Congruence of two Kalman Filter Composite Clock

Kurzfassung

This paper compares the corrected clock offsets of two composite clock algorithms based on Kalman filtering of measured clock differences: the original Jones-Tryon algorithm and Greenhall’s covariance-reduction modification. The theory is carried out for a general clock model that includes the model introduced by Davis et al: the sum of the the 3-state linear model and a set of Markov processes used to approximate flicker-frequency noise. Since measurement noise is allowed, the corrected clock offsets at each measurement time do not coincide but form a set of values, different for the two algorithms. The main result is that the two sets are congruent at each time and that their common difference, as a function of time, is a random walk. The congruency holds for time-varying measurement matrices. Therefore, the result is applicable to the measurement setup of laboratories as well as that of a Global Navigation Satellite System (GNSS) with varying visibilities of satellite clocks at ground stations. These results are illustrated by a simulated ensemble of three caesium clocks and two hydrogen masers measured against one of the hydrogen masers.