An Iterative Filter for FLL-Assisted-PLL Carrier Tracking At Low $C/N_0$ and High Dynamic Conditions

This article presents an iterative frequency lock loop (FLL)-assisted-phase lock loop (PLL) (FPLL) design in state space according to the minimum mean square error criterion. This is achieved by constructing a high fidelity carrier signal model with the consideration of the non-Gaussian nonwhite measurement noise characteristics. Two popular arctangent discriminators, e.g., two-quadrant (Atan) and four-quadrant (Atan2) are used to produce the PLL and FLL measurements for FPLL, respectively. The filter gain is selected to minimize the trace of the error covariance matrix and an iteration approach to quickly compute the steady-state filter gain is introduced. The nonlinearity in the discriminator and filter behaviors in FPLL at low $C/N_0$ and high dynamic conditions are investigated. The closed-form expressions of the closed-loop transfer function as well as error transfer function are clarified. The thermal noise induced tracking jitters on each carrier state, e.g., phase, doppler, and doppler rate, are derived, analyzed, and verified via Monte Carlo simulation, accordingly. The theoretical properties show that the iterative FPLL achieves the following. 1) The comparable tracking performance to the well-designed PLL-only. 2) The enhanced tracking accuracy over the well-designed FLL-only. 3) The improved tracking sensitivity over the conventional Kalman filter-based FPLL (KF-FPLL), at low $C/N_0$ condition and high dynamic conditions.