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Since the full system deployment of BDS-3 in July 2020, it has provided stable and reliable positioning, navigation and timing (PNT) services for users around the world. It is an urgent task to explore the potential performance of precise point positioning (PPP) based on the full constellation of BDS-2/BDS-3. This research presented the global satellite visibility of BDS-2/BDS-3, analyzed the stability and accuracy of BDS-2 and BDS-3 rubidium clocks and hydrogen clocks, jointly estimated the BDS-2 and BDS-3 fractional cycle biases (FCB) and evaluated the PPP performance with ambiguity resolution (AR). Due to the fact that International GNSS Service (IGS) precise products have a great impact on narrow-lane (NL) FCB estimation, the FCB obtained by using the precise products from CODE (Center for Orbit Determination in Europe) and GBM (Deutsches GeoForschungsZentrum) in two different analysis centers and the FCB obtained by using GBM precise products with different calculation strategies are analyzed. In addition, the experimental data from Multi-GNSS Experiment (MGEX), EUREF (EPN) and Germany (GPN) observation networks are used to evaluate the influence of orbital errors on BDS FCB estimation. For wide-lane (WL) FCB, MGEX WL FCB has the highest accuracy, followed by EPN and GPN. On the contrary, for NL FCB, MGEX NL FCB has the worst accuracy, followed by EPN, and GPN is the best. Eventually, numerous experiment results showed that compared with the static float solution, the PPP fixed solutions in East (E), North (N) and Up (U) directions are improved by 32.9%, 27.7%, 13.8% for BDS-3 and 10.0%, 7.5%, 3.8% for BDS-2/BDS-3. Compared with the kinematic float solution, the PPP fixed solutions in E, N and U directions are improved by 27.9%, 23.4%, 16.6% for BDS-3 and 15.9%, 8.9%, 5.3% for BDS-2/BDS-3. [ABSTRACT FROM AUTHOR]

The intelligent transportation systems (ITS) using radio frequency (RF) face challenges like interference and limited bandwidth compared to visible light communication (VLC). Integrating vehicular VLC (V-VLC) utilizing the existing light-emitting diodes (LEDs) in automobiles could provide a complementary approach to mitigate RF constraints. Performance degradation by background noise from sunlight can undermine signal quality. So, improving performance and managing interference are the keys to better V-VLC operation. This work proposes a solar noise suppression method for a V-VLC system, leveraging Allan variance and an extended Kalman filter (EKF). Based on the obtained Allan variance, updates are made to the observation model, state vector, and observation noise covariance matrix to achieve superior performance. Minimum mean square error (MMSE) equalization is used. The proposed filter efficiently minimizes the notable autocorrelation triggered by the solar noise, resulting in a bit error rate (BER) reduction of approximately 88% compared to the system without the adaptive filter. This increased convergence highlights the possibility of higher communication performance and reliability. Hence, this work provides a novel adaptive EKF design and offers valuable perspectives on the importance of Allan variance in enhancing the V-VLC system. [ABSTRACT FROM AUTHOR]

Due to the poor bias repeatability and large random noise of a micro electro mechanical system (MEMS), the Allan variance was used to analyze the random angle walk of MEMS. The information fusion algorithm of array gyro was designed by using Allan variance identification value and weighted least square method, which could effectively reduce the random angle walk and respond to the true angular rate in real time under both static and dynamic conditions. For the constant drift of MEMS gyro, a two-position calibration scheme was designed combined with the observability of the error of the inertial navigation system, so as to complete system-level calibration of constant drift. Simulation results show that the method proposed in this paper effectively reduces the random angle walk and the constant drift of MEMS gyro and significantly improves the inertial measurement accuracy of MEMS.

Abstract 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.

