Hybrid H2/H∞ estimation for phase-locked loop filter design

A method of combining Kalman filtering and minimax filtering is proposed and demonstrated in an application to phase-locked loop design. Kalman filtering suffers from a lack of robustness to departures from the assumed noise statistics. But minimax filtering has the drawback of ignoring the engineer´s (admittedly incomplete) knowledge of the noise statistics. It is shown in this paper that hybrid Kalman/minimax filtering can provide the best of both worlds. Phase-locked loop filter design is used in this paper to demonstrate an application of hybrid estimation.