(A) generalized RLS method and its application to DPLL

Abstract

In this dissertation, we deal with two major subjects. First, motivated by some limitations of the conventional adaptive algorithms like the standard recursive least squares (RLS) method and the Kalman filter, we propose a generalized RLS method as a hybrid between the two algorithms, and compare its performance with the two conventional algorithms. In addition, stability issue of the proposed algorithm and a method to solve its optimal forgetting factor are discussed. The generalized RLS method inherits respective merits from the conventional algorithms. That is, even if the statistics of the process and measurement noises are not fully known or not available at all, its optimal forgetting factor can be determined in some way so that its performance becomes comparable to the optimal Kalman filter, and at the same time, it is always stable on the condition of stochastic observability. Also, it shows satisfactory tracking perfomance to follow up a state change of the parameter by employing the state-space model in the algorithm, differently from the convention al RLS method. Second, as alternatives to the conventional digital phase-locked loop (DPLL) whose loop gains are designed based on the Kalman filter algorithm, we propose a dual-loop DPLL which is modified from the conventional single-loop structure, and a RLS-based DPLL whose loop gains are designed according to the generalized RLS method proposed in this dissertation. The dual-loop DPLL fits the Kalman filter in structure, but since it violates several assumptions of the standard Kalman filter, its optimal loop gains can not be obtained according to the algorithm, so it shows a little inferior performance to the conventional Kalman filter-based DPLL. Nevertheless, when loop gains designed according to a heuristic method developed in this dissertation are applied to the DPLL, it shows a robustness that it is insensive to the erroneous estimate of the measurement noise variance. Meanwhile, a problem on t...