Robust filtering for joint state-parameter estimation in distributed mechanical systems

Abstract

We present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an H ∞ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinitedimensional mechanical system, the H ∞ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment – using a test problem inspired from cardiac biomechanics – demonstrates the effectiveness of our approach.