In this paper, a modified estimation algorithm has been developed refers to Covariance Shaping Least Square (CSLS) estimation based on the quantum mechanical concepts and constraints. The algorithm has been applied to Auto Regressive Moving Average (ARMA models with various parameter values. The same models can be applied with Colored 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, we develop and discuss the performance of the CSLS estimator with the measure of mean square error (MSE) and it is compared with Least Square, James Stein, Shrunken and Ridge estimators for different applications. It proved that the CSLS estimator has low MSE and performed efficiently better than others at low to moderate, even when noise variation is having robust Signal to Noise Ratio (SNR).