Maximum-likelihood estimation of a process with random transitions (failures)

Author

Friedland, Bernard

Author_Institution

Singer Company, Little Falls, NJ, USA

Volume

24

Issue

6

fYear

1979

fDate

12/1/1979 12:00:00 AM

Firstpage

932

Lastpage

937

Abstract

A process with random transitions is represented by the difference equation $x_{n} = x_{n-1}+ u_{n}$ where unis a nonlinear function of a Gaussian sequence w_{n}. The nonlinear function has a threshold such that $u_{n} =0$ for $|w_{n}| \\leq W$ . This results in a finite probability of no failure at every step. Maximum likelihood estimation of the sequence $X_{n}={x_{0},...,x_{n}}$ given a sequence of observations $Y_{n} = { y_{1},...,y_{n} }$ gives rise to a two-point boundary value (TPBV) problem, the solution of which is suggested by the analogy with a nonlinear electrical ladder network. Examples comparing the nonlinear filter that gives an approximate solution of the TPBV problem with a linear recursive filter are given, and show the advantages of the former. Directions for further investigation of the method are indicated.

Keywords

Fault diagnosis; Stochastic processes; maximum-likelihood (ML) estimation; Application software; Computer network reliability; Difference equations; Differential equations; Filtering; Hardware; Maximum likelihood estimation; Nonlinear filters; Polynomials; Random variables;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1979.1102188

Filename

1102188