Recursive Estimation of Driving-Forces from Nonlinear Nonstationary Systems with Unknown Dynamics

Abstract

<p> We address a functional analysis-based method for the estimation of driving-forces from nonlinear dynamic systems in this thesis. The driving-forces account for the perturbation inputs or the irregular variations in the internal variables of a dynamic system. These inputs are hidden from the observer most of the time if not always. Reconstruction of such inputs when there is too little or no prior knowledge to build a mathematical model to describe the system's behavior is an important problem in many cases in physics and engineering. To this end, we propose a method for the recursive estimation of driving-forces without the availability of an analytic model of the unknown physical phenomenon. </p> <p> The underlying idea of the proposed estimator is to predict the observables onestep ahead of the current time instant, and then retrieve the driving-force from the prediction error. This idea is embodied by predicting the observables using a bank of echo state networks (ESN) in an online fashion, extracting the raw estimates from the prediction error, and then finally smoothing these estimates in separate adaptive filtering stages. The approach described herein distinguishes itself from the similar methods in the literature in its adaptivity and its greater immunity against varying environmental uncertainties. The adaptive nature of the estimator enables us to retrieve both slowly and rapidly varying driving-forces accurately in presence of model or sensor noises, which are illustrated by experiments in the subsequent chapters of this thesis. In particular, some chaotic/stochastic nonlinear models are studied in controlled experiments. The estimation quality of the proposed approach is judged with a reference to the Posterior Cramer-Rao Lower Bound as a theoretical lower limit on the estimation error. </p> <p> The Bayesian and Maximum-Likelihood (ML) methods are also studied for the estimation of driving-forces when partial or full information is available on the mathematical description of the unknown system. These methods serve as practical merits of assessment for the proposed driving-force estimator. Moreover, a direct performance comparison between the proposed estimator and a favorable estimation scheme of a similar kind is provided, which confirms the advantages of the proposed approach. The proposed method is tested on a real-world application on the extraction of sun's magnetic flux from the sunspot time series. It is illustrated that the results obtained by the proposed estimator are in close agreement with the results of two other analytical studies. </p> <p> Finally, a solution to a real problem in practice is proposed using the method. Specifically, extracting the signature of a small random target embedded in the sea surface is addressed using the live recorded data collected with the McMaster IPIX radar. This is the first specific realization of a radar scene analyzer for the cognitive radar reception in the literature to the author's best knowledge. </p> <p> The material in this thesis is presented in a sandwich thesis format, combining two peer reviewed, published journal articles, and another journal article that is prepared for submission. An additional chapter that provides the background material is included for the completeness of the presentation. </p>