Performance Optimization via Sequential Processing for Nonlinear State Estimation of Noisy Systems

Abstract

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. This framework comes out from the combination of a state norm estimator with a chain of filters, adaptively tuned by the state norm estimator. The state estimate is sequentially processed through the chain of filters. Each filter contributes to improving, by a certain amount, the estimation error performances of the previous filter in terms of noise sensitivity, and this amount is quantitatively evaluated using a comparison criterion, which considers the ratio of the asymptotic error norm bounds of two consecutive filters in the chain. A recursive algorithm is given for implementing the chain of filters and guaranteeing a sequential error performance optimization process. Simulations show the effectiveness of these chains of filters.