A review of reduced Kalman filters for clock ensembles

This paper reviews the author's previous work on free-running timescales based on Kalman filters that act upon clock comparisons. The natural Kalman clock ensemble algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each postmeasurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability. A new result on covariance matrix reduction is also stated.