Kalman vs H∞ filter in terms of convergence and accuracy: Application to carrier frequency offset estimation

H_∞ filtering is more and more used in the field of recursive estimation in signal processing. The purpose of this communication is to compare Kalman filtering and H_∞ filtering by considering their Ricatti-type equations. Our contribution is twofold: firstly, we show that the H_∞ filter can be seen as a Kalman filter with a model-noise covariance matrix that depends on the noise attenuation level and varies in time. Hence, this can explain the convergence properties of the H_∞ filter when estimating parameters. The convergence and accuracy properties of both Kalman and H_∞ filters are then illustrated by the estimation of a carrier frequency offset in a mobile communication system.