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. [ABSTRACT FROM AUTHOR]

Visible light communication (VLC) can serve as a supplement to the radio frequency to address its inherent constraints. VLC can be easily implemented in vehicles using their existing LED components. Sunlight interference can cause significant variation in the background noise powers, leading to signal-to-noise ratio (SNR) degradation in vehicular VLC (VVLC) communication. Hence, it is necessary to improve the performance besides interference. Allan variance is a temporal analysis approach that can extract the noise from the received data. In this article, an Allan variance-based adaptive noise canceller for a VVLC system is proposed and evaluated. Based on the Allan variance obtained, the step size and the number of taps of the adaptive filter are adjusted for superior performance. This proposed filter effectively mitigates the pronounced autocorrelation induced by the noise interference. It yields about an 85% bit error rate (BER) reduction compared to the conventional filter. This improved convergence underscores the potential for enhanced communication performance and reliability. The balanced distribution of the Manchester encoded signal outperforms NRZ encoding. Thus, this work contributes a novel adaptive noise canceller design for a VVLC system and also provides valuable insights to the significance of Allan variance in the VLC system performance. [ABSTRACT FROM AUTHOR]

A True Random Number Generator (TRNG) is an important component in cryptographic algorithms and protocols. The Rosin Autonomous Boolean Network (ABN) digital TRNG has been widely studied due to its nice properties, such as low energy consumption, high speed, strong platform portability, and strong randomness. However, there is still a lack of suitable entropy models to deduce the requirement of design parameters to ensure true randomness. The current model to evaluate the entropy of oscillator-based TRNGs is not applicable for Rosin ABN TRNGs due to low-frequency noise. This work presents a new, suitable stochastic model to evaluate the entropy of Rosin ABN TRNGs. Theoretical analysis and simulation experiments verify the correctness and the effectiveness of the model, and, finally, the appropriate sampling parameters for Rosin ABN TRNGs are given for sufficient entropy per random bit to ensure true randomness. [ABSTRACT FROM AUTHOR]

A common technique for navigation and positioning applications is the Global Positioning System (GPS)/Inertial Navigation System (INS) integration, which combines the strengths of GPS and INS to offer accurate and reliable information. However, the performance of the GPS/INS integration deteriorates during a GPS outage, which happens when natural or artificial factors block the GPS signal. The novelty of this paper is improving GPS/INS integration performance during GPS outages using Incremental Regularized Gated Recurrent Unit (IncRGRU) learning and Lifting Wavelet Transform (LWT). Incremental learning is a learning paradigm that can update the model parameters online from streaming data without forgetting the previous ones. Moreover, regularization is a technique that improves the network's generalization and avoids overfitting by adding some constraints or penalties to the model. In this way, the GPS signal is modeled by IncRGRU learning, and the Kalman filter corrects the INS output. Furthermore, LWT removes the noise from the sensors' signals. This algorithm has lower complexity and can work in real-time compared to conventional wavelet transforms. The performance of GPS/INS integration during GPS outages and the accuracy and robustness of GPS/INS integration is significantly improved by using LWT-IncRGRU on real-world datasets. The positioning errors are reduced by an average of 76% during GPS outages, and an average of 69% improves the GPS/INS integration compared to existing methods.

Featured Application: The potential use of presented methods for the selection of appropriate sensors for measurement systems and synthesis of measurement algorithms. The establishment of the application possibilities, limitations, and appropriate operating conditions of existing measurement systems. MEMS (micro-electro-mechanical system) gyroscopes and accelerometers are used in several applications. They are very popular due to their small size, low price, and accessibility. The design of MEMS accelerometers enables the measurement of vibrations, with frequencies from tenths of hertz to even 1 kHz. MEMS gyroscopes can be applied to measure angular rates, and indirectly also angular oscillations with frequencies similar to accelerometers. Despite significant stochastic errors, MEMS sensors are used not only in popular domestic appliances (e.g., smartphones) but also in safety-critical units, such as aeronautical attitude and heading reference systems (AHRSs). In engineering, methods of stochastic properties analysis are important tools for sensor selection, verification, and the design of measurement algorithms. In this article, three methods used for the analysis of stochastic properties of sensors are presented and comparative analyses are shown. The applied measurement frequencies (1 kHz) were much higher than those typically found in MEMS sensor applications. Additionally, an exemplary analysis of temperature drift frequency, as well as the possibility for the synthesis of complementary filter parameters with the use of the described methods, is shown. Assessment of the stochastic properties of MEMS accelerometers and gyroscopes was performed under both constant and variable temperature conditions (during warm-up after switching on) with the use of classic methods, such as power spectral density (PSD) and Allan variance (AV), as well as the less known but very promising generalized method of wavelet moments (GMWM). [ABSTRACT FROM AUTHOR]

