Theory of generalized particle filtering

在过去的十年里，粒子过滤凭借其处理由动态系统建模的数据的能力，在工程师和科学家中引起了惊人的兴趣。这些方法属于顺序信号处理的程序家族，其目标是从可用观测中过滤、预测或平滑未知和时变的信号。这项研究的总体工作领域是建立一类新的粒子过滤器，发展它们的理论，并将它们应用于一些重要的任务。已知的粒子滤波方法需要系统动力学的数学表示和关于状态转移概率分布函数的假设，以及状态的可能性。这些概率假设往往是不准确的，出于方便，在许多情况下会导致粒子过滤器性能的严重下降。我们开发了一类更一般的粒子过滤器，它不使用概率模型假设。取而代之的是，新的过滤器基于颗粒流和相关成本定义的离散测量，这些成本是按顺序更新的。随着理论的发展，我们能够制造出比传统的粒子过滤器更简单、更准确、更健壮、更灵活的粒子过滤器。然而，标准粒子滤镜是新滤镜的特殊实例。我们详细地研究了各种重要的问题，包括新滤波器的基础，它们的收敛，新理论与现有理论的联系，以及它对批处理类型信号处理的扩展。这些过滤器在各种具有挑战性的问题上进行了测试。

In the past decade, particle filtering has generated astounding interest among engineers and scientists with its capacity to process data that are modeled by dynamic systems. These methods belong to the family of procedures for sequential signal processing where the objectives are to filter, predict, or smooth unknown and time-varying signals from available observations. The general area of work in this research effort is the building of a new class of particle filters, the development of their theory, and their application to a number of important tasks.The known particle filtering methods require a mathematical representation of the system dynamics and assumptions about the state transition probability distribution function, and the likelihood of the states. These probabilistic assumptions are often inaccurate and made out of convenience, and in many cases lead to formidable degradations in performance of the particle filters. We develop a more general class of particle filters which do not use probabilistic model assumptions. Instead, the new filters are based on discrete measures defined by particle streams and associated costs that are sequentially updated. With the developed theory, we are able to build particle filters that are simpler, more accurate, more robust, and more flexible than the conventional ones. The standard particle filters, however, are particular instances of the new filters. We investigate in great detail various important issues including the foundations of the new filters, their convergence, connections of the new theory with existing theories, and its extensions to batch type signal processing. The filters are tested on various challenging problems.