Maximum-Likelihood Estimation of a Process with Random Transitions (Failures)

Bernard Friedland

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A process with random transitions is represented by the difference equation xn= xn-1 + Un where Unis a nonlinear function of a Gaussian sequence wn• The nonlinear function has a threshold such that Un= 0 for |Wn|<W. This results in a finite probability of no failure at every step. Maximum likelihood estimation of the sequence Xn = {x0., xn} given a sequence of observations Yn = {y1.,yn } 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.

Original languageEnglish (US)
Pages (from-to)932-937
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Dec 1979
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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