Estimating and detecting random processes on the unit circle

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 signal directly. The effectiveness of the proposed method in terms of estimation and detection is shown through numerical experiments, where the tracking accuracy and receiver operating curves, compared with the extended Kalman filter are shown under various process/measurement noise.