The application of Kalman filters and ARIMA models to the study of time prediction errors of clocks for use in the Defense Communication System (DCS)

Techniques for obtaining optimum timekeeping performance from precision station clocks are presented. Kalman filters and ARIMA models are used to study the predictability of precision clocks based on quartz, rubidium and cesium technology. The software performing the time prediction error analysis utilizes either Kalman filters or ARIMA models to estimate the time, frequency, and frequency aging of a clock over an initial calibration interval. Forecasts for intervals from one minute up to one year are given. The forecasts are compared to the actual time of the clock to determine the forecast error. After the RMS forecast error is updated for each interval, the starting point is advanced and the process is repeated. This technique is used to study the performance of thirteen clocks over a two year time period. Adaptive versions of both the ARIMA and Kalman approaches which were developed using real-time estimators of the filter/model parameters are discussed