Estimação de estados com restrições para sistemas dinâmicos lineares e não-lineares

Abstract

State estimators have been applied to disparate fields, such as in aerospace engineering, econometrics, and geophysics, to infer unobserved variables (states and, occasionally, parameters) of a dynamic system providing two uncertain sources of information, namely, the measurements and a mathematical model. Under linear model and Gaussian noise assumptions, the Kalman Filter is the well-known optimal recursive solution for the state-estimation problem, whereas the extended Kalman filter and, more recently, the unscented Kalman filter are the most commonly employed approximate solutions for the nonlinear case. In practice, however, additional information about the system may be available, and this third source of information may be useful for improving state estimates. A scenario we have in mind is the case in which the dynamics and the disturbances are such that the state vector of the system satisfies an assumed known equality or inequality constraint. Constrained state estimation has been receiving increasing attention in both academia and industry, especially in the last ten years. In addition to providing a wide overview of the current state of the art in constrained state estimation, the present work is concerned with the development of Kalman filtering methods for enforcing an equality constraint or inequality constraint on the state estimate. Both linear and nonlinear cases are considered. For the latter, algorithms based on the unscented Kalman filter are proposed. Furthermore, we also present a general framework for state estimation with an equality constraint on the estimator gain, aiming at indirectly enforcing special properties on the state estimate. Simulated and experimental examples are used to illustrate the applications of the algorithms studied and presented along this thesis.