Covariance matrix selection in covariance shaping least square estimation

The Covariance shaping least square (CSLS) estimator can obtain lower Mean square error (MSE) than Least square (LS) estimator at moderate to low Signal-to-noise ratio (SNR). The crux of CSLS is how to determine the error covariance matrix. In this paper, an algorithm is proposed to obtain the covariance matrix coefficient in white noise observation. The presented estimator restricts the bias to a certain range and keeps smaller variance than the CSLS. It also reaches the Cramer-Rao lower bound for biased estimator. As shown through both theory deduction and simulations, this method improves the performance of the CSLS.