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Spectrum feature extraction plays a crucial role in identifying seismic events and calculating structural response parameters. However, the criteria for identifying effective modal components in Variational Mode Decomposition (VMD) are not well-defined, resulting in inaccurate spectrum feature extraction. To address this issue, we propose a novel spectrum feature extraction method that combines Allan variance, VMD, and power spectral density (PSD). Firstly, VMD is applied to filter noise components from triaxial accelerometer observations and add effective signals. Secondly, PSD is utilized to extract three groups of seismic frequencies (tri-axial accelerometers). Finally, the Allan method is introduced to identify the group of accelerometer observations with the highest reliability as the vibration frequency caused by the seismic excitation. We validate the effectiveness of our method by analyzing a Mw 2.6 micro-seismic event that occurred in Huairou, Beijing in 2022. The result shows that our proposed method accurately extracts spectrum features of the Great Wall. Specifically, the seismic excitation vibration frequencies at four monitoring stations were found to be 26.95 Hz, 12.89 Hz, 12.89 Hz, and 12.5 Hz. These findings underscore our method's utility in evaluating the Great Wall's structural response to seismic loading, which has significant implications for the conservation and protection of heritage structures., (© 2024. The Author(s).)

The application of Allan variance to characterize the stability of optical signals affected by stochastic polarization fluctuations and the identification of the underlying power law noise processes is explored. Allan variance can ease the comparison regarding polarization stability of optical systems affected by polarization noise and define a near-optimum integration interval to reveal trends. Examples of the application of Allan variance to optical systems with stable polarization conditions show that white noise and random walk terms can be observed. Additionally, experiments show that the three Stokes parameters can exhibit different statistical behaviors in the Brownian-noise regime. Allan analysis can easily be used to define, in real-time systematically, the denoising strategy in polarization-based sensing and for the optimization of polarization-sensitive optical systems instead of the conventional approach relying on heuristics or information criteria.

Handheld Fourier transform infrared (FT-IR) spectrometers are very promising candidates for several applications where accurate real-time material detection and quantification are needed. Due to their compact size, their mode of operation which does not allow for long warm-up time, and changing environmental conditions, these spectrometers suffer from short-term noise and long-term instabilities which affect their performance. In this work, the effect of long-term multiplicative instabilities on the signal-to-noise ratio (S/N), measured using the 100% line-method, is studied. An expression for the variance, in this case, is deduced. The Allan variance technique is used to identify and quantify the presence of the different types of noises. The methodology is applied to a commercial NeoSpectra scanner module from Si-Ware Systems, Inc.

Allan variance has been widely utilized for evaluating the stability of the time series generated by atomic clocks and lasers, in time regimes ranging from short to extremely long. This multiscale examination capability of the Allan variance may also be beneficial in evaluating the chaotic oscillating dynamics of semiconductor lasers- not just for conventional phase stability analysis. In the present study, we demonstrated Allan variance analysis of the complex time series generated by a semiconductor laser with delayed feedback, including low-frequency fluctuations (LFFs), which exhibit both fast and slow dynamics. While the detection of LFFs is difficult with the conventional power spectrum analysis method in the low-frequency regime, the Allan variance approach clearly captured the appearance of multiple time-scale dynamics, such as LFFs. This study demonstrates that Allan variance can help in understanding and characterizing diverse laser dynamics, including LFFs, spanning a wide range of timescales.

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.

Single-molecule manipulation techniques have provided unprecedented insights into the structure, function, interactions, and mechanical properties of biological macromolecules. Recently, the single-molecule toolbox has been expanded by techniques that enable measurements of rotation and torque, such as the optical torque wrench (OTW) and several different implementations of magnetic (torque) tweezers. Although systematic analyses of the position and force precision of single-molecule techniques have attracted considerable attention, their angle and torque precision have been treated in much less detail. Here, we propose Allan deviation as a tool to systematically quantitate angle and torque precision in single-molecule measurements. We apply the Allan variance method to experimental data from our implementations of (electro)magnetic torque tweezers and an OTW and find that both approaches can achieve a torque precision better than 1 pN · nm. The OTW, capable of measuring torque on (sub)millisecond timescales, provides the best torque precision for measurement times ≲10 s, after which drift becomes a limiting factor. For longer measurement times, magnetic torque tweezers with their superior stability provide the best torque precision. Use of the Allan deviation enables critical assessments of the torque precision as a function of measurement time across different measurement modalities and provides a tool to optimize measurement protocols for a given instrument and application., (Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The Allan variance of signal and reference frequencies is measured by a least-square fit of the output of two analog-to-digital converters to ideal sine waves. The difference in the fit phase of the two channels generates the timing data needed for the Allan variance. The fits are performed at the signal frequency (≈10 MHz) without the use of heterodyning. Experimental data from a modified digital oscilloscope yield a residual Allan deviation of 3 × 10 -13 /τ, where τ is the observation time in s. This corresponds to a standard deviation in time of <300 fs or 20 μrad in phase. The experimental results are supported by statistical theory and Monte Carlo simulations which suggest that optimized devices may have one or two orders of magnitude better performance.

