Noise and Drift Analysis of Non-Equally Spaced Timing Data

F. Vernotte, G. Zalamansky, E. Lantz

Abstract:	Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators, is then performed by using a variance (Allan variance, modified Allan variance, Time variance) or a system of several variances (multi-variance method). However, in some cases, several samples, or even several set of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (I minute) and since the timing data sequence is very long (more than 10 years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. We used different interpolation algorithms (linear interpolation, cubic spline) to calculate variances in order to verify that they do neither lose information nor add erroneous information. A comparison of the results of the different algorithms will be given in the paper. Finally, we adapted the multi-variance method to the measurement sequence of the millisecond pulsar timing data: we calculated the responses of each variance of the system for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics and separability of this method will be given in the paper.
Published in:	Proceedings of the 25th Annual Precise Time and Time Interval Systems and Applications Meeting November 29 - 2, 1993 Ritz-Carlton Hotel Marina Del Rey, California
Pages:	379 - 388
Cite this article:	Vernotte, F., Zalamansky, G., Lantz, E., "Noise and Drift Analysis of Non-Equally Spaced Timing Data," Proceedings of the 25th Annual Precise Time and Time Interval Systems and Applications Meeting, Marina Del Rey, California, November 1993, pp. 379-388.
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