Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.     

改进的MMPHD机动目标跟踪方法

基于序列蒙特卡罗方法的经典多模概率假设密度滤波方法及其各种衍生方法,在预测过程中依据多个并行的状态转移模型,通过将大量粒子散布到下一时刻目标所有可能出现的状态空间实现目标状态的捕获,造成计算量大、目标跟踪精度差。为此,提出一种改进的多模粒子概率假设密度机动目标跟踪方法。该方法利用最新量测信息估计目标运动模型概率及模型参数,并将估计得到的目标模型应用到粒子概率假设密度滤波方法的预测过程中生成预测粒子,从而将大部分粒子聚合在目标最可能出现的状态空间邻域中,实现粒子的有效利用。数值仿真表明,所提方法不仅显著地减少了目标丢失个数,而且提高了目标跟踪精度。     

Rao-Blackwellized粒子概率假设密度滤波算法

针对多目标跟踪（MTT）,提出一种新的基于随机集的滤波算法,称为Rao-Blackwellized粒子概率假设密度滤波算法（RBP-PHDF）。算法运用Rao-Blackwellized思想,通过挖掘分析“混合线性/非线性模型”的结构,采用序列蒙特卡罗（SMC）方法预测与估计概率假设密度（PHD）迭代式中各个目标的非线性状态,并利用非线性状态粒子中包含的信息,使用卡尔曼滤波器（KF）对线性状态进行预测与估计。以更好地估计PHD进而提高各目标状态估计精度。分析与MTT仿真的结果表明,在相同的仿真条件下,与现有序列蒙特卡罗概率假设密度滤波算法（SMC-PHDF）相比,RBP-PHDF在降低粒子维数、减少计算量的同时,有效提升了估计精度。     

Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.     

残差滤波及其在密集多回波环境下机动多目标跟踪中的应用

 修正概率数据关联滤波（MPDAF）是目前解决密集多回波环境下机动多目标跟踪较为有效的方法,但当回波密度增高时,该方法容易失跟。本文针对此特点,在MPDAF基础上,提出了残差滤波（RF）方法,分别从理论和Monte carlo仿真两方面揭示了RF与数据关联的内在机理,结果表明该方法能大幅度提高跟踪滤波器捕捉目标和剔除关联域内多余回波的能力以及跟踪的性能,是一种解决高密集多回波环境下机动多目标跟踪的有效方法。     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values     

一种密集多回波环境下的机动多目标跟踪起始算法

 本文研究密集多回波环境下的机动多目标跟踪起始问题。文中首先提出主跟踪子空间和边缘跟踪子空间的定义与性质,接着修正Bayes轨迹确定方法BTC,并将其与具有残差滤波的修正概率数据关联滤波算法MPDAF-RF有机地结合起来,提出一种适合高密集多回波环境的机动多目环跟踪起始方法——“全邻”Bayes跟踪起始算法ABTI。Monte Carlo仿真表明,本文所给出的算法不仅克服了一类概率数据关联滤波方法没有跟踪起始机理的缺陷,而且辨别目标与虚警的能力很强,不失为解决高密集多回波环境下机动多目标跟踪起始的有效方法。     

A measurement-driven adaptive probability hypothesis density filter for multitarget tracking

This paper studies the dynamic estimation problem for multitarget tracking. A novel gating strategy that is based on the measurement likelihood of the target state space is proposed to improve the overall effectiveness of the probability hypothesis density(PHD) filter. Firstly, a measurement-driven mechanism based on this gating technique is designed to classify the measurements. In this mechanism, only the measurements for the existing targets are considered in the update step of the existing targets while the measurements of newborn targets are used for exploring newborn targets. Secondly, the gating strategy enables the development of a heuristic state estimation algorithm when sequential Monte Carlo(SMC) implementation of the PHD filter is investigated, where the measurements are used to drive the particle clustering within the space gate.The resulting PHD filter can achieve a more robust and accurate estimation of the existing targets by reducing the interference from clutter. Moreover, the target birth intensity can be adaptive to detect newborn targets, which is in accordance with the birth measurements. Simulation results demonstrate the computational efficiency and tracking performance of the proposed algorithm.     

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。     

Information type filters for tracking a maneuvering target

Two previously proposed adaptive covariance-type Kalman filtering techniques for tracking maneuvering targets (see Y.T. Chan et al. ibid., p.237-44, Mar. 1979, and Z. Tang et al. Report, Department of Electrical and Computer Engineering, Oregon State University, Corvallis, Oct. 1983) are developed further to utilize the information-type Kalman filter. These adaptive information-type filters are described in structurally decoupled forms, thereby greatly reducing the computational requirements while rendering the filters amenable to implementation on parallel processors. A coherent decision procedure for including partial coupling when necessary is developed via offline analysis of crosscorrelation functions     

Mixture Reduction Algorithms for Point and Extended Object Tracking in Clutter

The Bayesian solution to the problem of tracking a target with measurement association uncertainty gives rise to mixture distributions, which are composed of an ever increasing number of components. To produce a practical tracking filter, the growth of components must be controlled by approximating the mixture distribution. Two mixture reduction schemes (a joining algorithm and a clustering algorithm) have been derived for this purpose. If significant well spaced mixture components are present, these techniques can provide a useful improvement over the probabilistic data association filter (PDAF) approach, which reduces the mixture to a single Gaussian component at each time step. For the standard problem of tracking a point target in uniform random clutter, a Monte Carlo simulation study has been employed to identify the region of the problem parameter space where significant performance improvement is obtained over the PDAF. In the second part of this paper, the formal Bayesian filter is derived for an extended target consisting of an array of measurement sources with association uncertainty. A practical multiple hypothesis filter is implemented using mixture reduction and simulation results are presented.     