The stability of a fiber optic gyroscope (FOG) in measurement while drilling (MWD) could vary with time because of changing temperature, high vibration, and sudden power failure. The dynamic Allan variance (DAVAR) is a sliding version of the Allan variance. It is a practical tool that could represent the non-stationary behavior of the gyroscope signal. Since the normal DAVAR takes too long to deal with long time series, a fast DAVAR algorithm has been developed to accelerate the computation speed. However, both the normal DAVAR algorithm and the fast algorithm become invalid for discontinuous time series. What is worse, the FOG-based MWD underground often keeps working for several days; the gyro data collected aboveground is not only very time-consuming, but also sometimes discontinuous in the timeline. In this article, on the basis of the fast algorithm for DAVAR, we make a further advance in the fast algorithm (improved fast DAVAR) to extend the fast DAVAR to discontinuous time series. The improved fast DAVAR and the normal DAVAR are used to responsively characterize two sets of simulation data. The simulation results show that when the length of the time series is short, the improved fast DAVAR saves 78.93% of calculation time. When the length of the time series is long ( 6 × 10 5 samples), the improved fast DAVAR reduces calculation time by 97.09%. Another set of simulation data with missing data is characterized by the improved fast DAVAR. Its simulation results prove that the improved fast DAVAR could successfully deal with discontinuous data. In the end, a vibration experiment with FOGs-based MWD has been implemented to validate the good performance of the improved fast DAVAR. The results of the experience testify that the improved fast DAVAR not only shortens computation time, but could also analyze discontinuous time series., Competing Interests: The authors declare no conflict of interest.

Objective: The aim of this work was to develop a novel technique for digital processing of Doppler ultrasound blood flow sensor data from noisy blood flow velocity waveforms., Methods: To evaluate the fluctuating blood flow parameters, various nonlinear dynamics methods and algorithms are often being used. Here, for identification of chaotic and noise components in a fluctuating coronary blood flow, for the first time the Allan variance technique was used. Analysis of different types of noises (White, Brownian, Flicker) was carried out and their strong correlation with fractality of time series (the Hurst exponent) was revealed., Results: Based on a specialized software realizing the developed technique, numerical experiments with real clinical data were carried out. Recommendations for identification of noisy patterns of coronary blood flow in normal and pathological states were developed., Conclusion: The methodology gives us the possibility for the more detailed quantitative and qualitative analysis of a noisy fluctuating blood flow data.

The Allan variance was introduced 50 years ago for analyzing the stability of frequency standards. In addition to its metrological interest, it may be also considered as an estimator of the large trends of the power spectral density (PSD) of frequency deviation. For instance, the Allan variance is able to discriminate different types of noise characterized by different power laws in the PSD. The Allan variance was also used in other fields than time and frequency metrology: for more than 20 years, it has been used in accelerometry, geophysics, geodesy, astrophysics, and even finances. However, it seems that up to now, it has been exclusively applied for time series analysis. We propose here to use the Allan variance on spatial data. Interferometric synthetic aperture radar (InSAR) is used in geophysics to image ground displacements in space [over the synthetic aperture radar (SAR) image spatial coverage] and in time thanks to the regular SAR image acquisitions by dedicated satellites. The main limitation of the technique is the atmospheric disturbances that affect the radar signal while traveling from the sensor to the ground and back. In this paper, we propose to use the Allan variance for analyzing spatial data from InSAR measurements. The Allan variance was computed in XY mode as well as in radial mode for detecting different types of behavior for different space-scales, in the same way as the different types of noise versus the integration time in the classical time and frequency application. We found that radial Allan variance is the more appropriate way to have an estimator insensitive to the spatial axis and we applied it on SAR data acquired over eastern Turkey for the period 2003-2011. Spatial Allan variance allowed us to well characterize noise features, classically found in InSAR such as phase decorrelation producing white noise or atmospheric delays, behaving like a random walk signal. We finally applied the spatial Allan variance to an InSAR time series to detect when the geophysical signal, here the ground motion, emerges from the noise.

