In this paper, a modified estimation algorithm has been developed refers to covariance shaping least square estimation based on the quantum mechanical concepts and constraints. The algorithm has been applied to the speech signal and the performance is estimated using probability theories. The same models can be applied with additive white Gaussian Noise which estimates the bias in the parameter and the validity of the uncertainty estimates refers to Monte Carlo simulation. Building upon the problem of optimal quantum measurement design, the performance of the CSLS estimator is discussed and it is compared with LS, James Stein, Shrunken and Ridge estimators for speech analysis and it proved that the CSLS estimator attain appreciably improved than others at low to moderate SNR.