Estimation of sensor input signals that are neither bandlimited nor sparse

Abstract

The paper addresses the estimation of the continuous-time input signal to a linear sensor that is given in state-space form. In previous work, Bolliger et al. proposed to model the input signal as (continuous-time) white Gaussian noise and derived a corresponding estimator that is based on Kalman filtering. The present paper elaborates on this new estimator. In particular, it establishes the continuity (or the piecewise continuity) of the estimate, presents a new interpolation formula between samples, complements the Kalman-filter perspective by a Wiener-filter perspective, and demonstrates practicality by numerical experiments.