摘要：本文梳理了粒子滤波理论基本内容、发展脉络和最新研究进展，特别是对其在多目标跟踪应用中的一系列难点问题与主流解决思路进行了详细分析和报道。常规粒子滤波研究重点主要围绕重要性采样函数、计算效率、权值退化/样本匮乏和复杂系统建模展开。作为一类复杂估计问题，多目标跟踪一方面需要准确的目标新生/消亡与演变、虚警/漏检等建模技术，另一方面需要多传感器信息融合、航迹管理等复杂决策方法。暨有限集统计学应用于多目标跟踪后，粒子滤波进入一个新的发展阶段——随机集粒子滤波。基于不同的背景假设，可以构建不同近似形式的随机集贝叶斯滤波器并采用粒子滤波实现。但机动目标、未知场景、多目标航迹管理以及跟踪性能评价等仍是多目标粒子滤波的研究难点和重点。

Abstract:This paper reviews thetheory and state-of-the-art developments of the particle filter with emphasison the remaining challenges and corresponding solutions in the context ofmultitarget tracking. The research focuses of the general particle filter lieon importance proposal, computing efficiency, weight degeneracy, sample impoverishment, and complicated system modelling. Multi-target tracking involves a class of complex dynamic estimation problems that require both accuratemodels for target birth, death and evolution, false alarms and miss-detections,and efficient decision-making strategies regarding multi-sensor data fusion andtrack management. Specifically, with the introduction of finite set statisticsto multi-target tracking, recent years have seen the burgeoning development ofa new generation of particle filters, which is referred to as the random setparticle filter in this paper. Based on different scenario assumptions,different approximate forms of random set Bayesian filters can be establishedand implemented by the particle filter. However, manoeuvring target, unknownscenario, track management and tracker performance assessment remain keychallenges for the multi-target tracking particle filter.

引言

通过对某一随机变量的观测，对这一随机变量或者与之关联的另一随机变量进行状态估计(即“滤波”），是信号处理研究的核心问题之一，其广泛存在于航天航空、电子信息、控制工程以及机器人等科学、技术领域。贝叶斯估计是解决这类问题最为重要的基本理论工具之一，也是粒子滤波的理论基础，其采用一簇加权的样本(称为“粒子”)来近似表示状态变量的概率分布，通过粒子群迭代更新实现递归贝叶斯估计。自Bootstrap滤波器的出现，粒子滤波(Particle Filter, PF)迅速成为一种重要的非线性递归贝叶斯滤波方法。相比于卡尔曼滤波器(最小均方误差估计器)和H∞滤波器(最差情况下估计误差最小化)等，粒子滤波对系统要求达到最低(既不需要系统模型方程为线性，也不需要系统噪声为高斯分布)，具有更好的算法可扩展性和普适性。然而，虽然经历二十余年的发展，粒子滤波仍然存在一些理论、方法上的缺陷和实现上的挑战，特别是复杂条件下的多目标跟踪对滤波估计提出了更高的要求。

当前，多目标跟踪具有广泛的军事和民用背景，是状态估计最具代表性的一类问题，也是先进滤波理论和方法最为活跃的应用对象之一。多目标跟踪问题的复杂性、重要性以及相关理论、技术发展也推动了滤波理论、技术和方法的进步。特别是近年来，随着有限集统计学(Finite Set Statistics，FISST)应用于多目标跟踪问题，粒子滤波进入了一个新的发展阶段，本文称之为随机集粒子滤波，成为当前的研究热点。然而，多目标跟踪粒子滤波仍然面临诸如不确定性表示、机动目标、未知场景、传感信息融合、航迹管理以及性能评价一系列的难点和挑战，这些仍需要更先进的滤波理论与方法。

粒子滤波的广泛应用和不断发展也促生了一些重要的研究综述、报告、编著等(见文中表1)，详细地反映了粒子滤波的阶段性发展或者在某一领域的应用概况。然而系统归纳和分析粒子滤波算法从单目标跟踪到多目标跟踪应用的发展脉络和研究分支的文献综述目前尚还缺失。因此，本文对已有综述内容不做重述，而是特别强调以下两个方面：(一) 围绕目标跟踪这一统一研究主题，梳理从常规粒子滤波到随机集粒子滤波的完整发展脉络、算法重难点以及前后联系；(二) 细致回顾和分析单/多目标跟踪粒子滤波最新研究进展、仍面临的挑战以及主要解决思路，着重分析随机集粒子滤波算法重难点，并进而指出今后的发展趋势和研究要点。

    表1     近十年来粒子滤波部分综述与专著

本文章节安排如下：第2、3节阐述用于单目标跟踪的常规粒子滤波基本原理、方法、所存在的问题与主要解决思路。第4节阐述多目标跟踪粒子滤波主要思路、方法和最新研究进展，重点是随机集粒子滤波。第5节介绍多目标跟踪问题的难点与挑战，强调随机集粒子滤波依赖的重要支撑技术。第6节总结全文并简单展望。

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粒子滤波理论、方法及其在多目标跟踪中的应用(re).pdf

勘误：第1989和1992页的参考文献 [82]应该为[81]!!

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