基于自适应粒子滤波的涡扇发动机故障诊断

针对涡扇发动机非线性、非高斯的特点,提出了一种自适应的粒子滤波算法用于涡扇发动机气路部件突变故障的诊断.为了减小算法的计算量并且保证滤波精度,分析了滤波精度和样本数目的关系,提出根据滤波过程中状态的方差自适应地调整粒子数,在保证一定的滤波精度下可以有效地减少滤波过程中使用的粒子数,提高了算法的实时性.同时,引入扩展卡尔曼滤波(EKF)用于更新粒子,产生重要概率密度函数,在一定程度上避免了粒子的退化.通过某型涡扇发动机的仿真分析表明:改进的算法相比标准粒子滤波算法用于涡扇发动机气路部件故障诊断时,参数估计的方均根误差减小了50%左右,且算法的计算量减小了30%.     

Multi-EAP:Extended EAP for multi-estimate extraction for SMC-PHD filter

The ability to extract state-estimates for each target of a multi-target posterior, referred to as multi-estimate extraction (MEE), is an essential requirement for a multi-target filter, whose key performance assessments are based on accuracy, computational efficiency and reliability. The probability hypothesis density (PHD) filter, implemented by the sequential Monte Carlo approach, affords a computationally efficient solution to general multi-target filtering for a time-varying num-ber of targets, but leaves no clue for optimal MEE. In this paper, new data association techniques are proposed to distinguish real measurements of targets from clutter, as well as to associate par-ticles with measurements. The MEE problem is then formulated as a family of parallel single-estimate extraction problems, facilitating the use of the classic expected a posteriori (EAP) estima-tor, namely the multi-EAP (MEAP) estimator. The resulting MEAP estimator is free of iterative clustering computation, computes quickly and yields accurate and reliable estimates. Typical sim-ulation scenarios are employed to demonstrate the superiority of the MEAP estimator over existing methods in terms of faster processing speed and better estimation accuracy.     

Extended solution to multiple maneuvering target tracking

An improved algorithm for tracking multiple maneuvering targets is presented. This approach is implemented with an approximate adaptive filter consisting of the one-step conditional maximum-likelihood technique together with the extended Kalman filter and an adaptive maneuvering compensator. In order to avoid the extra computational burden of considering events with negligible probability, a validation matrix is defined in the tracking structure. With this approach, data-association and target maneuvering problems can be solved simultaneously. Detailed Monte Carlo simulations of the algorithm for many tracking situations are described. Computer simulation results indicate that this approach successfully tracks multiple maneuvering targets over a wide range of conditions     

Event-triggered cooperative target tracking in wireless sensor networks

Since the issues of low communication bandwidth supply and limited battery capacity are very crucial for wireless sensor networks, this paper focuses on the problem of event-triggered cooperative target tracking based on set-membership information filtering. We study some fundamental properties of the set-membership information filter with multiple sensor measure-ments. First, a sufficient condition is derived for the set-membership information filter, under which the boundedness of the outer ellipsoidal approximation set of the estimation means is guaranteed. Second, the equivalence property between the parallel and sequential versions of the set-membership information filter is presented. Finally, the results are applied to a 1D event-triggered target tracking scenario in which the negative information is exploited in the sense that the measurements that do not satisfy the triggering conditions are modelled as set-membership mea-surements. The tracking performance of the proposed method is validated with extensive Monte Carlo simulations.     

基于高斯混合概率假设密度滤波的扫描型光学传感器像平面多目标跟踪算法

高斯混合概率假设密度(GM-PHD)滤波是一种基于随机有限集理论的次优贝叶斯多目标跟踪方法,本文研究了该算法在扫描型光学传感器像平面的多目标跟踪问题.针对典型的锥扫模式和推扫模式,根据其扫描特性建立目标的运动模型和测量模型.介绍高斯混合概率假设密度滤波的基本原理.针对原算法在强杂波环境中的低效率问题,借鉴传统多目标跟踪...     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

混合线性/非线性模型的准高斯Rao-Blackwellized粒子滤波法

 针对混合线性/非线性模型,提出一种新的递推估计滤波算法,称为准高斯Rao-Blackwellized粒子滤波器（Q-GRBPF）。算法采用Rao-Blackwellized思想,将线性状态与非线性状态进行分离,对非线性状态运用准高斯粒子滤波（Q-GPF）算法进行估计,并将其后验分布近似为单个高斯分布,再利用非线性状态的估计值对线性状态进行卡尔曼滤波（KF）估计。将Q-GRBPF应用于目标跟踪的仿真结果表明,与Rao-Blackwellized粒子滤波器（RBPF）相比,Q-GRBPF在保证估计精度的前提下有效降低了计算复杂度,计算时间约为RBPF的58%;与Q-GPF相比,x坐标与y坐标的估计精度分别提升了45％和30％,而计算时间也节省了约30％。     

Transient Response of Tracking Filters with Randomly Interrupted Data

The transient responses during the initialization phase of a first-order ?-? tracking filter and a second-order Kalman filter are evaluated as a function of radar measurement accuracy and the probability of receiving valid data at the prescribed intervals. Monte Carlo simulation results are complemented by analysis of the filtering processes and curves are presented which clearly define the deterioration in filter performance attributable to reduced probabilities of data acquisition. In addition, the responses of ?-? and Kalman filters are shown to be identical when the ?, ? gains are selected optimally.