Loss of Lock in Minimum Noise Energy Phase Estimators

We give a positive answer to the classical question of whether phase estimators of different types, slip cycles. We develop a small noise analysis for the calculation of the mean time to lose lock (MTLL) of the minimum noise energy (MNE) filter and find that this MTLL is much longer than in other conventional phase estimators. The MNE criterion in filtering, in contrast to the minimal mean square estimation error (MSEE) criterion, bypasses Zakai¿s equation and stochastic differential equations that approximate the optimal estimator. We find that in the limit of small noise there is a huge gap between the MTLL of the MNE filter and the MTLL of existing phase estimators, such as the extended Kalman filter (EKF), other phase locked loops (PLL), and particle filters. It follows that the performance threshold of existing phase estimators can be considerably extended. We estimate the tradeoff between the complexity of the implementation of realizable MNE filters and the degradation of their MTLL relative to the true one.