Particle filters for tracking with out-of-sequence measurements

An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.     

Observability Requirements for Three-Dimensional Tracking via Angle Measurements

Observability requirements previously established for bearings-only tracking in two dimensions are extended to a class of three-dimensional estimation algorithms capable of processing any pairwise combination of azimuth bearing, conical bearing, and depth/elevation angle measurements. Although these algorithms are intrinsically nonlinear, it is shown that they can be analyzed in a linear framework without sacrificing mathematical rigor. A simplified observability criterion, applicable to both autonomous and nonautonomous linear systems, is presented and utilized to specify conditions on own-ship motion which are both necessary and sufficient for a unique tracking solution. Further analysis reveals that observability dependence on own-ship maneuvers for the three-dimensional algorithms considered here parallels the concomitant two-dimensional requirements. An interesting difference, however, is that under certain conditions, a unique tracking solution can be obtained in three dimensions for unaccelerated own-ship motion.     

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)     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

A non-Bayesian segmenting tracker for highly maneuvering targets

The segmenting track identifier (STI) is introduced as a new methodology for tracking highly maneuvering targets. This nonBayesian approach dynamically partitions a target track into a sequence of track segments, making hard estimates of when the target's maneuvering mode transitions occur, and then estimates the parameters of the target model for each segment. STI is compared with two variable structures interacting multiple model (VS-IMM) algorithms through simulations, where it is shown to have a three fold performance advantage in median absolute turn rate estimation errors, as well as better position estimation for very highly maneuvering targets. STI is also shown to outperform a Rauch-Tung-Striebel (RTS) fixed-interval smoother when estimates are retrospectively derived, and STI accurately characterize the temporal pattern of maneuvers.     

Reduced spatio-temporal complexity MMPP and image-based tracking filters for maneuvering targets

We present reduced-complexity nonlinear filtering algorithms for image-based tracking of maneuvering targets. In image-based target tracking, the mode of the target is observed as a Markov modulated Poisson process (MMPP) and the aim is to compute optimal estimates of the target's state. We present a reduced complexity algorithm in two steps. First, a gauge transformation is used to reexpress the filtering equations in a form that is computationally more efficient for time discretization than naive discretization of the filtering equations. Second, a spatial aggregation algorithm with guaranteed performance bounds is presented for the time-discretized filters. A numerical example illustrating the performance of the resulting reduced-complexity filtering algorithms for a switching turn-rate model is presented.     

修正的概率数据互联算法

阐明了概率数据互联(PDA)算法能很好地解决密集环境下的目标跟踪问题,在该算法基础上,人们又提出了联合概率数据互联(JPDA)算法和一些基于 PDA 的修正算法。在概率数据互联算法中,有一个很重要的参数就是杂波数密度(或波门内虚假量测期望数)。然而在许多实际情况中,这个参数是很难获取的。针对这一问题,文中提出了一种修正的概率数据互联算法,该算法通过实时地调整这一参数来获得对目标较为准确的估计结果。最后,给出了算法的仿真分析。     

基于倾斜角的多目标测向无源定位技术

对多目标测向无源定位问题进行了研究。虽然无源观测站不同,针对同一目标的方位角和俯仰角数据也不同,但它们有共同的倾斜角。基于此,提出了基于倾斜角的多目标测向无源定位算法。该算法分别计算一组与多个目标对应的倾斜角,然后利用倾斜角最接近原则对这2组数据进行关联判断,解决多目标测向数据的关联和定位问题,并通过仿真实验,对算法的有效性和可行性进行了验证。     

Tracking in Clutter using IMM-IPDA?Based Algorithms

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the: number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets.     

Estimating the Doppler centroid of SAR data

After reviewing frequency-domain techniques for estimating the Doppler centroid of synthetic-aperture radar (SAR) data, the author describes a time-domain method and highlights its advantages. In particular, a nonlinear time-domain algorithm called the sign-Doppler estimator (SDE) is shown to have attractive properties. An evaluation based on an existing SEASAT processor is reported. The time-domain algorithms are shown to be extremely efficient with respect to requirements on calculations and memory, and hence they are well suited to real-time systems where the Doppler estimation is based on raw SAR data. For offline processors where the Doppler estimation is performed on processed data, which removes the problem of partial coverage of bright targets, the ΔE estimator and the CDE (correlation Doppler estimator) algorithm give similar performance. However, for nonhomogeneous scenes it is found that the nonlinear SDE algorithm, which estimates the Doppler-shift on the basis of data signs alone, gives superior performance     

Bearings-only target motion analysis with acoustic propagation models of uncertain fidelity

The augmented bearings-only target motion analysis (TMA) problem arises when the bearing measurements of the classical bearings-only TMA problem are augmented with received signal-to-noise ratio (SNR) measurements. A combined acoustic propagation and sensor (CAPS) performance prediction model specifying the conditional density of the SNR measurements is assumed given; however, mismatch may exist between the CAPS model and the real world. We present a novel "missing data" formulation of the augmented bearings-only TMA problem using an empirical maximum a posteriori (EMAP) method for target parameter estimation, and show that it provides a natural and straightforward technique for mitigating CAPS model mismatch. The EMAP approach leads to an iteratively reweighted, linear least-squares algorithm for solving both the augmented bearings-only TMA problem and the classical (nonaugmented) bearings-only TMA problem. Examples are provided.     

