Characterizing Periodic Variations of Atomic Frequency Standards via Their Frequency Stability Estimates.

The onboard atomic frequency standard (AFS) is a crucial element of Global Navigation Satellite System (GNSS) satellites. However, it is widely accepted that periodic variations can influence the onboard AFS. The presence of non-stationary random processes in AFS signals can lead to inaccurate separation of the periodic and stochastic components of satellite AFS clock data when using least squares and Fourier transform methods. In this paper, we characterize the periodic variations of AFS using Allan and Hadamard variances and demonstrate that the Allan and Hadamard variances of the periodics are independent of the variances of the stochastic component. The proposed model is tested against simulated and real clock data, revealing that our approach provides more precise characterization of periodic variations compared to the least squares method. Additionally, we observe that overfitting periodic variations can improve the precision of GPS clock bias prediction, as indicated by a comparison of fitting and prediction errors of satellite clock bias.

Constrained MLAMBDA Method for Multi-GNSS Structural Health Monitoring.

Deformation monitoring of engineering structures using the advanced Global Navigation Satellite System (GNSS) has attracted research interest due to its high-precision, constant availability and global coverage. However, GNSS application requires precise coordinates of points of interest through quick and reliable resolution of integer ambiguities in carrier phase measurements. Conventional integer ambiguity resolution algorithms have been extensively researched indeed in the past few decades, although the application of GNSS to structural health monitoring is still limited. In particular, known a priori information related to the structure of a body of interest is not normally considered. This study proposes a composite strategy that incorporates modified least-squares ambiguity decorrelation adjustment (MLAMBDA) method with priori information of the structural deformation. Data from the observation sites of Baishazhou Bridge are used to test method performance. Compared to MLAMBDA methods that do not consider priori information, the ambiguity success rate (ASR) improves by 20% for global navigation satellite system (GLONASS) and 10% for Multi-GNSS, while running time is reduced by 60 s for a single system and 180 s for Multi-GNSS system. Experimental results of Teaching Experiment Building indicate that our constrained MLAMBDA method improves positioning accuracy and meets the requirements of structural health monitoring, suggesting that the proposed strategy presents an improved integer ambiguity resolution algorithm.

Predicting Long-Term Frequency Stability: Stochastic Oscillator Noise Analysis.

High-performance frequency standards are affected by power-law noises and characterized by structure functions (i.e., variances). These variances with specified averaging time quantify the frequency stability of the oscillator. To improve the stability estimated from the measured data and extend its maximum averaging time, a method called "StONA" (oscillator noise analysis under stochastic restrictions) is proposed based on convex optimization techniques. StONA also measures the intensity coefficients of noise processes as a by-product of extending averaging time. To test the method against real data, we recompute the distribution regions of total and Hadamard variances estimated from 14 days of satellite clock data and predict the stability of extended averaging time. The recomputed and predicted variances are inconsistent with the ones estimated from 168 days of data and have smaller uncertainty than those estimated from 84 days of time deviations.

Predicting Long-Term Stability of Precise Oscillators under Influence of Frequency Drift.

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.