An Inertial Navigation System (INS) is a standalone system that provides continuous navigation information on the position, velocity, and attitude in various conditions. Gyroscopes and accelerometers are essential components of INS. However, these sensors are prone to errors that accumulate over time and degrade the accuracy of the INS. Therefore, enhancing the performance of INS is a challenging problem. This paper aims to address this problem by proposing a method to reduce errors in real-time processing. The method uses Lifting Wavelet Transform (LWT), a popular denoising technique that belongs to the wavelet family and has an advantage over the classic wavelets in terms of time and computation complexity. Moreover, the method employs an optimization technique based on the Genetic algorithm as an intelligent averaging for combining different multi-level LWTs, which significantly improves the accuracy and efficiency of INSs. Finally, a new and implementable structure is introduced for denoising inertial sensors. The results show that the proposed method achieves an 83% and 59% improvement in gyroscope and accelerometer data for dynamic data, compared with raw data. Besides, for static data, there are 71% and 36% improvements in gyroscope and accelerometer data, respectively.

This article is a tutorial describing the process and issues related to developing a state-space model for the stochastic errors affecting an Inertial Measurement Unit (IMU). The starting point is the instrument error characterization data sheet provided by the manufacturer, which is typically either an Allan Variance graph or the parameters extracted from that graph. Along with this tutorial, supplementary software is available for open source distribution that calculates and plots the Allan Variance for a given set of data; extracts optimal parameters (e.g., $Q_N$, $Q_B$, $Q_K$, and $T_B$) from Allan Variance data for a given model structure; and, computes and simulates of the discrete-time equivalent model.

An Inertial Navigation System (INS) is a standalone system that provides continuous navigation information on the position, velocity, and attitude in various conditions. Gyroscopes and accelerometers are essential components of INS. However, these sensors are prone to errors that accumulate over time and degrade the accuracy of the INS. Therefore, enhancing the performance of INS is a challenging problem. This paper aims to address this problem by proposing a method to reduce errors in real-time processing. The method uses Lifting Wavelet Transform (LWT), a popular denoising technique that belongs to the wavelet family and has an advantage over the classic wavelets in terms of time and computation complexity. Moreover, the method employs an optimization technique based on the Genetic algorithm as an intelligent averaging for combining different multi-level LWTs, which significantly improves the accuracy and efficiency of INSs. Finally, a new and implementable structure is introduced for denoising inertial sensors. The results show that the proposed method achieves an 83% and 59% improvement in gyroscope and accelerometer data for dynamic data, compared with raw data. Besides, for static data, there are 71% and 36% improvements in gyroscope and accelerometer data, respectively. [ABSTRACT FROM AUTHOR]

To understand the error sources present in inertial sensors, both the white (time-invariant) and correlated noise sources must be properly characterized. To understand both sources, the standard approach (IEEE standards 647-2006, 952-2020) is to compute the Allan variance of the noise and then use human-based interpretation of linear trends to estimate the separate noise sources present in a sensor. Recent work has sought to overcome the graphical nature and visual-inspection basis of this approach leading to more accurate noise estimates. However, when using noise characterization in a filter, it is important that the noise estimates be not only accurate but also conservative, i.e., that the estimated noise parameters overbound truth. In this paper, we propose a novel method for automatically estimating conservative noise parameters using the Allan variance. Results of using this method to characterize a low-cost MEMS IMU (Analog Devices ADIS16470) are presented, demonstrating the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

