Mixed H2/H-infinity Approach to Robust Estimation and Adaptive Filtering

小行星9529325 该项目有两个不同但相关的目标。 第一个是混合H-2/H-inf控制和估计问题的研究;第二个是开发新的软件，使研究生和研究人员能够运行现实的项目，这些项目将要求他们综合统计信号处理和数值分析不同领域的知识。 经典的H-2方法（如维纳滤波和卡尔曼滤波）需要外生信号的二阶统计量的知识，并产生具有最佳平均性能的估计器。另一方面，最近的H-inf（或所谓的极大极小）估计方法不需要外生信号的统计知识，并产生保守的解决方案。 该方案的主要目标是：（1）尽可能完整地发展混合H-2/H-inf问题解的解析表征;（2）全面理解平均性能和最坏性能之间的权衡;（3）寻求最优性能的递归实现;（4）提供有效的数值算法。 ***

9529325 Kailath The project has two different but related objectives. The first is the study of mixed H-2/H-inf control and estimation problems; the second is to develop new software that will enable graduate students and researchers to run realistic projects that will call upon them to synthesize knowledge from different areas of statistical signal processing and numerical analysis. Classical H-2 methods (such as Wiener filtering and Kalman filtering) require knowledge of second-order statistics of the exogeneous signals and yield estimators that have best average performance. On the other hand, the more recent H-inf (or so called minimax) estimation methods require no statistical knowledge of the exogeneous signals and yield conservative solutions. The major goals of this proposal are (1) to develop, as completely as possible, an analytical characterization of the solution of mixed H-2/H-inf problem, (2) to obtain a through understanding of the tradeoffs between the average and worst-case performances, (3) to seek recursive implementations of the optimal, (4) to provide efficient numerical algorithms. ***