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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.
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.