At the Istituto Nazionale di Ricerca Metrologica (INRIM), a commercial dual source high resistance bridge has been optimized by means of the application of statistical tools and of the analysis of measurements distributions. These tools help to achieve the best precision for resistance ratio measurements in the range 10 TΩ ÷ 100 TΩ. A measurement procedure consisting of multiple steps, in which at each one the value of the resistor under calibration is updated and has been considered the best one. With this procedure, at the third step, the lowest standard deviation of the mean and the measurements distribution approximately normal are obtained regardless of the settle time, of the resistance ratio, of the measurement voltages and of the resistors under comparison. This comes from the achievement of the white noise regime and from a bridge balance close to the ideal. This measurement procedure therefore allows also to achieve the lowest measurement uncertainty due to the minimization of the type A uncertainty. The Allan variance and the power spectral density were used to identify the white noise analyzing the detector readings. Strict triangulation rules were also established and applied to validate both the measurement process and the chosen model to extrapolate the values of the standard resistors at low voltages. [ABSTRACT FROM AUTHOR]

The subject of study in this article is a method for industrial equipment vibration diagnostics that uses discrete Fourier transform and Allan variance to increase precision and accuracy of industrial equipment vibration diagnostics processes. We propose IoT-oriented solutions based on smart sensors. The primary objectives include validating the practicality of employing platform-oriented technologies for vibro-diagnostics of industrial equipment, creating software and hardware solutions for the IoT platform, and assessing measurement accuracy and precision through the analysis of measurement results in both time and frequency domains. The IoT system architecture for industrial equipment vibration diagnostics consists of three levels. At the autonomous sensor level, vibration acceleration indicators are obtained and transmitted via a BLE digital wireless data transmission channel to the second level, the hub, which is based on a BeagleBone single-board microcomputer. The computing power of BeagleBone is sufficient to work with artificial intelligence algorithms. At the third level of the server platform, the tasks of diagnosing and predicting the state of the equipment are solved, for which the Dictionary Learning algorithm implemented in the Python programming language is used. The verification of the accuracy and precision of the vibration diagnostics system was carried out on the developed stand. A comparison of the expected and measured results in the frequency and time domains confirms the correct operation of the entire system. [ABSTRACT FROM AUTHOR]

The integration of Inertial Navigation Systems and Global Navigation Satellite Systems (GNSS) represents the core navigation unit for mobile platforms in open sky environments. A realistic assessment of the accuracy of the navigation solution depends on the accurate modelling of inertial sensor errors. Sensor noise and biases contribute most to short-term navigation errors. For the latter, different models can be used, varying in complexity. This paper investigates how the use of two different models for the accelerometer bias affects the accuracy of the state estimate in an extended Kalman filter. For this purpose, the Allan variance technique is applied to a data sequence from a specific inertial sensor to identify and quantify the underlying noise processes. The estimated noise parameters are used to characterise a bias model for the accelerometers that in addition to the static bias model takes non-white noise processes of the inertial sensor under investigation into account. This detailed accelerometer bias model is compared to a classical modelling approach that only considers static biases. Both approaches are evaluated based on simulation studies for continuous and intermittent GNSS coverages. The results show no significant difference between the two modelling approaches in terms of horizontal position and attitude precision. Furthermore, the correctness of the accelerometer bias estimates is not significantly affected by the modelling approach. All in all, it can be concluded that a detailed bias model of the accelerometers does not outperform the classical modelling approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

