Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs

Jose A. Ramos; Paulo Lopes dos Santos

doi:10.1109/cdc.2007.4434438

Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs

Jose A. Ramos
, Paulo Lopes dos Santos

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we derive a set of approximate but general bilinear Kalman filter equations for a multi- input multi-output bilinear stochastic system driven by general autocorrelated inputs. The derivation is based on a convergent Picard sequence of linear stochastic state-space subsystems. We also derive necessary and sufficient conditions for a steady-state solution to exist. Provided all the eigenvalues of a chain of structured matrices are inside the unit circle, the approximate bilinear Kalman filter equations converge to a stationary value. When the input is a zero-mean white noise process, the approximate bilinear Kalman filter equations coincide with those of the well known bilinear Kalman filter model operating under white noise inputs.

Original language	American English
Pages	6196-6202
Number of pages	7
DOIs	https://doi.org/10.1109/cdc.2007.4434438
State	Published - Dec 1 2007
Event	2007 46th IEEE Conference on Decision and Control - New Orleans, United States Duration: Dec 12 2007 → Dec 14 2007 https://ieeexplore.ieee.org/xpl/conhome/4433999/proceeding

Conference

Conference	2007 46th IEEE Conference on Decision and Control
Country/Territory	United States
City	New Orleans
Period	12/12/07 → 12/14/07
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4433999/proceeding

ASJC Scopus Subject Areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Disciplines

Computer Sciences

Access to Document

10.1109/cdc.2007.4434438

Cite this

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title = "Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs",

abstract = " In this paper we derive a set of approximate but general bilinear Kalman filter equations for a multi- input multi-output bilinear stochastic system driven by general autocorrelated inputs. The derivation is based on a convergent Picard sequence of linear stochastic state-space subsystems. We also derive necessary and sufficient conditions for a steady-state solution to exist. Provided all the eigenvalues of a chain of structured matrices are inside the unit circle, the approximate bilinear Kalman filter equations converge to a stationary value. When the input is a zero-mean white noise process, the approximate bilinear Kalman filter equations coincide with those of the well known bilinear Kalman filter model operating under white noise inputs.",

author = "Ramos, \{Jose A.\} and \{Lopes dos Santos\}, Paulo",

year = "2007",

month = dec,

day = "1",

doi = "10.1109/cdc.2007.4434438",

language = "American English",

pages = "6196--6202",

note = "2007 46th IEEE Conference on Decision and Control ; Conference date: 12-12-2007 Through 14-12-2007",

url = "https://ieeexplore.ieee.org/xpl/conhome/4433999/proceeding",

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TY - CONF

T1 - Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs

AU - Ramos, Jose A.

AU - Lopes dos Santos, Paulo

PY - 2007/12/1

Y1 - 2007/12/1

N2 - In this paper we derive a set of approximate but general bilinear Kalman filter equations for a multi- input multi-output bilinear stochastic system driven by general autocorrelated inputs. The derivation is based on a convergent Picard sequence of linear stochastic state-space subsystems. We also derive necessary and sufficient conditions for a steady-state solution to exist. Provided all the eigenvalues of a chain of structured matrices are inside the unit circle, the approximate bilinear Kalman filter equations converge to a stationary value. When the input is a zero-mean white noise process, the approximate bilinear Kalman filter equations coincide with those of the well known bilinear Kalman filter model operating under white noise inputs.

AB - In this paper we derive a set of approximate but general bilinear Kalman filter equations for a multi- input multi-output bilinear stochastic system driven by general autocorrelated inputs. The derivation is based on a convergent Picard sequence of linear stochastic state-space subsystems. We also derive necessary and sufficient conditions for a steady-state solution to exist. Provided all the eigenvalues of a chain of structured matrices are inside the unit circle, the approximate bilinear Kalman filter equations converge to a stationary value. When the input is a zero-mean white noise process, the approximate bilinear Kalman filter equations coincide with those of the well known bilinear Kalman filter model operating under white noise inputs.

UR - https://nsuworks.nova.edu/gscis_facarticles/397

U2 - 10.1109/cdc.2007.4434438

DO - 10.1109/cdc.2007.4434438

M3 - Paper

SP - 6196

EP - 6202

T2 - 2007 46th IEEE Conference on Decision and Control

Y2 - 12 December 2007 through 14 December 2007

ER -

Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs

Abstract

Conference

ASJC Scopus Subject Areas

Disciplines

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