Timing estimation for a filtered Poisson process in Gaussian noise
Hero, A.O., III
Information Theory, IEEE Transactions on
Volume 37, Issue 1, Jan 1991 Page(s):92 - 106
Digital Object Identifier 10.1109/18.61107
Summary:The problem of estimation of time shift of an inhomogeneous
casually filtered Poisson process in the presence of additive Gaussian
noise is discussed. Approximate expressions for the likelihood function,
the MAP estimator, and the MMSE estimator that becomes increasingly
accurate as the per-unit-time density of superimposed filter responses
becomes small are obtained. The optimal MAP estimator takes the form of
a cascade of linear and memoryless nonlinear components. For smooth
point process intensities, the performance of the MAP estimator is
studied via local bias and local variance. A rate distortion type lower
bound on the MSE of any estimator of time delay is then derived by
identification of a communications channel that accounts for the mapping
from time delay to observation process. Results of numerical studies of
estimator performance are presented. Based on the examples considered it
is concluded: (1) the small-error MSE of the nonlinear MAP estimator can
be significantly better than the small-error MSE of the optimal linear
estimator: (2) the rate distortion lower bound can be significantly
tighter than the Poisson limited bounds determined in previous studies
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