Recently, an enormous number of concepts have been introduced as new insights into seismogeodetic tools and algorithms. Integration of Global Navigation Satellite Systems (GNSS) with accelerometers is a well-known and widely used approach for estimating co-seismic displacements. In this study, we present a two-stage Kalman Filtering (TSKF) approach for seismogeodetic applications with low-cost accelerometers embedded in smartphones. The TSKF is initialized after a cost-effective and magnetometer-aided attitude estimation of accelerations in the sensor frame with respect to the local geodetic (topocentric) frame using the Singular Value Decomposition (SVD) method. In the first stage of TSKF, correlated noise processes in GNSS positions identified by the Allan Variance (AV) analysis are estimated with a linear Kalman Filter (LKF) and displacements are reflected in the innovation sequence of the LKF. In the second stage, the innovation sequence of the first stage LKF is integrated with the smartphone accelerations by a multi-rate Kalman Filter. The performance of TSKF was evaluated with harmonic motion and earthquake experiments using a single-axis shake table in a high multipath environment. Results of harmonic motion experiments showed that TSKF can produce mm-level amplitude deviations however the effect of phase shift decreases the performance and may cause mm to cm-level root mean square (RMS). On the other hand, the performance of the TSKF in earthquake experiments resulted in mm-level RMS values. In addition, comparisons of TSKF with an existing method i.e. the Multi-Rate Kalman Filter (MKF) show that TSKF may significantly increase the performance of displacement estimations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

MEMS (micro-electro-mechanical system) gyroscopes and accelerometers are used in several applications. They are very popular due to their small size, low price, and accessibility. The design of MEMS accelerometers enables the measurement of vibrations, with frequencies from tenths of hertz to even 1 kHz. MEMS gyroscopes can be applied to measure angular rates, and indirectly also angular oscillations with frequencies similar to accelerometers. Despite significant stochastic errors, MEMS sensors are used not only in popular domestic appliances (e.g., smartphones) but also in safety-critical units, such as aeronautical attitude and heading reference systems (AHRSs). In engineering, methods of stochastic properties analysis are important tools for sensor selection, verification, and the design of measurement algorithms. In this article, three methods used for the analysis of stochastic properties of sensors are presented and comparative analyses are shown. The applied measurement frequencies (1 kHz) were much higher than those typically found in MEMS sensor applications. Additionally, an exemplary analysis of temperature drift frequency, as well as the possibility for the synthesis of complementary filter parameters with the use of the described methods, is shown. Assessment of the stochastic properties of MEMS accelerometers and gyroscopes was performed under both constant and variable temperature conditions (during warm-up after switching on) with the use of classic methods, such as power spectral density (PSD) and Allan variance (AV), as well as the less known but very promising generalized method of wavelet moments (GMWM).

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. [ABSTRACT FROM AUTHOR]

The impact of phase noise on the short-term frequency stability (i.e. the Allan deviation with smaller averaging time) of a frequency source has been discussed in detail in the paper. The paper also describes a technique to estimate the Allan deviation values of a frequency source from its measured phase noise plot. Using the technique described here, the Allan deviations of a 10 MHz Rubidium Atomic Frequency Source (RAFS) of an IRNSS (Indian Regional Navigation Satellite System) satellite have been estimated. The estimated Allan deviation values thus obtained from the measured phase noise plot of the RAFS are then compared with the measured Allan deviation values obtained by standard methods (such as the Standard Reference Source method and the 3-Corner Hat method) during Integrated Spacecraft Testing of the IRNSS satellites. [ABSTRACT FROM AUTHOR]

The gyroscope sensor has multiple applications in consumer electronics, aircraft navigation, and control systems. Significant errors that match the corresponding data are a typical disadvantage of this sensor. This needs to be done by making error models that can be used to get the right level of measurement accuracy. For high-precision space applications, the navigation design system should take into account the angle random walk (N), bias instability error (B), and rate random walk (K) of the BMG160 gyroscope. For this reason, this paper shows how to use Allan Variance (AVAR) and Power Spectral Density (PSD) for the experimental identification and modeling of the stochastic parameters of the Bosch BMG160 gyroscope embedded in a nanosatellite in order to get an accurate gyroscope model. This work also demonstrates the principle of operation of the equivalent electronic model intended to carry out advanced simulations without recourse to the real material in order to avoid the problem of bad manipulation and availability of the material in order to reduce the time and cost of development. The interpretation of the Allan curves and the PSD obtained from the measurements collected over a long period is presented, as well as a comparison between the real raw data of the BMG160 gyroscope and the designed hardware emulator in both the time and frequency domains. This is done to evaluate the accuracy of the gyroscope model emulating the real sensor in laboratory simulations. The experimental results show that the signals from the emulator and the BMG160 gyroscope are quite close. Therefore, the proposed prototype could be an optimal solution for laboratory calculations and simulations. [ABSTRACT FROM AUTHOR]

