The exit problem in optimal non-causal extimation

TL;DR

This paper investigates the loss of lock in optimal non-causal phase estimation, providing an asymptotic analysis of the mean time to lose lock and comparing it with causal methods, highlighting improved performance.

Contribution

It introduces a novel asymptotic approach to compute the distribution of estimation error and MTLL in non-causal smoothers, based on minimum noise energy criteria.

Findings

MTLL in non-causal smoothers exceeds that of causal Kalman filters.

The method directly uses noise energy optimality, avoiding state equations.

Results demonstrate significant performance improvements in lock retention.

Abstract

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.