The Allan variance is a method to characterize stochastic random processes. The technique was originally developed to characterize the stability of atomic clocks and has also been successfully applied to the characterization of inertial sensors. Inertial navigation systems (INS) can provide accurate results in a short time, which tend to rapidly degrade in longer time intervals. During the last decade, the performance of inertial sensors has significantly improved, particularly in terms of signal stability, mechanical robustness, and power consumption. The mass and volume of inertial sensors have also been significantly reduced, offering system-level design and accommodation advantages. This paper presents a complete methodology for the characterization and modeling of inertial sensors using the Allan variance, with direct application to navigation systems. Although the concept of sensor fusion is relatively straightforward, accurate characterization and sensor-information filtering is not a trivial task, yet they are essential for good performance. A complete and reproducible methodology utilizing the Allan variance, including all the intermediate steps, is described. An end-to-end (E2E) process for sensor-error characterization and modeling up to the final integration in the sensor-fusion scheme is explained in detail. The strength of this approach is demonstrated with representative tests on novel, high-grade inertial sensors. Experimental navigation results are presented from two distinct robotic applications: a planetary exploration rover prototype and an autonomous underwater vehicle (AUV).

Optical fiber links are known as the most performing tools to transfer ultrastable frequency reference signals. However, these signals are affected by phase noise up to bandwidths of several kilohertz and a careful data processing strategy is required to properly estimate the uncertainty. This aspect is often overlooked and a number of approaches have been proposed to implicitly deal with it. Here, we face this issue in terms of aliasing and show how typical tools of signal analysis can be adapted to the evaluation of optical fiber links performance. In this way, it is possible to use the Allan variance (AVAR) as estimator of stability and there is no need to introduce other estimators. The general rules we derive can be extended to all optical links. As an example, we apply this method to the experimental data we obtained on a 1284-km coherent optical link for frequency dissemination, which we realized in Italy.

The origins of the Allan variance trace back 50 years ago to two seminal papers, one by Allan (1966) and the other by Barnes (1966). Since then, the Allan variance has played a leading role in the characterization of high-performance time and frequency standards. Wavelets first arose in the early 1980s in the geophysical literature, and the discrete wavelet transform (DWT) became prominent in the late 1980s in the signal processing literature. Flandrin (1992) briefly documented a connection between the Allan variance and a wavelet transform based upon the Haar wavelet. Percival and Guttorp (1994) noted that one popular estimator of the Allan variance-the maximal overlap estimator-can be interpreted in terms of a version of the DWT now widely referred to as the maximal overlap DWT (MODWT). In particular, when the MODWT is based on the Haar wavelet, the variance of the resulting wavelet coefficients-the wavelet variance-is identical to the Allan variance when the latter is multiplied by one-half. The theory behind the wavelet variance can thus deepen our understanding of the Allan variance. In this paper, we review basic wavelet variance theory with an emphasis on the Haar-based wavelet variance and its connection to the Allan variance. We then note that estimation theory for the wavelet variance offers a means of constructing asymptotically correct confidence intervals (CIs) for the Allan variance without reverting to the common practice of specifying a power-law noise type a priori. We also review recent work on specialized estimators of the wavelet variance that are of interest when some observations are missing (gappy data) or in the presence of contamination (rogue observations or outliers). It is a simple matter to adapt these estimators to become estimators of the Allan variance. Finally we note that wavelet variances based upon wavelets other than the Haar offer interesting generalizations of the Allan variance.

The Modified Allan Variance (MAVAR) was originally defined in 1981 for measuring frequency stability in precision oscillators. Due to its outstanding accuracy in discriminating power-law noise, it attracted significant interest among telecommunications engineers since the early 1990s, when it was approved as a standard measure in international standards, redressed as Time Variance (TVAR), for specifying the time stability of network synchronization signals and of equipment clocks. A dozen years later, the usage of MAVAR was also introduced for Internet traffic analysis to estimate self-similarity and long-range dependence. Further, in this field, it demonstrated superior accuracy and sensitivity, better than most popular tools already in use. This paper surveys the last 25 years of progress in extending the field of application of the MAVAR in telecommunications. First, the rationale and principles of the MAVAR are briefly summarized. Its adaptation as TVAR for specification of timing stability is presented. The usage of MAVAR/TVAR in telecommunications standards is reviewed. Examples of measurements on real telecommunications equipment clocks are presented, providing an overview on their actual performance in terms of MAVAR. Moreover, applications of MAVAR to network traffic analysis are surveyed. The superior accuracy of MAVAR in estimating long-range dependence is emphasized by highlighting some remarkable practical examples of real network traffic analysis.

The Allan variance (AVAR) was introduced 50 years ago as a statistical tool for assessing the frequency standards deviations. For the past decades, AVAR has increasingly been used in geodesy and astrometry to assess the noise characteristics in geodetic and astrometric time series. A specific feature of astrometric and geodetic measurements, as compared with clock measurements, is that they are generally associated with uncertainties; thus, an appropriate weighting should be applied during data analysis. In addition, some physically connected scalar time series naturally form series of multidimensional vectors. For example, three station coordinates time series X, Y, and Z can be combined to analyze 3-D station position variations. The classical AVAR is not intended for processing unevenly weighted and/or multidimensional data. Therefore, AVAR modifications, namely weighted AVAR (WAVAR), multidimensional AVAR (MAVAR), and weighted multidimensional AVAR (WMAVAR), were introduced to overcome these deficiencies. In this paper, a brief review is given of the experience of using AVAR and its modifications in processing astrogeodetic time series.