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.

Low-cost micro-electromechanical systems (MEMS)-based inertial navigation system (INS) sensors present long-term drift and different stochastic errors over time, which, in turn, tends to degrade the positioning accuracy of the artificial intelligence (AI)-based GPS/INS navigation systems during GPS outages. We address this issue by analyzing and modeling various stochastic errors of these sensors and our efficient noise reduction method can improve the accuracy of such navigation systems. In the present work, we propose our efficient adaptive noise reduction method based on the Allan variance (AV) analysis technique in order to choose more reliable, appropriate, and optimum parameters of the noise reduction method, which can help remove stochastic noises efficiently while preserving vehicles motion information. In our low-cost AI-based GPS/INS navigation system, more accurate and smoother INS sensor measurements with less complexity, as an input of intelligence structure, can provide better training and less estimation error and better generalization ability in the uncertainty-oriented environment. Eventually, in order to assess the effect of the proposed noise reduction method based on the AV method on the low-cost AI-based GPS/INS navigation systems under the GPS signal blockages, two different candidates from AI-based models are selected according to their ability in modeling random noise inputs. Then, their performance with and without the proposed noise reduction method is evaluated. The obtained results indicate that the proposed noise reduction method significantly improves positioning accuracy in AI-based low-cost GPS/INS integrated systems under GPS signal blockages using real data collected even with a high-speed test vehicle. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

In real-time precise point positioning (RT-PPP), PPP one-way timing is used to steer local oscillators, but the timing performance could be significantly affected by the datum stability of the satellite clock product. To measure the stability of a satellite clock datum relative to the hydrogen maser (H-MASER) clock, a new GNSS satellite clock datum stability assessing model based on the overlapping Allan variance (AVAR) is proposed for both PPP one-way timing and time synchronization. Experiments were carried out with nine Global Navigation Satellite System (GNSS) stations at time laboratories with an external H-MASER clock to analyze the datum stability performance. In the experiments, RT satellite products from five RT Analysis Centers (ACs): CNES, ESA, GFZ, GMV, WHU, and the final satellite product from IGS were used in the comparison. Results show that the datum stability of all RT products tended to be similar, i.e., 6 to 8E−15/day, where WHU and GMV outperformed other RT ACs. Moreover, these datum stability results indicate that RT-PPP for steering local oscillators improves stability to 6 to 8E−15/day when selected with an appropriate RT product. The estimation noise in all RT ACs was at about the same level, i.e., 1 to 2E−15/day, but WHU delivered the most stable performance. Thus, datum stability is an effective guide for setting parameters and making long-term stability predictions when steering local oscillators, and satellite clock datum stability can be measured conveniently and quickly using the GNSS satellite clock datum stability assessing model proposed in this paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A circular error probability (CEP) metric in ballistic missile science is an experimental indicator of the accuracy of a missile system. There are a lot of error sources that cause a ballistic missile to deviate from its ideal trajectory, and that causes a deviation from required CEP. This work discusses the problems of dispersion of ballistic missiles due to inertial navigation system (INS) errors. INS deterministic errors are usually calibrated and compensated using some proper techniques. However, INS stochastic errors can be modeled and analyzed. In this study, a chosen missile is thoroughly analyzed using the six degrees-of-freedom missile flight trajectory simulator. A Monte Carlo simulation is used to generate a large number of flight trajectories to inspect the effect of INS stochastic noise on missile CEP. Moreover, a strategy for selecting an adequate sensor according to mission requirements and its corresponding sensor errors is introduced. [ABSTRACT FROM AUTHOR]

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A common technique for navigation and positioning applications is the Global Positioning System (GPS)/Inertial Navigation System (INS) integration, which combines the strengths of GPS and INS to offer accurate and reliable information. However, the performance of the GPS/INS integration deteriorates during a GPS outage, which happens when natural or artificial factors block the GPS signal. The novelty of this paper is improving GPS/INS integration performance during GPS outages using Incremental Regularized Gated Recurrent Unit (IncRGRU) learning and Lifting Wavelet Transform (LWT). Incremental learning is a learning paradigm that can update the model parameters online from streaming data without forgetting the previous ones. Moreover, regularization is a technique that improves the network's generalization and avoids overfitting by adding some constraints or penalties to the model. In this way, the GPS signal is modeled by IncRGRU learning, and the Kalman filter corrects the INS output. Furthermore, LWT removes the noise from the sensors' signals. This algorithm has lower complexity and can work in real-time compared to conventional wavelet transforms. The performance of GPS/INS integration during GPS outages and the accuracy and robustness of GPS/INS integration is significantly improved by using LWT-IncRGRU on real-world datasets. The positioning errors are reduced by an average of 76% during GPS outages, and an average of 69% improves the GPS/INS integration compared to existing methods. [ABSTRACT FROM AUTHOR]

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.

The available road grade information makes a significant impact on improving the quality of vehicle control. In order to solve the limited application scenario and insufficient accuracy of current road grade estimation methods, this paper presents a novel model-based road grade estimation approach. First, a Quaternion Unscented Kalman Filter (QUKF) using the three-axle angular velocities and three-axle accelerations from a low-cost Inertial Measurement Unit (IMU) and the vehicle speed from CAN bus is designed to estimate the pitch angle of the vehicle. In particular, the measurement noise of UKF is analyzed by integrating Allan variance method. Second, a simplified vehicle-road model is derived to represent the road grade with the estimated pitch angle and longitudinal acceleration. Then, the performance of the proposed algorithm is tested by co-simulation of MATLAB/Simulink and CarSim, which indicates that the error rate of estimation is within 4%. Finally, the feasibility and accuracy of the proposed method implemented in the embedded prototype are verified in experiments conducted on standard slopes. [ABSTRACT FROM AUTHOR]

A novel fusion algorithm is proposed based on Improved Adaptive Wavelet Threshold De-noising (IAWTD), C-means Support Vector Machine (CSVM) and Ensemble Empirical Mode Decomposition (EEMD) method to eliminate the humidity drift of MEMS gyroscope. Firstly, the IAWTD method is employed to decrease the humidity drift component in MEMS gyroscope output signal. Then, the humidity drift compensation model is established: the input elements are the relative humidity, the change rate of relative humidity and the humidity drift, and the output is the compensated MEMS gyroscope output signal by EEMD method. In order to verify the compensation effect of the fusion algorithm, the gyroscope outputs are collected and analyzed with the relative humidity ranged from 40% to 90% based on the temperature varying from 20°C to 60°C. The results show that the IAWTD-CSVM-EEMD method significantly reduces the influence of relative humidity drift on the gyroscope output, according to the quantitative analysis of Allan variance, the quantization noise of the gyroscope output decreases by 87.78%, 96.37%, 97.77%, 99.17% and 92.62% respectively under the relative humidity ranging from 40% to 90%, as the temperature rose from 20 °C to 60 °C at intervals of 10 °C. In addition, the bias stability decreases by 96.9%, 99.41%, 99.1%, 99.46%, and 99.78% respectively and the angle random walk decreases by 88.16%, 96.54%, 98.16%, 94.43%, and 92.05% respectively at different temperatures. It is worth mentioning that, to further verify the applicability of the fusion algorithm, a group of comparative experiments are added to consider the influence of temperature changes on the gyroscope output under different relative humidity. The experimental results show that the quantization noise, bias stability and angle random walk of the MEMS gyroscope are significantly reduced compared with the original output after processing by IAWTD-CSVM-EEMD. Therefore, the method proposed in this paper is beneficial to reduce the humidity drift in the MEMS gyroscope output.

