的机动目标跟踪算法,通过实时自适应的改变滤波模型提高对机动目标跟踪精度。对这种方法与Kalman滤波算法进行了计算机仿真比较,结果表明,该方法计算量小,可实时精确地自适应匹配目标的运动模型,可实现对机动目标稳定可靠的跟踪。     

A Decision?Directed Adaptive Tracker

In the design of a tracking filter for air traffic control (ATC) applications, a maneuvering aircraft can be modelled by a linear system with random noise accelerations. A Kalman filter tracker, designed on the basis of a variance chosen according to the distribution of the potential maneuver accelerations, will maintain track during maneuvers and provide some improvement in position accuracy. However, during those portions of the flight path where the aircraft is not maneuvering, the tracking accuracy will not be as good as if no acceleration noise had been allowed in the tracking filter. In this paper, statistical decision theory is used to derive an optimal test for detecting the aircraft maneuver; a more practical suboptimal test is then deduced from the optimal test. As long as no maneuver is declared, a simpler filter, based on a constant-velocity model, is used to track the aircraft. When a maneuver is detected, the tracker is reinitialized using stored data, up-dated to the present time, and then normal tracking is resumed as new data arrives. In essence, the tracker performs on the basis of a piecewise linear model in which the breakpoints are defined on-line using the maneuver detector. Simulation results show that there is a significant improvement in tracking capability using the decision-directed adaptive tracker.     

Target tracking in maneuver-centered coordinates

Aircraft targets normally maneuver on circular paths, which has led to tracking filters based on circular turns. A coordinate system to track circular maneuvers with a simple Kalman filter is introduced. This system is a polar coordinate system located at the center of the maneuver. It leads to a tracking filter with range, angle, and angular velocity in the state vector. Simulation results are presented, showing that the algorithm displays improved performance over methods based on constant x-y acceleration when tracking circular turns     

A tracking algorithm for maneuvering targets

A methodology for the tracking of maneuvering targets is presented. A quickest-detection scheme based on the innovation sequence is developed for a prompt detection of target maneuvers. The optimal length of a sliding window that minimizes the maneuver detection delay for a given false-alarm rate is determined. After maneuver detection, the system model is modified by adding a maneuver term. A recursive algorithm is proposed to estimate the maneuver magnitude. With this estimate, a modified Kalman filter is used for tracking. Simulation results demonstrate the superior performance of the algorithm, especially during target maneuvers     

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.     

Optimal Tracking of Maneuvering Targets

Maneuvering target motion is modeled by introducing a binary random variable in the target state equation. The optimal estimate is shown to be a weighted combination of two Kalman filter estimates with weights depending on the likelihood ratio for the detection of a maneuver. A tracking scheme is proposed for maneuvering target tracking and illustrated in an example.     

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.     

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation     

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 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.     

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.     

基于IMMKF算法的ADS-B监视应用目标跟踪

目标跟踪是机载广播式自动相关监视（ADS-B）应用的基础功能,对提升航空器周边的弱机动民航飞机目标跟踪性能具有重要意义。提出一种基于交互式多模型卡尔曼滤波（IMMKF）算法的ADS-B 监视应用目标跟踪方法。首先,针对弱机动背景下的民航飞机的飞行特点,建立包含匀速模型和标准协同转弯模型的运动模型集,并对模型进行线性化近似;然后,将模型预测和ADS-B 状态矢量量测数据作为IMMKF 算法中多个并行卡尔曼滤波器的输入,进行并行滤波;最后,计算得到目标状态矢量的估计和模型近似概率,并作为下一次迭代的输入。结果表明：相比于基于匀速模型的卡尔曼滤波目标跟踪方法,IMMKF 方法的位置跟踪误差降低了59%,速度跟踪误差降低了77%,显著提升了状态估计性能,具备较高的跟踪精度、稳健性与计算效率,在ADS-B 监视应用中具有实际应用价值与借鉴意义。     

基于强跟踪滤波的GPS/INS组合导航系统对准技术研究

针对卡尔曼滤波鲁棒性较差的问题,研究了基于强跟踪滤波方法的GPS/INS对准。建立了GPS/INS组合导航系统对准的误差模型,对机载装备系统进行GPS/INS组合导航系统的对准仿真分析,验证该方案的可行性及强跟踪滤波器的性能。仿真结果表明,采用强跟踪滤波能够根据残差的变化求出渐消因子,能够在机动过程中有效跟踪系统状态量,从而提高对准精度和速度。采用强跟踪滤波的GPS/INS组合导航系统对准技术可以保证对准的快速性及对准精度,对工程应用具有重要的参考价值。     

Robust extended Kalman filter with input estimation for maneuver tracking

This study investigates the problem of tracking a satellite performing unknown continuous maneuvers. A new method is proposed for estimating both the state and maneuver acceleration of the satellite. The estimation of the maneuver acceleration is obtained by the combination of an unbiased minimum-variance input and state estimation method and a low-pass filter. Then a threshold-based maneuver detection approach is developed to determinate the start and end time of the unknown maneuvers. During the maneuvering period, the estimation error of the maneuver acceleration is modeled as the sum of a fluctuation error and a sudden change error. A robust extended Kalman filter is developed for dealing with the acceleration estimate error and providing state estimation. Simulation results show that, compared with the Unbiased Minimum-variance Input and State Estimation (UMISE) method, the proposed method has the same position estimation accuracy, and the velocity estimation error is reduced by about 5 times during the maneuver period. Besides, the acceleration detection and estimation accuracy of the proposed method is much higher than that of the UMISE method.     

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.