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 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.

As a noise analysis method for inertial sensors, the traditional Allan variance method requires the storage of a large amount of data and manual analysis for an Allan variance graph. Although the existing online estimation methods avoid the storage of data and the painful procedure of drawing slope lines for estimation, they require complex transformations and even cause errors during the modeling of dynamic Allan variance. To solve these problems, first, a new state-space model that directly models the stochastic errors to obtain a nonlinear state-space model was established for inertial sensors. Then, a neural-extended Kalman filter algorithm was used to estimate the Allan variance coefficients. The real noises of an ADIS16405 IMU and fiber optic gyro-sensors were analyzed by the proposed method and traditional methods. The experimental results show that the proposed method is more suitable to estimate the Allan variance coefficients than the traditional methods. Moreover, the proposed method effectively avoids the storage of data and can be easily implemented using an online processor.

Single-molecule manipulation instruments, such as optical traps and magnetic tweezers, frequently use video tracking to measure the position of a force-generating probe. The instruments are calibrated by comparing the measured probe motion to a model of Brownian motion in a harmonic potential well; the results of calibration are estimates of the probe drag, α, and spring constant, κ. Here, we present both time- and frequency-domain methods to accurately and precisely extract α and κ from the probe trajectory. In the frequency domain, we discuss methods to estimate the power spectral density (PSD) from data (including windowing and blocking), and we derive an analytical formula for the PSD which accounts both for aliasing and the filtering intrinsic to video tracking. In the time domain, we focus on the Allan variance (AV): we present a theoretical equation for the AV relevant to typical single-molecule setups and discuss the optimal manner for computing the AV from experimental data using octave-sampled overlapping bins. We show that, when using maximum-likelihood methods to fit to the data, both the PSD and AV approaches can extract α and κ in an unbiased and low-error manner, though the AV approach is simpler and more robust.

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.

The Allan variance has historically been estimated using heterodyne measurement systems, which have low noise and preserve the carrier phase information needed for long-term stability. The single-sideband phase noise has traditionally been estimated using phase detectors that suppress the carrier to achieve even lower noise. The recent development of the direct-digital phase noise measurement technique makes it possible to estimate both statistics accurately and simultaneously from the same time series of the phase. Our comparison of the 3 techniques has revealed several challenges to the accurate estimation of the Allan variance including undesired aliasing, biased estimators, and spurious signal generation. Investigation of these difficulties has led to several opportunities to improve Allan variance estimation, including the ability to estimate the instrumentation noise floor during a measurement and the existence of an optimum measurement bandwidth. In the end, this has led to faster, easier, more reliable, and more accurate measurement methods.

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.

Much effort is put into minimizing noise in optical tweezers experiments because noise and drift can mask fundamental behaviours of, e.g., single molecule assays. Various initiatives have been taken to reduce or eliminate noise but it has been difficult to quantify their effect. We propose to use Allan variance as a simple and efficient method to quantify noise in optical tweezers setups.We apply the method to determine the optimal measurement time, frequency, and detection scheme, and quantify the effect of acoustic noise in the lab. The method can also be used on-the-fly for determining optimal parameters of running experiments.

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.

Experiments in spintronics necessarily involve the detection of spin polarization. The sensitivity of this detection becomes an important factor to consider when extending the low temperature studies on semiconductor spintronic devices to room temperature, where the spin signal is weaker. In pump-probe experiments, which optically inject and detect spins, the sensitivity is often improved by using a photoelastic modulator (PEM) for lock-in detection. However, spurious signals can arise if diode lasers are used as optical sources in such experiments, along with a PEM. In this work, we eliminated the spurious electromagnetic coupling of the PEM onto the probe diode laser, by the double modulation technique. We also developed a test for spurious modulated interference in the pump-probe signal, due to the PEM. Besides, an order of magnitude enhancement in the sensitivity of detection of spin polarization by Kerr rotation, to 3x10(-8) rad was obtained by using the concept of Allan variance to optimally average the time series data over a period of 416 s. With these improvements, we are able to experimentally demonstrate at room temperature, photoinduced steady-state spin polarization in bulk GaAs. Thus, the advances reported here facilitate the use of diode lasers with a PEM for sensitive pump-probe experiments. They also constitute a step toward detection of spin-injection in Si at room temperature.

An exact solution to the well-known integral transform that relates the spectral density of the instantaneous fractional frequency deviation, Sy(f), to the Allan variance, sigma2y(tau), is presented for the case of a power-law representation of Sy(f). The approximate solution to this integral transform, which is found throughout the literature, also is derived. A graphical convergence analysis is presented, showing the range of applicability of the approximate solution. The results reinforce the use of the approximate solution, which converges quickly to the exact solution under virtually all reasonable measurement conditions.

