The phenomenon of loss of lock in tracking systems is ubiquitous in engineering practice. However, the key problem of loss of lock in non-causal estimation or smoothing is a marked exception in this well researched area. The methods that were developed for the treatment of the former are not suitable for the analysis of the latter problem. The main purpose of this research is to provide the missing theory and investigate the phenomenon of loss of lock in smoothers. We concentrate in this dissertation on the carrier phase estimation problem, a benchmark problem in nonlinear estimation.Our results include an asymptotic computation of the mean time to lose lock (MTLL) in the optimal minimum noise energy (MNE) smoother. We show that the MTLL in the first and second order smoother is significantly longer than that in the causal phase locked loop(PLL). We give a complete description of the steady state error regime in linear and nonlinear smoothers, in case the inputs are polynomial in time. We show that the steady-state error in the optimal smoother is significantly smaller than that in the optimal filter.

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