The use of multi-variance for likelihood weighted drift estimation in a disciplined oscillator algorithm

Our recent research at JHU/APL has focused on advancing algorithms and software control developments for a next generation, disciplined USO based clock system. This research shows promise that incorporating an in-situ control system for removing USO deterministic frequency error based on multi-variance methods and a Bayesian maximum likelihood estimation (MLE) process could mitigate the burden of post processing spacecraft clock data. We found the effects caused by sudden frequency changes and perturbations could be diminished with a dynamic, multi-variance algorithm used to augment the drift estimation process. We used the complementary aspects of the Allan and Hadamard variance to form an MLE function. We then used the output of the MLE function to drive the weighted decision process of a simulated frequency correction control algorithm. Our paper will discuss the mathematical approach used to formulate the multi-variance MLE and discuss our findings on its implementation in the disciplining algorithm developed from the research. Using laboratory collected USO data, we will show simulated USO timekeeping performance to a maximum time interval error of <; 1 μs over 70 days of operation and discuss the impact of frequency anomalies and short term rate changes to the behavior of the multi-variance approach.