## Abstract

The optimum estimate is defined as one which maximizes the conditional probability density function of the sequence of states X_{n} = {x_{0}, ..., x_{n}} in a discrete-time dynamic process, given a sequence of observations Y_{n} = {y_{1}, ..., y_{n}}. The equations governing this estimate are derived for nonlinear processes in the presence of nongaussian noise and disturbances. A recursive technique is given for computing an approximation x̄_{n} to the optimum estimate x̄_{n} given x_{n-1} and y_{n}. This technique reduces to the Kalman-Busy algorithm for linear processes with gaussian noise and disturbances. An algorithm for correcting the approximate estimate is also derived. The discrete-time results are formally extended to continuous-time processes.

Original language | English (US) |
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Pages (from-to) | 455-480 |

Number of pages | 26 |

Journal | Journal of the Franklin Institute |

Volume | 281 |

Issue number | 6 |

State | Published - Jun 1 1966 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Signal Processing
- Computer Networks and Communications
- Applied Mathematics