Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances

Bernard Friedland; Irwin Bernstein

doi:10.1016/0016-0032(66)90434-0

Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances

Bernard Friedland, Irwin Bernstein

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

The optimum estimate is defined as one which maximizes the conditional probability density function of the sequence of states X_n = {x₀, ..., x_n} in a discrete-time dynamic process, given a sequence of observations Y_n = {y₁, ..., 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)
Pages (from-to)	455-480
Number of pages	26
Journal	Journal of the Franklin Institute
Volume	281
Issue number	6
DOIs	https://doi.org/10.1016/0016-0032(66)90434-0
State	Published - Jun 1966
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1016/0016-0032(66)90434-0

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title = "Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances",

abstract = "The optimum estimate is defined as one which maximizes the conditional probability density function of the sequence of states Xn = {x0, ..., xn} in a discrete-time dynamic process, given a sequence of observations Yn = {y1, ..., yn}. 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 {\=x}n to the optimum estimate {\=x}n given xn-1 and yn. 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.",

author = "Bernard Friedland and Irwin Bernstein",

year = "1966",

month = jun,

doi = "10.1016/0016-0032(66)90434-0",

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AU - Bernstein, Irwin

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AB - The optimum estimate is defined as one which maximizes the conditional probability density function of the sequence of states Xn = {x0, ..., xn} in a discrete-time dynamic process, given a sequence of observations Yn = {y1, ..., yn}. 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 x̄n to the optimum estimate x̄n given xn-1 and yn. 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.

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Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances

Abstract

All Science Journal Classification (ASJC) codes

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