Accurate linear parameter estimation in colored noise

Estimation of the parameters of an unknown system is an important problem in signal processing. The classical mean squared error (MSE) criterion and its variants have been widely used to solve this problem. However, it is well known that the MSE criterion produces biased parameter estimates when the signals of interest (especially the input) are corrupted with additive noise having arbitrary or no coloring (white). Alternative approaches require additional system constraints and explicit estimation of the noise covariances. Recently, we proposed a new criterion called the error whitening criterion (EWC) along with associated algorithms that solved the problem when the additive disturbances are white. However, the performance of EWC is not satisfactory when the disturbances are correlated (colored). In this paper, we propose a method based on the principles of the EWC that can consistently estimate the parameters of an unknown arbitrary linear system in colored input noise without estimating the noise covariances. We then present a novel stochastic gradient algorithm that estimates the optimal parameters in an on-line fashion. We briefly discuss the convergence of this algorithm and present extensive simulation results to show the superiority of this criterion over MSE.