Estimation in linear time-delay system with coloured observation noise

Shukla, Vedant

doi:10.1049/el:19730001

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2010

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“…4 is a regular state-space system, with the same state x n (rather than an augmented one x * n ), correlated process and measurement noises, and with pseudomeasure y n . For model 4 the KF has been derived e.g., in [16,[18][19][20], the RTS algorithm in [18,20], an FLS algorithm in [22,23], and a two-filter smoother (for the continuous time case) in [24].…”

Section: Remarkmentioning

confidence: 99%

Fixed-Interval Kalman Smoothing Algorithms in Singular State–Space Systems

Ait‐El‐Fquih¹,

Desbouvries²

2010

J Sign Process Syst

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Fixed-interval Bayesian smoothing in statespace systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e., with positive definite covariance matrix; and the perfect measurement case, i.e., with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov model with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.

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