On the problem of estimating a signal correlated with observation noise

In this letter, a recently presented solution to the problem of estimating a signal uncorrelated with observation noise is extended to include correlation between the signal and the noise. We propose a suboptimum estimator that estimates efficiently the signal through a recursive algorithm. For that, and firstly, by using the finite Karhunen-Loeve expansion, we derive a new design procedure of the optimum estimator of the signal alternative to the classic form obtained through the direct solving of the Wiener-Hopf equation. Then, on the basis of this new approach, we devise the proposed suboptimum estimator.