Analysis of Kalman filter in timing acquisition in data storage read channels

In data storage systems, the phase-locked loop (PLL) in timing recovery can be modeled as a Kalman filter. Goal of the acquisition stage is to estimate the initial phase and frequency disturbances. Kalman filter achieves linear minimum mean square error (LMMSE) estimation, but it requires knowing the exact prior information. In practice, the prior information is not precisely known. In this paper we develop closed form expressions for the mean squared error (MSE) of phase and frequency estimation by Kalman filter with imprecise prior information. With them, we can quantitatively tell how much prior information mismatch can be tolerated