Cooperative Approaches to Design of Nonlinear Filters

本课题研究基于噪声测量的（非线性）离散随机动力系统的状态估计。状态估计在许多需要系统状态知识的应用中起着关键作用，例如（多步骤）预测、控制、故障检测或通常用于决策制定。导航、跟踪、定位和最优控制等重要应用可以在机器人和自动化领域找到。在过去的几十年里，非线性滤波器的设计在文献中引起了极大的关注，并且提出了许多在假设、估计质量、效率和目的上不同的（近似）滤波方法。绝大多数提出的过滤器都不是最优的；因此，它是为特定的环境量身定制的。因此，为应用程序选择合适的过滤器是一项具有挑战性的任务。通常，必须进行大量的模拟，其中不同的非线性滤波器相互竞争。这个项目的目标是将非线性滤波器的竞争使用转变为合作方法。特别是，重点放在设计一个总体框架的概念上新的合作方法非线性滤波器的设计。这种方法在某种意义上利用了各种非线性-通常是近似-滤波器的互补特性的组合。本项目分析了局部滤波器的四种可能的合作行为（集成、监控、组合和反馈），并开发了相应的算法。在滤波器设计中同时使用多种合作类型，可以得到一个全局合作滤波器。与竞争激烈的传统滤波器设计相比，协同全局滤波器将提供在准确性、可信度和完整性方面具有更高估计质量的估计。

This project is devoted to the state estimation of (nonlinear) discrete-time stochastic dynamic systems based on noisy measurements. State estimation plays a key role in many applications where the knowledge of a system state is required for, e.g., (multistep) prediction, control, fault detection, or generally for a decision making. Important applications such as navigation, tracking, localization, and optimal control can be found in the areas of robotics and automation.In the past decades, the design of nonlinear filters has attracted a significant attention in literature and many (approximate) filtering approaches differing in assumptions, estimation quality, efficiency, and purpose have been proposed. The vast majority of the proposed filters are not optimal; and hence, tailored to specific settings. As a consequence, it is a challenging task to select an appropriate filter for an application. Typically, extensive simulations have to be performed in which different nonlinear filters compete against each other.The objective of this project is to shift from a competitive use of nonlinear filters to a cooperative approach. In particular, the stress is laid on the design of a general framework for a conceptually new cooperative approach to nonlinear filter design. This approach takes an advantage of a combination of, in some sense, complementary properties of various nonlinear - usually approximate - filters. The project analyzes four types of possible cooperative behavior of local filters (integration, monitoring, combination, and feedback) and develops respective algorithms. Using several cooperation types in filter design simultaneously leads to a cooperative global filter. Compared to the traditional filter design, which is rather competitive, the cooperative global filter will provide estimates with generally higher estimation quality in terms of accuracy, credibility, and integrity.