Sequential Monte Carlo Smoothing with Finite Set Statistics

有限集统计的顺序蒙特卡罗平滑

• 批准号: EP/H010866/1
• 负责人: Daniel Clark
• 金额: $ 12.95万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH010866%2F1
• 关键词: Sequential; Monte; Carlo; Smoothing; Finite

There has been considerable interest in stochastic filtering and smoothing in the last half-century, motivated by the discovery in 1960 of the solution to the linear filtering problemby Kalman. Applications of this work were found almost immediately through the incorporation into NASA's Apollo navigation computer for trajectory estimation. The importance of Kalman's discovery is illustrated by the the impact it has had in control theory, probability theory, financial mathematics, and signal processing. Since the 1960's, soon after the solutions to various filtering problems came corresponding solutions to the smoothing problems. More recent work on non-linear filtering and smoothing has been inspired by sequential Monte Carlo theory.Stochastic filtering, prediction, and smoothing are fundamental concepts in the theory of estimation of dynamic systems. The system is a partially observed physical object whose behaviour over time is governed by a set of equations modelling the dynamics and the relationship between the observations and the object state. Uncertainty in the system is due to the noisy nature of the problem, either from unknown and unpredictable motion of the system, or from inaccuracy in observing measurements of the system through a noisy sensor. Filtering, prediction and smoothing are precise mathematical descriptionsof the problem of estimating the state of the system based on noisy observations of its behaviour over time: Prediction is the forecasting of the state of the system at some future point in time based on measurements up to the current time. Filtering is the estimation at each point in time of the state of the system based on all of the measurements up to that point. Typically prediction and filtering are used together to form a set of recursive equations for predicting and updating the estimate of the state of a system. Smoothing differs from prediction and filtering in that the estimate of the state of the system at a specific point in time can be determined from a batch of measurements, some of which may be collected later than the time that we are interested in. This means that there is inevitably a delay in producing the estimate of the state at that time, though more accurate estimates can be obtained since more information is available about the system.Despite the wealth of research in single-object filtering, a mathematically principled generalisation of filtering concepts to multi-object systems is a recent development, formulated in the framework of Finite Set Statistics (FISST) motivated by the problem of multiple-target tracking in aerospace applications. The purpose of multiple target tracking algorithms is to detect, track and identify targets from sequences of noisy observations of the targets provided by one or more sensors. This problem is complicated by the fact that these observations tend to have many false alarms and targets may not always give rise to observations. The extension from a single-target scenario to a multiple-target environment is non-trivial since the number of targets may not be known and varies with time, there are missed detections where the target is not observed and observations may be false alarms due to clutter. In addition, the identities of the targets may need to be known to determine their trajectories. This work will develop new methodologies for smoothing of multi-object systems. This work proposed here aims to investigate multi-object smoothers for jointly estimating the number of objects and their state vectors in environments where there can be many false alarms and the targets are not always observed. Solutions to this problem could lead the way to practical implementations using sequential Monte Carlo approximations. The successful solution to this problem would be directly applicable to a range of industrial multi-sensor multi-target tracking problems in many sensor applications including radar, electro-optics and sonar.

在过去的半个世纪里，由于卡尔曼在1960年发现了线性滤波问题的解决方案，人们对随机滤波和平滑产生了相当大的兴趣。这项工作的应用几乎立即被发现，通过纳入美国宇航局的阿波罗导航计算机的轨迹估计。卡尔曼发现的重要性可以通过它在控制论、概率论、金融数学和信号处理中的影响来说明。自20世纪60年代以来，在各种滤波问题的解决方案之后不久，就出现了相应的平滑问题的解决方案。最近的非线性滤波和平滑的工作受到序贯蒙特卡罗理论的启发。随机滤波、预测和平滑是动态系统估计理论中的基本概念。该系统是一个部分观测的物理对象，其行为随时间的推移是由一组方程建模的动态和观测和对象状态之间的关系。系统中的不确定性是由于问题的噪声性质，或者来自系统的未知和不可预测的运动，或者来自通过噪声传感器观察系统的测量的不准确性。滤波、预测和平滑是基于对系统随时间变化的行为的噪声观测来估计系统状态的问题的精确数学解释：预测是基于到当前时间的测量来预测系统在未来某个时间点的状态。滤波是基于直到该点的所有测量在每个时间点估计系统的状态。通常，预测和滤波一起使用以形成用于预测和更新系统的状态的估计的递归方程组。平滑与预测和滤波的不同之处在于，可以根据一批测量值来确定特定时间点系统状态的估计，其中一些测量值可能是在我们感兴趣的时间之后收集的。这意味着在产生当时状态的估计时不可避免地存在延迟，尽管可以获得更准确的估计，因为可以获得关于系统的更多信息。尽管在单对象滤波方面有大量的研究，但将滤波概念数学上原则性地推广到多对象系统是最近的发展，在有限集统计（FISST）的框架内制定的多目标跟踪在航空航天应用中的问题的动机。多目标跟踪算法的目的是从由一个或多个传感器提供的目标的噪声观测序列中检测、跟踪和识别目标。这个问题是复杂的事实，这些观察往往有许多假警报和目标可能并不总是引起观察。从单目标场景到多目标环境的扩展是不平凡的，因为目标的数量可能是未知的并且随时间变化，存在未观测到目标的漏检测，并且观测可能是由于杂波引起的假警报。此外，可能需要知道目标的身份以确定其轨迹。这项工作将开发新的方法来平滑多目标系统。这里提出的这项工作的目的是研究多对象平滑器，用于联合估计的对象和它们的状态向量的数量在环境中，可能有许多虚警和目标并不总是观察到。这个问题的解决方案可能会导致实际的实施方式，使用顺序蒙特卡罗近似。该问题的成功解决方案将直接适用于许多传感器应用（包括雷达、光电和声纳）中的一系列工业多传感器多目标跟踪问题。

项目成果

On the ordering of the sensors in the iterated-corrector probability hypothesis density (PHD) filter

• DOI: 10.1117/12.884618
• 发表时间: 2011-05
• 作者: S. Nagappa;Daniel E. Clark

Adaptive Target Birth Intensity for PHD and CPHD Filters

• DOI: 10.1109/taes.2012.6178085
• 发表时间: 2012-04-01
• 期刊: IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
• 影响因子: 4.4
• 作者: Ristic, B.;Clark, D.;Vo, Ba-Tuong
• 通讯作者: Vo, Ba-Tuong

A Tractable Forward- Backward CPHD Smoother

• DOI: 10.1109/taes.2017.2649978
• 发表时间: 2017-02-01
• 期刊: IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
• 影响因子: 4.4
• 作者: Nagappa, Sharad;Delande, Emmanuel D.;Houssineau, Jeremie
• 通讯作者: Houssineau, Jeremie

Fast sequential Monte Carlo PHD smoothing

• 发表时间: 2011-07
• 期刊: 14th International Conference on Information Fusion
• 作者: S. Nagappa;Daniel E. Clark

Incorporating track uncertainty into the OSPA metric

• 发表时间: 2011-07
• 期刊: 14th International Conference on Information Fusion
• 作者: S. Nagappa;Daniel E. Clark;R. Mahler