Auditory-nerve spike trains exhibit fractal behavior, and therefore traditional renewal-point-process models fail to describe them adequately. Previous measures of the fractal exponent of these spike trains are based on the Fano factor and consequently cannot exceed unity. Two estimates of the fractal exponent are considered which do not suffer from this limit: one derived from the Allan variance, which was developed by the authors, and one based on the periodogram. These measures indicate that fractal exponents do indeed exceed unity for some nerve-spike recordings from stimulated primary afferent cat auditory-nerve fibers.

As a MEMS gyroscope is susceptible to environmental interference, its performance is degraded due to random noise. Accurate and rapid analysis of random noise of MEMS gyroscope is of great significance to improve the gyroscope's performance. A PID-DAVAR adaptive algorithm is designed by combining the PID principle with DAVAR. It can adaptively adjust the length of the truncation window according to the dynamic characteristics of the gyroscope's output signal. When the output signal fluctuates drastically, the length of the truncation window becomes smaller, and the mutation characteristics of the intercepted signal are analyzed detailed and thoroughly. When the output signal fluctuates steadily, the length of the truncation window becomes larger, and the intercepted signals are analyzed swiftly and roughly. The variable length of the truncation window ensures the confidence of the variance and shortens the data processing time without losing the signal characteristics. Experimental and simulation results show that the PID-DAVAR adaptive algorithm can shorten the data processing time by 50%. The tracking error of the noise coefficients of angular random walk, bias instability, and rate random walk is about 10% on average, and the minimum error is about 4%. It can accurately and promptly present the dynamic characteristics of the MEMS gyroscope's random noise. The PID-DAVAR adaptive algorithm not only satisfies the requirement of variance confidence but also has a good signal-tracking ability.

Mutations in SARS-CoV-2 have shown effective evasion of population immunity and increased affinity to the cellular receptor angiotensin-converting enzyme 2 (ACE2). However, in the dynamic environment of the respiratory tract, forces act on the binding partners, which raises the question of whether not only affinity but also force stability of the SARS-CoV-2-ACE2 interaction might be a selection factor for mutations. Using magnetic tweezers, we investigate the impact of amino acid substitutions in variants of concern (Alpha, Beta, Gamma and Delta) and on force-stability and bond kinetic of the receptor-binding domain-ACE2 interface at a single-molecule resolution. We find a higher affinity for all of the variants of concern (>fivefold) compared with the wild type. In contrast, Alpha is the only variant of concern that shows higher force stability (by 17%) compared with the wild type. Using molecular dynamics simulations, we rationalize the mechanistic molecular origins of this increase in force stability. Our study emphasizes the diversity of contributions to the transmissibility of variants and establishes force stability as one of the several factors for fitness. Understanding fitness advantages opens the possibility for the prediction of probable mutations, allowing a rapid adjustment of therapeutics, vaccines and intervention measures., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Magnetic tweezers are a single-molecule force and torque spectroscopy technique that enable the mechanical interrogation in vitro of biomolecules, such as nucleic acids and proteins. They use a magnetic field originating from either permanent magnets or electromagnets to attract a magnetic particle, thus stretching the tethering biomolecule. They nicely complement other force spectroscopy techniques such as optical tweezers and atomic force microscopy (AFM) as they operate as a very stable force clamp, enabling long-duration experiments over a very broad range of forces spanning from 10 fN to 1 nN, with 1-10 milliseconds time and sub-nanometer spatial resolution. Their simplicity, robustness, and versatility have made magnetic tweezers a key technique within the field of single-molecule biophysics, being broadly applied to study the mechanical properties of, e.g., nucleic acids, genome processing molecular motors, protein folding, and nucleoprotein filaments. Furthermore, magnetic tweezers allow for high-throughput single-molecule measurements by tracking hundreds of biomolecules simultaneously both in real-time and at high spatiotemporal resolution. Magnetic tweezers naturally combine with surface-based fluorescence spectroscopy techniques, such as total internal reflection fluorescence microscopy, enabling correlative fluorescence and force/torque spectroscopy on biomolecules. This chapter presents an introduction to magnetic tweezers including a description of the hardware, the theory behind force calibration, its spatiotemporal resolution, combining it with other techniques, and a (non-exhaustive) overview of biological applications., (© 2024. The Author(s).)

This paper addresses the problem of stochastic modeling of atomic ensembles under multi-source noise and makes the model interpretable. First, based on Itô's lemma and Allan variance analysis (ITÔ-AVAR), an approach is proposed to model nonstationary stochastic submodels of atomic ensembles. On this basis, the variance decomposition and nonlinear optimization algorithms are utilized to hybridize modeling atomic ensembles with nonlinear and nonstationary properties. Second, an Itô's lemma dynamic allan variance analysis (ITÔ-DAVAR) approach is developed for online modeling of atomic ensembles. Further, an atomic ensembles sensitivity enhancement scheme based on the proposed approach is given, which effectively promotes the progress of quantum instrument engineering. Finally, the proposed scheme are deployed in the optical pumping magnetometer and spin-exchange relaxation-free comagnetometer, respectively, while experimentally verifying the sensitivity of the spin-exchange relaxation-free comagnetometer reaches 5.36×10 -6 degs -1 Hz -1/2 ., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.)

