The Corrected Allan Variance: Stability Analysis of Frequency Measurements With Missing Data.

Atomic clocks are essential elements in a variety of applications, such as global navigation satellite systems. Consequently, monitoring their performances is fundamental. The Allan variance is the key statistical tool for the performance characterization of atomic clocks. This paper proves that the Allan variance computed from frequency measurements with missing data is affected by a bias, which can make it dramatically different from the expected behavior in the full data case. Furthermore, it shows how to eliminate (or largely reduce) this bias by correcting the Allan variance. The corrected Allan variance is obtained for some of the most common atomic clock noise components, and it is validated through numerical simulations.

A comparison of contact force and remote magnetic navigation on lesion formation for the ablation of atrial fibrillation.

RATIONALE: Pulmonary vein isolation (PVI) is the method of choice for the treatment of drug-resistant atrial fibrillation (AF). However, arrhythmia recurrences are frequent due to suboptimal lesions formation and pulmonary vein reconnection. Contact force (CF)- and remote magnetic navigation (RMN)-guided catheters are both capable of improving contact and energy transfer to the tissue, possibly improving PVI outcome. OBJECTIVE: The objective of our study was to compare CF- and RMN-guided PVI in patients with paroxysmal AF in terms of surrogate parameters of the dimension and quality of the lesions. METHODS AND RESULTS: Between March 2014 and March 2016, 44 patients affected by paroxysmal AF underwent a circumferential PVI procedure, 22 with a CF catheter and 22 with a RMN catheter. Signals were recorded before and after 30 seconds of radiofrequency point-by-point delivery. For each location, signal energy attenuation and impedance drop were evaluated as lesion dimension surrogates and signal fragmentation and shrinkage were estimated as lesion quality surrogates. Statistical analysis shows that CF catheter achieves higher attenuation and impedance drop than RMN-guided catheter, which instead performs better in terms of shrinkage and fragmentation. There were no differences in terms of PVI rate and sinus rhythm maintenance 1 year after the procedure (77.2% in both groups). CONCLUSIONS: CF-guided catheters produce lesions that are larger but less homogeneous than those produced by RMN-guided catheters in terms of surrogate parameters. These two features could possibly offset each other, resulting in identical acute and long-term outcomes.

Robust Detection of Fast and Slow Frequency Jumps of Atomic Clocks.

This paper presents a frequency jump detector for atomic clocks. The detector considers both fast frequency jumps, which are abrupt variations of the clock frequency trend, and slow frequency jumps, which correspond to variations of the frequency trend over a finite time interval. These anomalies are particularly critical to space clocks in global navigation satellite systems (GNSSs). The developed detector is robust in the sense that it can deal with time-varying frequency trends, sinusoidal terms, outliers, and missing data. The detection performances are analyzed both analytically and numerically, and the effectiveness of the detector is shown by applying it to GNSS experimental data, as well as to simulated clock data.

Atrial Conduction Velocity Correlates with Frequency Content of Bipolar Signal.

BACKGROUND: Anisotropy in conduction velocity (CV) is a key substrate abnormality influencing atrial arrhythmias. In skeletal muscle fibers, CV and frequency content of the surface electromyogram signal are directly related. We hypothesized that in human atria the frequency content of the bipolar signal, recorded on the endocardial surface, is directly related to the local CV. METHODS: In 15 patients submitted to ablation of supraventricular arrhythmias, incremental pacing was performed through an octapolar catheter inserted into the coronary sinus (CS), alternatively from both extremities in two different sequences: CS bipole 1-2 as the pacing site and CS bipole 7-8 as the detection site in the first, and vice versa in the second. The pacing cycle length (PCL) was stepwise decreased from 600 ms to 500 ms, 400 ms, 300 ms, until 250 ms. Estimation of the CV was performed as the ratio between the distance traveled by the propagating pulse and the propagation time. The frequency distribution of the signal energy was estimated using the fast Fourier transform, and the characteristic frequency (CF) was estimated as the barycenter of the frequency spectrum. RESULTS: A total of 2,496 bipolar signals were analyzed; CV and CF were estimated and compared. The single patient and group data analysis showed a significant direct correlation between CV and CF of the local bipolar signal. CONCLUSIONS: Comparing the degree of spectral compression among signals registered in different points of the endocardial cardiac surface in response to decreasing PCL enables to map local differences in CV, a useful arrhythmogenic substrate index.

