Linear recursive discrete-time estimators using covariance information under uncertain observations

This paper, using the covariance information, proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain observations in linear discrete-time stochastic systems. The observation equation is given by y( k)= γ( k) Hx( k)+ v( k), where { γ( k)} is a binary swit...

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Bibliographic Details
Published in:Signal processing Vol. 83; no. 7; pp. 1553 - 1559
Main Authors: Nakamori, Seiichi, Caballero-Águila, Raquel, Hermoso-Carazo, Aurora, Linares-Pérez, Josefa
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.07.2003
Elsevier Science
Subjects:
Applied sciences
Covariance information
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Information, signal and communications theory
Linear discrete-time systems
Recursive estimation
Services and terminals of telecommunications
Signal and communications theory
Signal, noise
Stochastic process
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Telemetry. Remote supervision. Telewarning. Remote control
Transmission and modulation (techniques and equipments)
Wiener-Hopf equation
Covariance information
Wiener-Hopf equation
Linear discrete-time systems
Stochastic process
Recursive estimation
Filtering
Probabilistic approach
Information system
Discrete time systems
Data transmission
Probability distribution
Conditional probability
Algorithm
Modeling
Remote sensing
Binary sequence
Covariance
Least squares method
Discrete time
White noise
Recursive method
Multiple channel
Matrix system
Fixed point
ISSN:0165-1684, 1872-7557
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Summary:This paper, using the covariance information, proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain observations in linear discrete-time stochastic systems. The observation equation is given by y( k)= γ( k) Hx( k)+ v( k), where { γ( k)} is a binary switching sequence with conditional probability distribution verifying Eq. (3). This observation equation is suitable for modeling the transmission of data in multichannels as in remote sensing situations. The estimators require the information of the system matrix Φ concerning the state variable which generates the signal, the observation vector H, the crossvariance function K xz ( k, k) of the state variable with the signal, the variance R( k) of the white observation noise, the observed values, the probability p( k)= P{ γ( k)=1} that the signal exists in the uncertain observation equation and the (2,2) element [ P( k| j)] 2,2 of the conditional probability matrix of γ( k), given γ( j).
ISSN:0165-1684
1872-7557
DOI:10.1016/S0165-1684(03)00056-2