Efficient target tracking using dynamic programming

A dynamic programming (DP) algorithm has been developed for the detection and tracking of subpixel-sized, low signal-to-noise ratio (SNR) targets observed by side-or forward-looking imaging sensors. A distinguishing feature of this approach is that target detection and tracking are combined into a single optimization procedure that takes into account statistical models of target motion, background noise, and clutter. Current work has led to a number of technical innovations that improve the performance and efficiency of the DP tracking algorithm, including the development of a new track scoring function, and an extension to the basic DP algorithm that reduces computation requirements by over an order of magnitude. A prototype infrared (IR) target tracking system incorporating these enhancements has been implemented for a step-starting IR camera application. Sensitivity improvements of several decibels over conventional sequential detection and tracking algorithms were realized     

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.     

Optimal Cooperative Sensing using a Team of UAVs

The authors investigates the joint optimal estimation of both the position and velocity of a ground moving target (GMT) using pulse Doppler radars on-board unmanned aerial vehicles (UAVs). The problem of cooperative estimation using a UAV team and the optimization of the team's configuration to achieve optimal GMT position and velocity estimates are addressed. Based on the Cramer-Rao bound, the minimum achievable error variance of the GMT position and velocity estimates is derived. The expression of the minimum achievable estimation error variance for unbiased estimation provided by the Cramer-Rao bound is minimized yielding the optimal configuration of the UAV team. Our solution is complete in that it addresses various GMT tracking scenarios and an arbitrary number of UAVs. Optimal sensor geometries for typical applications are illustrated     

Multitarget tracking using the joint multitarget probability density

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).     

基于CPHD的双层粒子滤波目标跟踪算法

常规基于势概率假设密度滤波(Cardinalized Probability Hypothesis Density,CPHD)的粒子滤波(Particle Fil? ter,PF)跟踪算法应用于多目标跟踪时,容易遇到因粒子数量增加而带来的运算效率下降、目标数目估计不准的问题。文章基于常规粒子滤波 CPHD跟踪算法,通过部署双层粒子,提出基于势概率假设密度滤波的双层粒子滤波 (Two-Layer Particle Filter-CPHD,TLPF-CPHD)算法,以便提高目标数目及状态估计精度。仿真实验结果证明,相比于常规 PF-CPHD算法,新算法具有更好的目标数目和状态估计准确性。     

地空协同防空目标抗差跟踪算法

针对现有系统误差配准算法以已知系统误差变化模型为前提条件、相应的目标状态估计易受系统误差配准结果影响等不足之处,在机载雷达与地基雷达协同防空预警体系下,对系统误差存在情况下的目标跟踪问题进行了研究,并提出了有效的地空协同防空目标抗差跟踪算法。仿真结果表明所提算法可得到无偏、稳定、有效的目标状态估计,并且相对于系统误差目标状态联合估计算法,所提算法计算量小,对系统误差变化有很强的鲁棒性,可适应实际工程应用中可能出现的异常情况,为后续决策提供稳定有效的目标信息。     

Comments on “Discrete-time observability and estimabilityanalysis for bearings-only target motion analysis”

Discusses the extensive mathematical analysis carried out by the authors of the original paper [see ibid., vol. 33, no. 1, p. 178-201, 1997] and submits the following points. The authors used pseudo measurements for recasting the observability problem into a linear framework. They treated the bearings-only passive target tracking system as a deterministic system. It is already established that for deterministic systems, the pseudo measurements are linear functions of the states of the system, though the coefficient matrix is a nonlinear function of the original measurements, By using the pseudo measurements in a linear observer, global stability can be shown. However, if the pseudo measurement observer, for which the analysis is mostly carried out by the authors, is used in a noisy environment as a pseudo measurement filter (PMF), biased estimates are arrived at. Hence, though the approach of authors is quite direct and provides insights about the algebraic structure of the BOT problem, as pseudo measurements are used throughout the analysis is not of much use to the TMA community, as the nonlinear measurement equation along with measurement noise are required to be considered in the BOT problem to obtain unbiased results     

Novel passive localization algorithm based on double side matrix-restricted total least squares

In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares (DSMRTLS) is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.