Set membership state and parameter estimation for nonlinear differential equations with sparse discrete measurements

Abstract

This paper presents a method to perform parameter and state estimation in a bounded-error context for nonlinear continuous-time systems with sparse, discrete measurements. Direct application of a guaranteed parameter estimation method can be fruitless when few data measurements are available. This lack of measurements results in what we term “phantom” sets of parameter values that cannot be correctly discarded due to instability in the estimation method caused by the lack of information. Preprocessing the measurements through the addition of application specific stabilizing bounds vastly improves bounded parameter and state estimations. Comparisons between applying guaranteed estimation methods to raw and preprocessed data measurements are illustrated with an example application.