Autonomous and Robust Time Scale Algorithm for a Swarm of Nanosatellites

A new robust time scale algorithm, Autonomous Time scale using the Student’s T-distribution (ATST), has been proposed and validated using simulated clock data. Designed for use in a nanosatellite swarm, ATST addresses phase jumps, frequency jumps, anomalous measurement noise, and missing data by making a weighted average of the residuals contained in the Basic Time Scale Equation (BTSE). The weights come from an estimator that assumes the BTSE residuals are modeled by a Student’s t-distribution.
Despite not detecting anomalies explicitly, the ATST algorithm performs similarly to a version of the AT1 time scale that detects anomalies perfectly in simulated data. However, ATST is best for homogeneous clock types, requires a high number of clocks, adds computational complexity, and makes no distinction of anomaly types. Despite these identified limitations, the robustness achieved is a promising contribution.
The implementation of ATST includes a method that maintains phase and frequency continuity when clocks are removed or reintroduced into the ensemble by resetting appropriate clock weights to zero. A Least Squares (LS) estimator is also presented to pre-process inter-satellite measurements, reducing noise and estimating missing data. The LS estimator is also compatible with anomaly detection which removes anomalous inter-satellite measurements because it can replace the removed measurements with their estimates.
The thesis also explores optimal estimation of parameters of two heavy-tailed distributions: the Student’s t and Bimodal Gaussian mixture. The Misspecified Cram´er Rao Bound (MCRB) confirms that assuming heavy-tailed distributions handles outliers better compared to assuming a Gaussian distribution. We also observe that at least 25 clocks are required for asymptotic efficiency when estimating the mean of the clock residuals. The methodology also aids in analyzing other anomaly types fitting different distributions.
Future research proposals include addressing ATST’s limitations with diverse clock types, mitigating performance loss with fewer clocks, and exploring robust time scale generation using machine learning to weight BTSE residuals. Transient anomalies can be targeted using machine learning or even a similar method of robust estimation of clock frequencies over a window of past data. This is interesting to research and compare to the ATST algorithm that is instead proposed for instantaneous anomalies.