Improving separating function estimation tests using Bayesian approaches

Ali Ghobadzadeh, Raviraj Adve

Abstract: Separating function estimation tests (SFETs) replace detection problems with an estimation problem. In this paper, we study the relationship between improving the estimation of unknown parameters using Bayesian approaches and the performance of the corresponding SFET. Although the estimation method in the SFET is deterministic, we show that applying Bayesian methods to estimate the rest of unknown parameters that are not involved in the SF provide improved SFET performance. We illustrate this idea using two important problems. In the first example, we consider a sinusoid signal with unknown parameters in white noise. We show that a softmax function using the Fourier transform of the signal is a proper probability density function (pdf) for the frequency to improve the performance of the SFET. In the second example, a more accurate estimation of the unknown parameters of the signal is achieved, using the Minimum Mean Square Error (MMSE) estimation of the random signal corrupted by white noise.