Deterministic asymptotic Cramér-Rao bound for the multidimensional harmonic model

  • Authors:
  • Rémy Boyer

  • Affiliations:
  • Laboratoire des Signaux et Systemes, CNRS - Université Paris-Sud - Supélec, 3, rue Joliot-Curie, 91190 Gif-sur-Yvette, France

  • Venue:
  • Signal Processing
  • Year:
  • 2008

Quantified Score

Hi-index 0.08

Visualization

Abstract

The harmonic model sampled on a P-dimensional grid contaminated by an additive white Gaussian noise has attracted considerable attention with a variety of applications. This model has a natural interpretation in a P-order tensorial framework and an important question is to evaluate the theoretical lowest variance on the model parameter (angular-frequency, real amplitude and initial phase) estimation. A standard Mathematical tool to tackle this question is the Cramer-Rao bound (CRB) which is a lower bound on the variance of an unbiased estimator, based on Fisher information. So, the aim of this work is to derive and analyze closed-form expressions of the deterministic asymptotic CRB associated with the M-order harmonic model of dimension P with P1. In particular, we analyze this bound with respect to the variation of parameter P.