Spectrum feature extraction method combining Allan variance, VMD, and PSD.

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.

Modeling of nonlinear and nonstationary stochasticity for atomic ensembles.

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 5.36×10-6degs-1Hz-1/2.

Adaptive Dynamic Analysis of MEMS Gyroscope Random Noise Based on PID-DAVAR.

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.

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.

Innovative Fusion Strategy for MEMS Redundant-IMU Exploiting Custom 3D Components.

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.

An Algorithm for Online Stochastic Error Modeling of Inertial Sensors in Urban Cities.

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.

Yoctonewton force detection based on optically levitated oscillator.

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/Hz1/2 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.

Attitude Solving Algorithm and FPGA Implementation of Four-Rotor UAV Based on Improved Mahony Complementary Filter.

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.

A Novel Wireless Low-Cost Inclinometer Made from Combining the Measurements of Multiple MEMS Gyroscopes and Accelerometers.

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.

Closed-Loop Control and Output Stability Analysis of a Micromechanical Resonant Accelerometer.

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.

Magnetic tweezers: development and use in single-molecule research.

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.

Performance Enhancement of Consumer-Grade MEMS Sensors through Geometrical Redundancy.

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.

Adaptive filtering for MEMS gyroscope with dynamic noise model.

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.

Requirement Assessment of the Relative Spatial Accuracy of a Motion-Constrained GNSS/INS in Shortwave Track Irregularity Measurement.

Modern railway track health monitoring requires high accuracy measurements to ensure comfort and safety. Although Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integration has been extended to track geometry measurements to improve the work efficiency, it has been questioned due to its positioning accuracy at the centimeter or millimeter level. We propose the relative spatial accuracy based on the accuracy requirement of track health monitoring. A requirement assessment of the spatial relative accuracy is conducted for shortwave track irregularity measurements based on evaluation indicators and relative accuracy calculations. The threshold values of the relative spatial accuracy that satisfy the constraints of shortwave track irregularity measurements are derived. Motion-constrained GNSS/INS integration is performed to improve the navigation accuracy considering the dynamic characteristics of the track geometry measurement trolley. The results of field tests show that the mean square error and the Allan deviation of the relative position errors of motion-constrained GNSS/INS integration are smaller than 0.67 mm and 0.16 mm, respectively, which indicates that this approach meets the accuracy requirements of shortwave track irregularities, especially vertical irregularities. This work can provide support for the application of GNSS/INS systems in track irregularity measurement.

On the Noise Complexity in an Optical Motion Capture Facility.

Optical motion capture systems are state-of-the-art in motion acquisition; however, like any measurement system they are not error-free: noise is their intrinsic feature. The works so far mostly employ a simple noise model, expressing the uncertainty as a simple variance. In the work, we demonstrate that it might be not sufficient and we prove the existence of several types of noise and demonstrate how to quantify them using Allan variance. Such a knowledge is especially important for using optical motion capture to calibrate other techniques, and for applications requiring very fine quality of recording. For the automated readout of the noise coefficients, we solve the multidimensional regression problem using sophisticated metaheuristics in the exploration-exploitation scheme. We identified in the laboratory the notable contribution to the overall noise from white noise and random walk, and a minor contribution from blue noise and flicker, whereas the violet noise is absent. Besides classic types of noise we identified the presence of the correlated noises and periodic distortion. We analyzed also how the noise types scale with an increasing number of cameras. We had also the opportunity to observe the influence of camera failure on the overall performance.

Random Error Analysis of MEMS Gyroscope Based on an Improved DAVAR Algorithm.

In view that traditional dynamic Allan variance (DAVAR) method is difficult to make a good balance between dynamic tracking capabilities and the confidence of the estimation. And the reason is the use of a rectangular window with the fixed window length to intercept the original signal. So an improved dynamic Allan variance method was proposed. Compared with the traditional Allan variance method, this method can adjust the window length of the rectangular window adaptively. The data in the beginning and terminal interval was extended with the inverted mirror extension method to improve the utilization rate of the interval data. And the sliding kurtosis contribution coefficient and kurtosis were introduced to adjust the length of the rectangular window by sensing the content of shock signal in terminal interval. The method analyzed the window length change factor in different stable conditions and adjusted the rectangular window's window length according to the kurtosis, sliding kurtosis contribution coefficient. The test results show that the more the kurtosis stability threshold was close to 3, the stronger the dynamic tracking ability of DAVAR would be. But the kurtosis stability threshold was too close to 3, there was a misjudgement in kurtosis analysis of signal stability, resulting in distortion of DAVAR analysis results. When using the improved DAVAR method, the kurtosis stability threshold can be close to 3 to improve the tracking ability and the estimation confidence in stable interval. Therefore, it solved the problem that the dynamic Allan variance tracking ability and confidence level were difficult to take into account, and also solved the problem of misjudgement in the stability analysis of kurtosis.

Vibration Noise Modeling for Measurement While Drilling System Based on FOGs.

Aiming to improve survey accuracy of Measurement While Drilling (MWD) based on Fiber Optic Gyroscopes (FOGs) in the long period, the external aiding sources are fused into the inertial navigation by the Kalman filter (KF) method. The KF method needs to model the inertial sensors' noise as the system noise model. The system noise is modeled as white Gaussian noise conventionally. However, because of the vibration while drilling, the noise in gyros isn't white Gaussian noise any more. Moreover, an incorrect noise model will degrade the accuracy of KF. This paper developed a new approach for noise modeling on the basis of dynamic Allan variance (DAVAR). In contrast to conventional white noise models, the new noise model contains both the white noise and the color noise. With this new noise model, the KF for the MWD was designed. Finally, two vibration experiments have been performed. Experimental results showed that the proposed vibration noise modeling approach significantly improved the estimated accuracies of the inertial sensor drifts. Compared the navigation results based on different noise model, with the DAVAR noise model, the position error and the toolface angle error are reduced more than 90%. The velocity error is reduced more than 65%. The azimuth error is reduced more than 50%.

Reduced-Drift Virtual Gyro from an Array of Low-Cost Gyros.

A Kalman filter approach for combining the outputs of an array of high-drift gyros to obtain a virtual lower-drift gyro has been known in the literature for more than a decade. The success of this approach depends on the correlations of the random drift components of the individual gyros. However, no method of estimating these correlations has appeared in the literature. This paper presents an algorithm for obtaining the statistical model for an array of gyros, including the cross-correlations of the individual random drift components. In order to obtain this model, a new statistic, called the "Allan covariance" between two gyros, is introduced. The gyro array model can be used to obtain the Kalman filter-based (KFB) virtual gyro. Instead, we consider a virtual gyro obtained by taking a linear combination of individual gyro outputs. The gyro array model is used to calculate the optimal coefficients, as well as to derive a formula for the drift of the resulting virtual gyro. The drift formula for the optimal linear combination (OLC) virtual gyro is identical to that previously derived for the KFB virtual gyro. Thus, a Kalman filter is not necessary to obtain a minimum drift virtual gyro. The theoretical results of this paper are demonstrated using simulated as well as experimental data. In experimental results with a 28-gyro array, the OLC virtual gyro has a drift spectral density 40 times smaller than that obtained by taking the average of the gyro signals.

Application of Fast Dynamic Allan Variance for the Characterization of FOGs-Based Measurement While Drilling.

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.

Analysis of chaotic and noise processes in a fluctuating blood flow using the Allan variance technique.

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.