Riccati and Chandrasekhar Algorithms for Signal Filtering from Uncertain Observations

S. Nakamori (Japan), A. Hermoso, J. Jiménez, and J. Linares (Spain)

Keywords

Estimation. Statistical modelling. Chandrasekhar-type filter. Uncertain observations. Covariance information.

Abstract

In this paper, the least mean-squared error linear filtering problem of a wide-sense stationary scalar signal from uncertain observations is analyzed, assuming that the state space model is not completely known. We suppose that the variables modelling the uncertainty are not independent; moreover, the observations are perturbed by white plus coloured additive noises. We propose two algorithms: one of them is based on Chandrasekhar-type difference equations and, the other, on Riccati-type ones. By comparing both algorithms it is observed that the Chandrasekhar-type algorithm is computationally better than the Riccati-type one since the number of difference equations contained in it is less than that required in the Riccati-type algorithm. Finally, we illustrate the results obtained by means of a numerical example on estimation of signals transmitted in multichannel.

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