Figure 1 above shows the performance of four units during holdover. The data in this figure was obtained by simply using an oscillator control voltage, which was an average voltage computed during a period of GPS availability. No attempt was made to dynamically correct for the effects of temperature changes, and no attempt was made to predict and compensate the aging rate of the oscillator.

While the simple average yields good performance in many cases, much better results are obtained when the effects of temperature and aging rate are included. The most natural way to include these additional variables is to use a Kalman filter. Figure 2 below shows the performance of the same four units with a Kalman filter.

The general approach is to run the Kalman filter during periods of GPS availability to obtain an estimate of the DAC voltage, the aging coefficient, and the temperature coefficient. When a holdover event occurs (for whatever reason) the DAC voltage is predicted based on the following equation.

dac voltage = dac voltage + (age coef.) * d(time) + (temp coef) * d(temp)

The input voltage and corresponding performance for a pair of CDMA clocks using the Kalman filter are shown in Figure 3 and Figure 4 above. In both cases a 24-hour period of GPS availability (training period) is followed by a 24-hour period of holdover. The DAC voltage during training is "fuzzy", reflecting the effects of selective availability present during the training period. The dac voltage during holdover changes with both time and temperature as the predicted aging and temperature coefficients are applied using the equation above. The temperature profile used was a rather severe diurnal model, and is shown in Figure 5 below.

In both cases the total range of the bias ordinate is +/- 3500 nanoseconds, which is one half the usual specified range for bias drift during holdover for a CDMA clock. The bias drift during holdover was about one microsecond in both examples. This data is better than typical, but does illustrate what can be done with a careful blend of a good quartz oscillator coupled with the Kalman predictor. Both of these locks would have maintained adequate holdover performance for "days" even with the severe diurnal temperature cycle used.