We present the frequency stability performances of a vapor cell Rb clock based on the pulsed optically pumping (POP) technique. The clock has been developed in the frame of a collaboration between INRIM and Leonardo SpA, aiming to realize a space-qualified POP frequency standard. The results here reported were obtained with an engineered physics package, specifically designed for space applications, joint to laboratory-grade optics and electronics. The measured frequency stability expressed in terms of Allan deviation is [Formula: see text] at 1s and achieves the value of [Formula: see text] for integration times of 40000 s (drift removed). This is, to our knowledge, a record result for a vapor-cell frequency standard. In the paper, we show that in order to get this result, a careful stabilization of microwave and laser pulses is required., (© 2023. The Author(s).)

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.

In recent years, the overall performances of inertial Micro-Electro Mechanical Sensors (MEMSs) exhibited substantial improvements to values very close or similar to so-called tactical-grade sensors. However, due to their high costs, numerous researchers are currently focusing on the performance enhancement of cheap consumer-grade MEMS inertial sensors for all those applications (as an example, small unmanned aerial vehicles, UAVs), where cost effectiveness is a relevant request; the use of redundancy proves to be a feasible method for this purpose. In this regard, the authors propose, hereinafter, a suitable strategy aimed at fusing raw measurements provided by multiple inertial sensors mounted on a 3D-printed structure. In particular, accelerations and angular rates measured by the sensors are averaged according to weights associated with the results of an Allan variance approach; the lower the noise figure of the sensors, the greater their weight on the final averaged values. On the other hand, possible effects on the measurements due to the use of a 3D structure in reinforced ONYX (a material capable of providing better mechanical specifications for avionic applications with respect to other solutions for additive manufacturing) were evaluated. The performance of a prototype implementing the considered strategy is compared with that of a tactical-grade inertial measurement unit in stationary conditions, exhibiting differences as low as 0.3 degrees in heading measurements. Moreover, the reinforced ONYX structure does not significantly affect the measured values in terms of both thermal and magnetic field while assuring better mechanical characteristics with respect to other 3D printing materials, thanks to a tensile strength of about 250 MPa and a specific stacking sequence of continuous fibers. Finally, a test conducted on an actual UAV highlights performance very close to that of a reference unit, with root-mean-square error in heading measurements as low as 0.3 degrees in observation intervals up to 140 s.

Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models.

Optically levitated oscillators in high vacuum have excellent environmental isolation and low mass compared with conventional solid-state sensors, which makes them suitable for ultrasensitive force detection. The force resolution usually scales with the measurement bandwidth, which represents the ultimate detection capability of the system under ideal conditions if sufficient time is provided for measurement. However, considering the stability of a real system, a method based on the Allan variance is more reliable to evaluate the actual force detection performance. In this study, a levitated optomechanical system with a force detection sensitivity of 6.33 ± 1.62 zN/Hz 1/2 was demonstrated. And for the first time, the Allan variance was introduced to evaluate the system stability due to the force sensitivity fluctuations. The force detection resolution of 166.40 ± 55.48 yN was reached at the optimal measurement time of 2751 s. The system demonstrated in this work has the best force detection performance in both sensitivity and resolution that have been reported so far for optically levitated particles. The reported high-sensitivity force detection system is an excellent candidate for the exploration of new physics such as fifth force searching, high-frequency gravitational waves detection, dark matter research and so on., Competing Interests: The authors declare that they have no conflicts of interest in this work., (© 2022 The Authors. Publishing Services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.)

Networks of optical clocks find applications in precise navigation 1,2 , in efforts to redefine the fundamental unit of the 'second' 3-6 and in gravitational tests 7 . As the frequency instability for state-of-the-art optical clocks has reached the 10 -19 level 8,9 , the vision of a global-scale optical network that achieves comparable performances requires the dissemination of time and frequency over a long-distance free-space link with a similar instability of 10 -19 . However, previous attempts at free-space dissemination of time and frequency at high precision did not extend beyond dozens of kilometres 10,11 . Here we report time-frequency dissemination with an offset of 6.3 × 10 -20  ± 3.4 × 10 -19 and an instability of less than 4 × 10 -19 at 10,000 s through a free-space link of 113 km. Key technologies essential to this achievement include the deployment of high-power frequency combs, high-stability and high-efficiency optical transceiver systems and efficient linear optical sampling. We observe that the stability we have reached is retained for channel losses up to 89 dB. The technique we report can not only be directly used in ground-based applications, but could also lay the groundwork for future satellite time-frequency dissemination., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

