An Adaptive Algorithm to Evaluate Clock Performance

Kalman filters and ARIMA models provide optimum control and evaluation techniques (in a minimum squared error sense) for clocks and precision oscillators. Typically, before the models can be used, an analyeie of data provides estimates of the model parameters (e.g., the phi's and theta's for an ARIMA model). These model parameters are often evaluated in a batch mode on a computer after a large amount of data is obtained. An alternative approach is to devise an adaptive algorithm which Yearns" the important parameters while the device is being used and up-dates the parameters recursively. Clearly, one must give up some amount of precision if one deviates even slightly from the truly optimum techniques, but, as this study shows, the costs in performance are not large at all. If one chooses the best sampling intervals, the loss in precision can be negligible. The physical models used in this paper are baaed on the assumptiaa of a combination of white PM, white FM, random walk FM, and linear frequency drift. In ARIMA models, this is equivalent to an ARIMA(0,2,2) with a non-zero average second difference. Using simulation techniques, this paper compares real-time estimation techniques with the conventional batch mode. The criterion for judging perforinance is to compare the mean square errors of prediction between the batch mode and the recursive mode of parameter estimation operating on the same data sets. INTRODUCTION Before working directly on the ARIMA(0,2,2) models [I], it is of value to establish a few important relations. An ARIMA(1,0,0) model is often referred to as an exponential filter since its impulse response function is an exponential, That is: