Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

The GPS Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS Cesium frequency standards, and for fine tuning the MCS's state estimation of...

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Bibliographic Details
Main Author: Hutsell, Steven T
Format: Report
Language:English
Subjects:
ATOMIC CLOCKS
FREQUENCY STANDARDS
GLOBAL POSITIONING SYSTEM
KALMAN FILTERING
Navigation and Guidance
Statistics and Probability
TIME DOMAIN
TIME SERIES ANALYSIS
VARIATIONS
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Summary:The GPS Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS Cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the noise types of a less than or equal to -3, and can be greatly affected by frequency drift. Because GPS Rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = -3 and alpha = -4. As the GPS program progresses, we will utilize a larger percentage of Rubidium frequency standards than ever before. Hence, GPS Rubidium clock characterization will require more attention than ever before. The three-sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha -5, and thus has utility for modeling noise in GPS Rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman Filter process noises (qs). Presented at the Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (27th) held in San Diego, CA on 29 Nov-1 Dec 1995. Published in the Annual Precise Time and Time Interval Applications and Planning Meeting Proceedings, p291-302, Dec 1995.