With the development of modern industry, small UAVs have been widely used in agriculture, mapping, meteorology, and other fields. There is an increasing demand for the core attitude-solving algorithm of UAV flight control. In this paper, at first, a novel attitude solving algorithm is proposed by using quaternions to represent the attitude matrix and using Allan variance to analyze the gyroscope error and to quantify the trend of the error over time, so as to improve the traditional Mahony complementary filtering. Simulation results show that the six-axis data from the initial sensors (gyroscope and accelerometer) agree well with the measured nine-axis data with an extra magnetometer, which reduces the complexity of the system hardware. Second, based on the hardware platform, the six-axis data collected from MPU6050 are sent to FPGA for floating-point operation, transcendental function operation, and attitude solution module for processing through IIC communication, which effectively validates the attitude solution by using the proposed method. Finally, the proposed algorithm is applied to a practical scenario of a quadrotor UAV, and the test results show that the RMSE does not exceed 2° compared with the extended Kalman filter method. The proposed system simplifies the hardware but keeps the accuracy and speed of the solution, which may result in application in UAV flight control.

In this study, a dynamic equation for a micromechanical resonant accelerometer based on electrostatic stiffness is analyzed, and the parameters influencing sensitivity are obtained. The sensitivity can be increased by increasing the detection proof mass and the area facing the detection capacitor plate and by decreasing the stiffness of the fold beams and the initial distance between the plate capacitors. Sensitivity is also related to the detection voltage: the larger the detection voltage, the greater the sensitivity. The dynamic equation of the closed-loop self-excited drive of the accelerometer is established, and the steady-state equilibrium point of the vibration amplitude and the stability condition are obtained using the average period method. Under the constraint conditions of the PI controller, when the loading acceleration changes, the vibration amplitude is related to the reference voltage and the pre-conversion coefficient of the interface circuit and has nothing to do with the quality factor. When the loading voltage is 2 V, the sensitivity is 321 Hz/g. Three Allan variance analysis methods are used to obtain the frequency deviation of 0.04 Hz and the amplitude deviation of 0.06 mVwithin 30 min at room temperature. When the temperature error in the incubator is ±0.01 °C, the frequency deviation decreases to 0.02 Hz, and the resolution is 56ug. The fully overlapping Allan variance analysis method (FOAV) requires a large amount of data and takes a long time to implement but has the most accurate stabilityof the three methods.

Structural damage detection using inclinometers is getting wide attention from researchers. However, the high price of inclinometers limits this system to unique structures with a relatively high structural health monitoring (SHM) budget. This paper presents a novel low-cost inclinometer, the low-cost adaptable reliable angle-meter (LARA), which combines five gyroscopes and five accelerometers to measure inclination. LARA incorporates Internet of Things (IoT)-based microcontroller technology enabling wireless data streaming and free commercial software for data acquisition. This paper investigates the accuracy, resolution, Allan variance and standard deviation of LARA produced with a different number of combined circuits, including an accelerometer and a gyroscope. To validate the accuracy and resolution of the developed device, its results are compared with those obtained by numerical slope calculations and a commercial inclinometer (HI-INC) in laboratory conditions. The results of a load test experiment on a simple beam model show the high accuracy of LARA (0.003 degrees). The affordability and high accuracy of LARA make it applicable for structural damage detection on bridges using inclinometers.

Exceptional points (EP) are non-Hermitian degeneracies where eigenvalues and their corresponding eigenvectors coalesce 1-4 . Recently, EPs have attracted attention as a means to enhance the responsivity of sensors, through the abrupt resonant detuning occurring in their proximity 5-20 . In many cases, however, the EP implementation is accompanied by noise enhancement, leading to the degradation of the sensor's performance 15-20 . The excess noise can be of fundamental nature (owing to the eigenbasis collapse) or of technical nature associated with the amplification mechanisms utilized for the realization of EPs. Here we show, using an EP-based parity-time symmetric 21,22 electromechanical accelerometer, that the enhanced technical noise can be surpassed by the enhanced responsivity to applied accelerations. The noise owing to eigenbasis collapse is mitigated by exploiting the detuning from a transmission peak degeneracy (TPD) - which forms when the sensor is weakly coupled to transmission lines - as a measure of the sensitivity. These TPDs occur at a frequency and control parameters for which the biorthogonal eigenbasis is still complete and are distinct from the EPs of the parity-time symmetric sensor. Our device shows a threefold signal-to-noise-ratio enhancement compared with configurations for which the system operates away from the TPD., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

The use of magnetic tweezers for single-molecule micromanipulation has evolved rapidly since its introduction approximately 30 years ago. Magnetic tweezers have provided important insights into the dynamic activity of DNA-processing enzymes, as well as detailed, high-resolution information on the mechanical properties of DNA. These successes have been enabled by major advancements in the hardware and software components of these devices. These developments now allow for a much richer mechanistic understanding of the functions and mechanisms of DNA-binding enzymes. In this review, the authors briefly discuss the fundamental principles of magnetic tweezers and describe the advancements that have made it a superlative tool for investigating, at the single-molecule level, DNA and its interactions with DNA-binding proteins.

