Method of recurrent best estimators of second degree for optimal filtering of random signals

Authors:
Anatoli Torokhti;Phil Howlett
Affiliations:
School of Mathematics, CIAM, University of South Australia, Mawson Lakes, Boulevard - The Level Campus, Mawson Lakes, SA 5095, Australia and Applied Mathematics Department, University of Adelaide, ...;School of Mathematics, CIAM, University of South Australia, Mawson Lakes, Boulevard - The Level Campus, Mawson Lakes, SA 5095, Australia
Venue:
Signal Processing
Year:
2003

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Abstract

A new approach to random signal filtering from observed data is proposed. The differences from the known methods are as follows. First, the signal is estimated by a special iterative procedure aimed at improving the accuracy of estimates obtained for the preceding iterative loops. Second, a new best quadratic estimation problem is solved on each iterative loop, providing better estimation accuracy compared with customary linear least-squares methods. The combination of these two new techniques results in a significant improvement in the filtering procedure performance compared with known methods. We call the proposed approach the method of recurrent best estimators of second degree. The efficiency of the method is illustrated by simulations with signals given by digitized images.