Report Number: CSL-TR-93-560
Institution: Stanford University, Computer Systems Laboratory
Title: The Cramer Rao Bound for Discrete-Time Edge Position
Author: Gatherer, Alan
Date: February 1993
Abstract: The problem of estimating the position of an edge from a series of samples often occurs in the fields of machine vision and signal processing. It is therefore of interest to assess the accuracy of any estimation algorithm. Previous work in this area has produced bounds for the continuous time estimator. In this paper we derive a closed form for the minimum variance bound (or Cramer Rao bound) for estimating the position of an arbitrarily shaped edge in white Gaussian noise for the discrete samples case. We quantify the effects of the sampling rate, the bandwidth of the edge, the shape of the edge and the size of the observation window on the variance of the estimator. We describe a maximum likelihood estimator and show that in practice this estimator requires fewer computations than standard correlation.
http://i.stanford.edu/pub/cstr/reports/csl/tr/93/560/CSL-TR-93-560.pdf