The paper deals with performance enhancement of low-cost, consumer-grade inertial sensors realized by means of Micro Electro-Mechanical Systems (MEMS) technology. Focusing their attention on the reduction of bias instability and random walk-driven drift of cost-effective MEMS accelerometers and gyroscopes, the authors hereinafter propose a suitable method, based on a redundant configuration and complemented with a proper measurement procedure, to improve the performance of low-cost, consumer-grade MEMS sensors. The performance of the method is assessed by means of an adequate prototype and compared with that assured by a commercial, expensive, tactical-grade MEMS inertial measurement unit, taken as reference. Obtained results highlight the promising reliability and efficacy of the method in estimating position, velocity, and attitude of vehicles; in particular, bias instability and random walk reduction greater than 25% is, in fact, experienced. Moreover, differences as low as 0.025 rad and 0.89 m are obtained when comparing position and attitude estimates provided by the prototype and those granted by the tactical-grade MEMS IMU.

Vascular complications following solid organ transplantation may lead to graft ischemia, dysfunction or loss. Imaging approaches can provide intermittent assessments of graft perfusion, but require highly skilled practitioners and do not directly assess graft oxygenation. Existing systems for monitoring tissue oxygenation are limited by the need for wired connections, the inability to provide real-time data or operation restricted to surface tissues. Here, we present a minimally invasive system to monitor deep-tissue O 2 that reports continuous real-time data from centimeter-scale depths in sheep and up to a 10-cm depth in ex vivo porcine tissue. The system is composed of a millimeter-sized, wireless, ultrasound-powered implantable luminescence O 2 sensor and an external transceiver for bidirectional data transfer, enabling deep-tissue oxygenation monitoring for surgical or critical care indications., (© 2021. The Author(s), under exclusive licence to Springer Nature America, Inc.)

This paper introduces a differential vibrating beam MEMS accelerometer demonstrating excellent long-term stability for applications in gravimetry and seismology. The MEMS gravimeter module demonstrates an output Allan deviation of 9 μGal for a 1000 s integration time, a noise floor of 100 μGal/√Hz, and measurement over the full ±1 g dynamic range (1 g = 9.81 ms -2 ). The sensitivity of the device is demonstrated through the tracking of Earth tides and recording of ground motion corresponding to a number of teleseismic events over several months. These results demonstrate that vibrating beam MEMS accelerometers can be employed for measurements requiring high levels of stability and resolution with wider implications for precision measurement employing other resonant-output MEMS devices such as gyroscopes and magnetometers.

MEMS (Micro-Electro-Mechanical Systems) gyroscope is the core component in the posture recognition and assistant positioning, of which the complex noise limits its performance. It is essential to filter the noise and obtain the true value of the measurements. Then an adaptive filtering method was proposed. Firstly, noises of MEMS gyroscope were analyzed to build the basic framework of the dynamic noise model. Secondly, the dynamic Allan variance was improved with a novel truncation window based on the entropy features, which referred to the parameters in the noise model. Thirdly, the adaptive Kalman filter was derived from the dynamic noise model. Finally, the simulation and experiment were carried out to verify the method. The results prove that the improved dynamic Allan variance can extract noise feature distinctly, and the filtering precision in the new method is relatively high., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.)

In many studies of environmental risk factors for disease, researchers use the location at diagnosis as a geographic reference for environmental exposures. However, many environmental pollutants change continuously over space and time. The dynamic characteristics of these pollutants coupled with population mobility in the United States suggest that for diseases with long latencies like cancer, historic exposures may be more relevant than exposure at the time of diagnosis. In this article, we evaluated to what extent the commonly used assumption of no population mobility results in increased bias in the estimates of the relationship between environmental exposures and long-latency health outcomes disease in a case-control study. We conducted a simulation study using the residential histories of a random sample from the National Institutes of Health-AARP (formerly American Association of Retired Persons) Diet and Health Study. We simulated case-control status based on subject exposure and true exposure effects that varied temporally. We compared estimates from models using only subject location at diagnosis to estimates where subjects were assumed to be mobile. Ignoring population mobility resulted in underestimates of subject exposure, with largest deviations observed at time points further away from study enrollment. In general, the effect of population mobility on the bias of the estimates of the relationship between the exposure and the outcome was more prominent with exposures that showed substantial spatial and temporal variability. Based on our results, we recommend using residential histories when environmental exposures and disease latencies span a long enough time period that mobility is important., (© 2020 John Wiley & Sons, Ltd.)