Time-delay estimation for filtered Poisson processes using anEM-type algorithm
Antoniadis, N.; Hero, A.O.
Signal Processing, IEEE Transactions on
Volume 42, Issue 8, Aug 1994 Page(s):2112 - 2123
Digital Object Identifier 10.1109/78.301846
Summary:We develop a modified EM algorithm to estimate a nonrandom time
shift parameter of an intensity associated with an inhomogeneous Poisson
process Nt, whose points are only partially observed as a
noise-contaminated output X of a linear time-invariant filter excited by
a train of delta functions, a filtered Poisson process. The exact EM
algorithm for computing the maximum likelihood time shift estimate
generates a sequence of estimates each of which attempt to maximize a
measure of similarity between the assumed shifted intensity and the
conditional mean estimate of the Poisson increment dNt. We
modify the EM algorithm by using a linear approximation to this
conditional mean estimate. The asymptotic performance of the modified EM
algorithm is investigated by an asymptotic estimator consistency
analysis. We present simulation results that show that the linearized EM
algorithm converges rapidly and achieves an improvement over
conventional time-delay estimation methods, such as linear matched
filtering and leading edge thresholding. In these simulations our
algorithm gives estimates of time delay whose mean square error
virtually achieves the CR lower bound for high count rates
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