Application of Kalman filtering techniques to the precision clock with non-constant aging

The availability of onboard intelligence has created the possibility of compensating for systematic effects in time and frequency subsystems. To that end, a Kalman filter approach to compensate for aging in precision oscillators is presented. The approach predicts the frequency based upon past measurements taken at arbitrary intervals. In an earlier algorithm, the aging rate was assumed to be constant after the most recent measurement, so that the predicted frequency change was always linear with time. This assumption is not generally satisfied in quartz oscillators. In the new approach, the oscillation frequency is described by a weighted sum of logarithmic functions. The weighting parameters are random variables estimated by the Kalman algorithm. Quartz oscillator examples are presented to show that the new algorithm is superior to the earlier one