## Abstract

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 language | English (US) |
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Pages (from-to) | 932-937 |

Number of pages | 6 |

Journal | IEEE Transactions on Automatic Control |

Volume | 24 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1979 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

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