On a phase tracking problem: Non-linear filtering approaches

The concept of phase tracking has found its applications in GPS systems, radar systems, signal processing and communication systems etc. The phase tracking problem is generally formalized as a non-linear noisy observation equation in which the measurement non-linearity is sinusoid added with additive noise. From the dynamical systems' viewpoint, we state the evolution of the phase angle of the measurement equation. As a result of this, we wish to estimate the phase angle from given observations using two non-linear filters: (i) the extended Kalman filter (ii) a Gaussian non-linear filter. This paper develops two non-linear filters for a filtering model for the phase tracking in which the Ornstein-Uhlenbeck process is the process noise and the Brownian noise process is the observation noise. The filter efficacy is examined by utilizing quite extensive numerical experimentations with two different sets of data. This paper unfolds a connection between coloured noise processes, stochastic filtering methods in systems and control and communications.