Posterior Cramer-Rao bounds for discrete-time nonlinear filtering
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A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality and is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems.Abstract:
A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.read more
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Single tone parameter estimation from discrete-time observations
D. Rife,R. Boorstyn +1 more
TL;DR: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed and appropriate Cramer-Rao bounds and maximum-likelihood estimation algorithms are derived.