Recursive Bayes risk parameter estimation from the cyclic autocorrelation matrix

We present a new method for recursively estimating the frequency and timing parameters of a second order cyclostationary signal with known cyclic autocorrelation matrix (CAM). This problem appears in the context of radar as well as asynchronous communications in highly non-stationary environments (e.g. telemetry) due to the Doppler effect. The parameters evolution is modelled by a zero-order random walk. The estimates are obtained from the instantaneous CAM (ICAM) of the signal. While nonlinear Kalman filter theory is a possible approach to this problem, Bayes risk theory is used instead. In this way the Riccati equation and gain matrices become independent of the estimates, thus allowing a look-up table solution. The folded normal density (FND) is assumed as parameters´ prior. The prior is recursively updated in mean (estimates) and variance. By comparing the obtained equations with linear Kalman filter equations we show that with few modifications a first-order random walk model can be easily incorporated to cope with highly non-stationary frequency evolution