The Dynamic Allan Variance V: Recent Advances in Dynamic Stability Analysis.

The dynamic Allan variance (DAVAR) measures the stability variations of precise clocks and oscillators. When an anomaly occurs, the DAVAR changes with time, its shape depending on the anomaly. In this work, we first discuss our current knowledge about the DAVAR, by focusing on the meaning of dynamic stability. Then, we extend our knowledge by obtaining additional properties of the DAVAR. Furthermore, we visually investigate the DAVAR for the main anomalies of precise clocks and oscillators. Finally, we review a variety of applications based on the DAVAR.

The dynamic Allan Variance IV: characterization of atomic clock anomalies.

The number of applications where precise clocks play a key role is steadily increasing, satellite navigation being the main example. Precise clock anomalies are hence critical events, and their characterization is a fundamental problem. When an anomaly occurs, the clock stability changes with time, and this variation can be characterized with the dynamic Allan variance (DAVAR). We obtain the DAVAR for a series of common clock anomalies, namely, a sinusoidal term, a phase jump, a frequency jump, and a sudden change in the clock noise variance. These anomalies are particularly common in space clocks. Our analytic results clarify how the clock stability changes during these anomalies.

Time-frequency analysis of the endocavitarian signal in paroxysmal atrial fibrillation.

We apply the time-frequency analysis to the endocavitarian signal of patients suffering from paroxysmal atrial fibrillation. The time-frequency spectrum reveals the components of the endocavitarian signal. These components are located in the regions of the time-frequency domain that differ for in-rhythm and in-atrial fibrillation signals. By using experimental data, we perform a statistical study of these regions, and we obtain their average value. The difference in the shape of these regions is caused by the re-entry circuits that characterize atrial fibrillation. We propose a propagation model for atrial fibrillation based on the re-entry circuits, which explains the shape of the time-frequency spectrum.

Detection of atomic clock frequency jumps with the Kalman filter.

Frequency jumps are common anomalies in atomic clocks aboard navigation system satellites. These anomalous behaviors must be detected quickly and accurately to minimize the impact on user positioning. We develop a detector for frequency jumps based on the Kalman filter. Numerical simulations show that the detector is fast, with high probability of detection and low probability of false alarms. It also has a low computational cost because it takes advantage of the recursive nature of the Kalman filter. Therefore, it can be used in applications in which little computational power is available, such as aboard navigation system satellites.

The dynamic Allan variance III: confidence and detection surfaces.

The dynamic Allan variance (DAVAR) is a surface which describes the stability of a high-precision clock with respect to time. When the DAVAR is evaluated from experimental data, its surface shows random fluctuations caused by the estimation process. It is fundamental to assign a statistical significance to these fluctuations, so that they can be differentiated from the variations of the surface caused by clock anomalies. First, we develop confidence surfaces to assign a statistical significance to the random fluctuations of the DAVAR estimator. Then, we introduce detection surfaces to reveal the variations of the surface caused by clock anomalies. We validate the obtained results through numerical simulations.

A control theory approach to clock steering techniques.

Several clock and time scale steering methods have been developed according to different viewpoints by various time laboratories. By resorting to control theory ideas, we propose a common theoretical framework encompassing these methods. A comparison of the most common steering methodologies, namely, the classical steering approach, the GPS bang-bang method, and the linear quadratic Gaussian technique, is carried out. We believe that the use of control theory methods can potentially lead to a better understanding of clock steering algorithms.

The dynamic Allan variance II: a fast computational algorithm.

The stability of an atomic clock can change with time due to several factors, such as temperature, humidity, radiations, aging, and sudden breakdowns. The dynamic Allan variance, or DAVAR, is a representation of the time-varying stability of an atomic clock, and it can be used to monitor the clock behavior. Unfortunately, the computational time of the DAVAR grows very quickly with the length of the analyzed time series. In this article, we present a fast algorithm for the computation of the DAVAR, and we also extend it to the case of missing data. Numerical simulations show that the fast algorithm dramatically reduces the computational time. The fast algorithm is useful when the analyzed time series is long, or when many clocks must be monitored, or when the computational power is low, as happens onboard satellites and space probes.

The dynamic Allan variance.

We present and discuss the dynamic Allan variance, a measure of the time-varying stability of an atomic clock. First, the dynamic Allan variance is mathematically defined, then its behavior is extensively tested on simulated and experimental data. The results prove the validity and the effectiveness of the proposed new tool.