Loss of Lock and Steady-State Errors In a non Causal Phase Estimator
A study of rare events in optimal smoothing
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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 resul...
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.
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