Efficient Algorithms and Structures for Robust Signal Processing

摘要

The research efforts supported by AFOSR Grant AFOSR-84-0381 were directed towards development and analysis of robust estimation techniques for autoregressive (AR) and autoregressive-moving average (ARMA) models. Work on related system theoretic problems associated with parameter estimation problems for times series models and on square-root filtering for least squares state estimation applications was also carried out. Finally, an adaptive estimation technique for a class of piecewise (in time) stationary signals was developed. The motivation for our research arises from applications in signal processing including linear predictive singal modeling, signal detection, dynamic state estimation (Kalman filtering), and spectral analysis. The general goal of this research has been to put together ideas and techniques from statistics, signal processing, and system theory to bring new perspectives to such problems. Our research on various autoregressive modeling problems resulted from a desire to relax some of the assumptions made by previous researchers, in order to broaden the domain of application of the basic technique which has proved to be useful in a range of signal processing tasks. In particular, our efforts have been directed at the goal of obtaining allowing robust estimates in the presence of outliers in the observed signal and in modeling of signals whose spectral characteristics change abruptly from time to time.