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16 pages, 900 KiB

Open AccessArticle

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

by Weiwei Cheng, Guigen Nie and Jian Zhu

Sensors 2023, 23(11), 5356; https://doi.org/10.3390/s23115356 - 5 Jun 2023

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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. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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7 pages, 2865 KiB

Open AccessProceeding Paper

Watermark Embedding Scheme with Variance of Chromatic Components

by Dur-e-Jabeen, Faiza Waqqas, Habib Shaukat, Maria Fatima, Rumaisa Iftikhar and Tehmina Khan

Eng. Proc. 2023, 32(1), 26; https://doi.org/10.3390/engproc2023032026 - 24 May 2023

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Abstract

This paper contains the idea of inserting a watermark with the variance of color components of the image. The color image is converted into CIE color space. Chromatic components are transformed into a sequency domain by applying the complex Hadamard transform. The variance of the spatio-chromatic coefficients is calculated and the watermark is selected from the transformed image based on the variance by setting the threshold value. The watermark is only inserted in image blocks that have a smaller value of variance than the threshold value. Simulation results are presented and discussed using the two variants of complex Hadamard transform and discrete cosine transform. Full article

(This article belongs to the Proceedings of The 2nd International Conference on Emerging Trends in Electronic and Telecommunication Engineering)

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21 pages, 750 KiB

Open AccessArticle

Voltage Based Electronic Control Unit (ECU) Identification with Convolutional Neural Networks and Walsh–Hadamard Transform

by Gianmarco Baldini

Electronics 2023, 12(1), 199; https://doi.org/10.3390/electronics12010199 - 31 Dec 2022

Cited by 3 | Viewed by 2630

Abstract

This paper proposes an identification approach for the Electronic Control Units (ECUs) in the vehicle, which are based on the physical characteristics of the ECUs extracted from their voltage output. Then, the identification is not based on cryptographic means, but it could be used as an alternative or complementary means to strengthen cryptographic solutions for vehicle cybersecurity. While previous research has used hand-crafted features such as mean voltage, max voltage, skew or variance, this study applies Convolutional Neural Networks (CNNs) in combination with the Walsh–Hadamard Transform (WHT), which has useful properties of compactness and robustness to noise. These properties are exploited by the CNN, and in particular, the pooling layers, to reduce the size of the feature maps in the CNN. The proposed approach is applied to a recently public data set of ECU voltage fingerprints extracted from different automotive vehicles. The results show that the combination of CNN and the WHT outperforms, in terms of identification accuracy, robustness to noise and computing times, and other approaches proposed in the literature based on shallow machine learning and tailor-made features, as well as CNN with other linear transforms such as the Discrete Fourier Transform (DFT) or CNN with the original time domain representations. Full article

(This article belongs to the Special Issue Wireless Communications Security and Privacy for Connected and Autonomous Vehicles)

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11 pages, 2974 KiB

Open AccessCommunication

Noise Analysis and Combination of Hydrology Loading-Induced Displacements

by Chang Xu, Xin Yao and Xiaoxing He

Remote Sens. 2022, 14(12), 2840; https://doi.org/10.3390/rs14122840 - 14 Jun 2022

Cited by 1 | Viewed by 1844

Abstract

Large uncertainties exist in the available hydrology loading prediction models, and currently no consensus is reached on which loading model is superior or appears to represent nature in a more satisfactory way. This study discusses the noise characterization and combination of the vertical loadings predicted by different hydrology reanalysis (e.g., MERRA, GLDAS/Noah, GEOS-FPIT, and ERA interim). We focused on the hydrology loading predictions in the time span from 2011 to 2014 for the 70 Global Positioning System (GPS) sites, which are located close to the great rivers, lakes, and reservoirs. The maximum likelihood estimate with Akaike information criteria (AIC) showed that the auto-regressive (AR) model with an order from 2 to 5 is a good description of the temporal correlation that exists in the hydrology loading predictions. Moreover, significant discrepancy exists in the root mean square (RMS) of different hydrology loading predictions, and none of them have the lowest noise level for the all-time domain. Principal component analysis (PCA) was therefore used to create a combined loading-induced time series. Statistical indices (e.g., mean overlapping Hadamard variance, Nash-Sutcliffe efficiency, and variance reduction) showed that our proposed algorithm had an overall good performance and seemed to be potentially feasible for performing corrections on geodetic GPS heights. Full article

(This article belongs to the Special Issue Modelling Geodetic Time Series and Applications for Earth Science and Environmental Monitoring)

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Graphical abstract

23 pages, 74104 KiB

Open AccessArticle

Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

by Sorin Nistor, Norbert-Szabolcs Suba, Ahmed El-Mowafy, Michal Apollo, Zinovy Malkin, Eduard Ilie Nastase, Jacek Kudrys and Kamil Maciuk

Remote Sens. 2021, 13(17), 3478; https://doi.org/10.3390/rs13173478 - 2 Sep 2021

Cited by 4 | Viewed by 3719

Abstract

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT). Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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12 pages, 273 KiB

Open AccessArticle

Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions

by Alessandro De Gregorio and Roberto Garra

Fractal Fract. 2021, 5(2), 48; https://doi.org/10.3390/fractalfract5020048 - 23 May 2021

Cited by 8 | Viewed by 2496

Abstract

In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation. Full article

(This article belongs to the Special Issue Fractional and Anomalous Diffusions on Regular and Irregular Domains)

23 pages, 992 KiB

Open AccessArticle

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

by Weiwei Cheng and Guigen Nie

Sensors 2018, 18(2), 502; https://doi.org/10.3390/s18020502 - 7 Feb 2018

Cited by 2 | Viewed by 4323

Abstract

High-performance oscillators, atomic clocks for instance, are important in modern industries, finance and scientific research. In this paper, the authors study the estimation and prediction of long-term stability based on convex optimization techniques and compressive sensing. To take frequency drift into account, its influence on Allan and modified Allan variances is formulated. Meanwhile, expressions for the expectation and variance of discrete-time Hadamard variance are derived. Methods that reduce the computational complexity of these expressions are also introduced. Tests against GPS precise clock data show that the method can correctly predict one-week frequency stability from 14-day measured data. Full article

(This article belongs to the Collection Modeling, Testing and Reliability Issues in MEMS Engineering)

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