Maximum-likelihood estimation and optimal filtering in the nondirectional, one-dimensional binomial germ-grain model

摘要

The one-dimensional binomial germ–grain model is a random process where discrete random-length intervals are placed at discrete random points on the line. Each line segment has a designated center which is aligned with outcomes of the point process to form coverings of the discrete line. In the directional model, the center is placed at the left-hand endpoint of the random segments. In the continuous case, the same coverage process is produced no matter where grain centers are chosen, but in the discrete case, the coverage process is different when different centers are used. This paper provides a general formulation and analysis of the nondirectional discrete one-dimensional binomial germ–grain model. It derives probabilities of a set of fundamental covering events used in coverage analysis, provides analytic formulation for the windowed optimal nonlinear filter for the signal-union-noise model, and characterizes parametric maximum-likelihood estimation of distributions governing grains in the nondirectional discrete model.