  We study the phenomenon of loss of lock in the optimal non-causal phase
estimation problem, a benchmark problem in nonlinear estimation. Our method is
based on the computation of the asymptotic distribution of the optimal
estimation error in case the number of trajectories in the optimization problem
is finite. The computation is based directly on the minimum noise energy
optimality criterion rather than on state equations of the error, as is the
usual case in the literature. The results include an asymptotic computation of
the mean time to lose lock (MTLL) in the optimal smoother. We show that the
MTLL in the first and second order smoothers is significantly longer than that
in the causal extended Kalman filter.
