The design of Kalman smoothers for Global Positioning System data

Measurements of clocks aboard Global Positioning System (GPS) satellites as well as GPS system time are used for positioning, navigation, and timing. Different biases in a sequence of time-difference measurements repeated each sidereal day produce apparent diurnal effects in the data. A composite time and frequency Kalman estimator is used. A one-day average of frequency at each measurement allows updates of clocks at time intervals of less than one day while aliasing diurnal variations. This technique is applied to data taken many times per day at time-standards laboratories around the world according to a tracking schedule issued by the Bureau International des Poids et Mesures (BIPM). The author computes Kalman-smoothed estimates of the time of clocks in the standards labs to define a global time base, then computes Kalman-smoothed estimates of the time of GPS clocks against this time base