## Abstract

A process with random transitions is represented by the difference equation x//n equals x//n// minus //1 plus u//n where u//n is a nonlinear function of a gaussian sequence w//n. The nonlinear function has a threshold that results in a finite probability of no failure at every step. Maximum likelihood estimation of the sequence X//n equals left brace x//0,. . . ,x//n right brace given a sequence of observations Y//n equals left brace y//1,. . . ,y//n right brace 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.

Original language | English (US) |
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Pages (from-to) | 427-432 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

State | Published - Jan 1 1978 |

Externally published | Yes |

Event | Proc IEEE Conf Decis Control Incl Symp Adapt Processes 17th - San Diego, CA, USA Duration: Jan 10 1979 → Jan 12 1979 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization