Predicting Long-Term Frequency Stability In The Framework Of Convex Optimization

High-performance oscillators,atomic clocks for instance,are important in modern industries,finance and scientific researches.These devices are affected by power-law noises,and characterized by structure functions(ie.variances).These variances with specified period(averaging time)quantify the frequency stability of the oscillator.In some applications,for example,navigation satellite or deep space exploration,it is im-portant to compute long-term variances from limited data reliably.In this paper,the author study the computation of long-term stability by using modern convex optimiza-tion methods.Based on the characteristic of clock noises,the investigation can be separated into three parts roughly:·In the simplest case,we only need to consider the influence of white phase modula-tion(f2 noise),flicker phase modulation(f1 noise),white frequency modulation(f0 noise),flicker frequency modulation(f-1 noise)and random walk frequency mod-ulation(f-2 noise),and a deterministic frequency drift.The author modified the classical oscillator noise analysis model based on methods of convex optimization,e.g.,primal-dual interior-point methods,compressive sensing,probabilistic restric-tions,etc.Such,techniques overcome the ill-posed problem we might encounter in classical oscillator noise analysis,enable us to make estimations from observations with asymmetric error distribution,and predict ranging intervals of long-term sta-bilities.The author names the modified oscillator noise analysis method as StONA.Predictions made by StONA based on short term satellite and ground atomic clock data axe consistent with stabilities computed from long term observations.·Since the frequency drift of an atomic clock may be inconstant,the author for-mulates the influence of deterministic drift on Allan and modified Allan variances are formulated,and derives expressions of discrete-time Hadamard variance and its uncertainty.Methods which,reduce the computational complexity of these expres-sions are also introduced.Tests against GPS precise clock data show the method can correctly predict one week frequency stability from 14 day measured data.·In a more general case,the number of power-law noise processes and their types are unknown.The abrupt change of environment or accidence bring unexpected changes to clock behaviors too.To tackle the former problem,the author defines noise intensity function by using Stieltjes integral,and thus generalizes StONA to GSONA.Compressive sensing is also used to minimize the influence of the second problem in GSONA.Test against 32 GPS satellite clocks shows that predictions made by GSONA are more reliable than Allan,modified Allan and Hadamard variances computed from three times more data.