Wiener Filtering Without Covariance Matrix Inversion

This paper presents several approximate formulas for the Wiener filter (WF), the optimal linear filter minimizing the mean-squared error. Compared to the WF, our formulas do not directly involve inverting the observation covariance matrix. An important consequence is that our approximate filters do not suffer from the ill-conditioning of the covariance matrix and are numerically reliable to compute. In addition, we prove that the approximate formulas converge to the WF as certain approximate terms vanish. Finally, our performance-complexity tradeoff analysis with empirical data show that our filters are two orders of magnitude faster than the WF without compromising any accuracy.