Estimating and detecting random processes on the unit circle

Abstract

Detecting random processes on a circle has been studied for many decades. The Neyman-Pearson detector, which evaluates the likelihood ratio, requires first the conditional mean estimate of the circle-valued signal given noisy measurements, which is then correlated with the measurements for detection. This is the estimator-correlator detector. However, generating the conditional mean estimate of the signal is very rarely solvable. In this paper, we propose an approximate estimator-correlator detector by estimating the truncated moments of the signal, with estimated signal substituted into the likelihood ratio. Instead of estimating the random phase, we estimate the complex circle-valued signa..