Optimal Quantum Measurement Design on Speech Signal: Blind Minimax Estimator Improving MSE Over LS Estimators

We consider the problem of estimating an unknown, deterministic speech signal parameters based on quantum measurements corrupted by white Gaussian noise. We design and analyze blind minimax estimator (BME), which consist of a bounded parameter set. Using minimax estimator, the parameter set is itself estimated from quantum measurements. Thus, our approach does not require any prior knowledge of bounded parameters, and the designed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the least-square (LS) estimator, i.e., they achieve lower mean-squared error (MSE) for any speech signal. Our approach can be readily compared with wide class of nonlinear estimators like James Stein’s estimator, which is defined for white noise. The result suggest that over a wide range of samples and signal to noise ratio the mean square error for Ellipsoidal Blind Minimax Estimator(EBME) is lower when compared with linear and non-linear estimators. KeywordsQuantum measurements, Minimax Estimator, White Gaussian noise, linear regression, Mean square error, Biased Estimation