Derivation of fixed-interval smoothing algorithm using covariance information in distributed parameter systems

• Published in: Applied mathematics and computation Vol. 176; no. 2; pp. 662 - 672
• Main Authors: Nakamori, S., García-Ligero, M.J., Hermoso-Carazo, A., Linares-Pérez, J.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.05.2006; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Covariance information; Distributed parameter systems; Exact sciences and technology; Fixed-interval smoothing; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Pattern recognition. Digital image processing. Computational geometry; Probability and statistics; Probability theory and stochastic processes; Recursive estimation; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Wiener–Hopf equation; Wiener–Hopf equation; Covariance information; Distributed parameter systems; Fixed-interval smoothing; Recursive estimation; Smoothing methods; Wiener Hopf equation; Error estimation; State space method; Image restoration; Numerical analysis; Applied mathematics; Smoothing parameter; White noise; Mean error; Wiener-Hopf equation; Distributed parameter system
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.10.012

This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the algorithm only requires the second-order moments of the signal and the white noise perturbing its observations. Practical application of the proposed algorithm is illustrated with a restoration image problem.