Skip to Main Content
The output of an ideal photodetector that is modeled as a doubly stochastic Poisson process is used to excite a phase-locked loop. The rate of this Poisson process contains an angle-modulated subcarrier process that is modeled as a Gauss-Markov process. A measure transformation involving a martingale translation is applied to the suboptimal filter used to estimate the phase. Cycle slipping is then discussed with respect to the evolution of the phase error process under the new measure. The approach is in the context of a first-passage problem and uses a Kramers-Moyal expansion of the equation satisfied by the mean slip time. Various approximations to the jump rate and size are assumed, and a perturbation analysis results in asymptotic representations of the corresponding solutions. Comparisons with solutions obtained from so-called diffusion approximations are also included, as well as a specific example to illustrate the procedure.
Date of Publication: Mar 1987