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.

The problem of physical implementation in working and secondary standards of the atomic time scales that maximally approximate the UTC(SU) time scale is considered. The results of an analysis of the steady-state regime of automatic steering of the time scale of the hydrogen frequency standard relative to UTC(SU) are presented. A differential method of comparison of time scales based on code measurements of signals of the global navigation satellite systems is used. The parameters of the Kalman filter and of a linear quadratic regulator are calculated. A comparison of the theoretical and experimental estimates of the characteristics of the error of automatic steering is presented. The results obtained may be used to increase the precision of knowledge of the time scales of working and secondary standards. [ABSTRACT FROM AUTHOR]

Visible Light Communications (VLC) is the type of communication, which processes high-speed data transmission using the visible Light Emitting Diodes (LED). The VLC acts as an important supplementary that is used to define the hotspots for heterogeneous networks and plays an important role for 5G networks in wireless communications. However, performance of visible light systems is affected by various noises and Allan variance is used to analyze such noises in 5G networks. The Massive Multiple-Input and Multiple-Output (M-MIMO) technique is used for noise modeling which utilizes the mitigation circuit to find whether the noise is white noise, shot noise, random walk noises or typical noises. The existing Kalman Filter approach failed to attain the required bandwidth and higher spectral efficiency. Therefore, to achieve high data rates, the spectral efficient technologies such as Single Carrier Frequency Division Multiplexing (SCFDM) is performed in the research. The Allan Variance is utilized for analyzing the time-series that extracts the noise features of the data and the major noise is verified and considered by the M-MIMO technique. The present research uses the Extended Kalman Filter (EKF) which determines the observation models and the state transition that does not need linear functions to define the states. The proposed SCFDM was constructed based on the VLC for 5G networks that analyzes in terms of Bit Error Rate (BER) and Signal to Noise Ratio (SNR). The proposed SCFDM obtains a high SNR of 14% for the channels with white LED option when compared to the existing methods. [ABSTRACT FROM AUTHOR]

An optical scheme for simultaneous detection of hydrogen sulfide (H2S) and carbon dioxide (CO2) is demonstrated. A near infrared tunable diode laser operating at 1.578 μm including the absorption lines of H2S at 6336.62 cm−1 and CO2 at 6336.24 cm−1 was used as the light source for spectroscopic measurements of H2S and CO2. A high‐finesse cavity with a base length of 21 cm and a pair of high reflectivity mirrors with a reflectivity of 99.999% were employed based on off‐axis integrated cavity output spectroscopy. Allan variance analysis shows that the minimum detection limits of 150 ppbv for H2S in 170 s averaging time and 1.03 ppmv for CO2 in 209 s, respectively. [ABSTRACT FROM AUTHOR]

A photoacoustic spectroscopy sensor for nitrogen dioxide (NO2) detection was presented based on a high‐power broadband blue diode laser emitting at 446 nm. An optical chopper was replaced by a transistor transistor logic modulation signal generated by the signal generator to reduce mechanical noise. The detection limit of NO2 sensor system reached to 46 ppt by the Allan variance analysis on the benefit of reflection‐enhanced. A continuous detection of NO2 in the atmosphere for 48 h was implemented in collaboration with an adaptive Kalman filter for lessening the noise in the measurement. The experimental results were highly consistent with the data of the China National Environmental Monitoring Center, demonstrating the accuracy and reliability of our NO2 sensor system. This work provides a promising method for NO2 and other atmospheric pollution gasses. [ABSTRACT FROM AUTHOR]