Abstract
High-performance oscillators, atomic clocks for instance, are important in modern industries, finance and scientific research. In this paper, the authors study the estimation and prediction of long-term stability based on convex optimization techniques and compressive sensing. To take frequency drift into account, its influence on Allan and modified Allan variances is formulated. Meanwhile, expressions for the expectation and variance of discrete-time Hadamard variance are derived. Methods that reduce the computational complexity of these expressions are also introduced. Tests against GPS precise clock data show that the method can correctly predict one-week frequency stability from 14-day measured data.
Highlights
Timing technology is important in modern finance [1], industries and scientific research [2].High frequency trading, real-time navigation and the verification of relativistic effects require accurate and high-resolute time and/or frequency information
This paper studies the estimation of oscillator stability under the influence of frequency drift
It should be noted that the method discussed in this paper assumes power-law processes and deterministic frequency drift being the major sources of time-series data
Summary
Timing technology is important in modern finance [1], industries and scientific research [2]. Allan (AVAR), modified Allan (MVAR) and Hadamard variance (HVAR) are commonly-used methods. The authors proposed an oscillator noise analysis method called stochastic. We introduce a method that greatly reduces the computational complexity of Walter’s characterization of AVAR and MVAR From these works, we can predict long-term frequency contaminated by deterministic linear frequency drift. The one-week AVAR, MVAR and HVAR predicted by stochastic ONA from 14-day measured data are consistent with those estimated from 84-day data. The fifteen-day variances predicted by stochastic ONA have more compact confidence regions than those estimated from 42–60-day data
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