Wiener Filter Approximations without Covariance Matrix Inversion

In this paper, we address the problem of ill-conditioning Wiener filter, optimal linear minimum mean square error estimator. Computing filter involves inverse observation covariance matrix. practice, matrix has a large condition number, resulting in unreliable numerical computation filter. To issue, develop four approximate formulas using truncation technique based on principal components composite Our do not directly involve As result, our filters are well-conditioned and numerically reliable to compute. We also present an asymptotic analysis show that they converge as certain approximating terms vanish. Using real data, evaluate performance accuracy time against performance-computation tradeoff results that, unlike have stable without significantly more computation, even when is ill-conditioned.