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Register a new userApplication of the Allan Variance to Time Series Analysis in Astrometry and Geodesy: A Review
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Zinovy Malkin
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The Allan variance (AVAR) was introduced 50 years ago as a statistical tool for assessing of the frequency standards deviations. For the past decades, AVAR has increasingly being used in geodesy and astrometry to assess the noise characteristics in geodetic and astrometric time series. A specific feature of astrometric and geodetic measurements, as compared with the clock measurements, is that they are generally associated with uncertainties; thus, an appropriate weighting should be applied during data analysis. Besides, some physically connected scalar time series naturally form series of multi-dimensional vectors. For example, three station coordinates time series $X$, $Y$, and $Z$ can be combined to analyze 3D station position variations. The classical AVAR is not intended for processing unevenly weighted and/or multi-dimensional data. Therefore, AVAR modifications, namely weighted AVAR (WAVAR), multi-dimensional AVAR (MAVAR), and weighted multi-dimensional AVAR (WMAVAR), were introduced to overcome these deficiencies. In this paper, a brief review is given of the experience of using AVAR and its modifications in processing astro-geodetic time series.
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We investigated the suitability of the astronomical 15 GHz VLBA observing program MOJAVE-5 for estimation of geodetic parameters, such as station coordinates and Earth orientation parameters. We processed contemporary geodetic dual-band RV and CN experiments observed at 2.3 GHz and 8.6 GHz starting on September 2016 through July 2020 as reference dataset. We showed that the baseline length repeatability from MOJAVE-5 experiments is only a factor of 1.5 greater than from the dedicated geodetic dataset and still below 1~ppb. The wrms of the difference of estimated EOP with respect to the reference IERS C04 time series are a factor of 1.3 to 1.8 worse. We isolated three major differences between the datasets in terms their possible impact on the geodetic results, i.e. the scheduling approach, treatment of the ionospheric delay, and selection of target radio sources. We showed that the major factor causing discrepancies in the estimated geodetic parameters is the different scheduling approach of the datasets. We conclude that systematic errors in MOJAVE-5 dataset are low enough for these data to be used as an excellent testbed for further investigations on the radio source structure effects in geodesy and astrometry.
2019 marked the 20th anniversary of the International VLBI Service for Geodesy and Astrometry (IVS). This service is the largest and most authoritative organization that coordinates international activities in radio astrometry and VLBI sub-system of space geodesy. Currently, about 60 antennas located in many countries on all continents participate in the IVS observing programs. The IVS Data Centers have accumulated more than 18 million observations obtained during more than 17000 sessions, including more than 10,000 Intensive sessions for rapid determination of Universal Time. The paper traces the dynamics of IVS development based on statistical processing of the array of observations collected in the IVS Data Centers for the period of 1979-2018. Various statistics by the years, stations, baselines, and radio sources are provided. The evolution of the IVS observational data and the accuracy of results obtained from processing VLBI observations is considered.
Certain instrumental effects and data reduction anomalies introduce systematic errors in photometric time-series. Detrending algorithms such as the Trend Filtering Algorithm (TFA) (Kov{a}cs et al. 2004) have played a key role in minimizing the effects caused by these systematics. Here we present the results obtained after applying the TFA, Savitszky-Golay (Savitzky & Golay 1964) detrending algorithms and the Box Least Square phase folding algorithm (Kov{a}cs et al. 2002) to the TFRM-PSES data (Fors et al. 2013). Tests performed on this data show that by applying these two filtering methods together, the photometric RMS is on average improved by a factor of 3-4, with better efficiency towards brighter magnitudes, while applying TFA alone yields an improvement of a factor 1-2. As a result of this improvement, we are able to detect and analyze a large number of stars per TFRM-PSES field which present some kind of variability. Also, after porting these algorithms to Python and parallelizing them, we have improved, even for large data samples, the computing performance of the overall detrending+BLS algorithm by a factor of $sim$10 with respect to Kov{a}cs et al. (2004).
This paper presents a systematic review of Python packages with a focus on time series analysis. The objective is to provide (1) an overview of the different time series analysis tasks and preprocessing methods implemented, and (2) an overview of the development characteristics of the packages (e.g., documentation, dependencies, and community size). This review is based on a search of literature databases as well as GitHub repositories. Following the filtering process, 40 packages were analyzed. We classified the packages according to the analysis tasks implemented, the methods related to data preparation, and the means for evaluating the results produced (methods and access to evaluation data). We also reviewed documentation aspects, the licenses, the size of the packages community, and the dependencies used. Among other things, our results show that forecasting is by far the most frequently implemented task, that half of the packages provide access to real datasets or allow generating synthetic data, and that many packages depend on a few libraries (the most used ones being numpy, scipy and pandas). We hope that this review can help practitioners and researchers navigate the space of Python packages dedicated to time series analysis. We will provide an updated list of the reviewed packages online at https://siebert-julien.github.io/time-series-analysis-python/.
The expert system for time series analysis of irregularly spaced signals is reviewed. It consists of a number of complementary algorithms and programs, which may be effective for different types of variability. Obviously, for a pure sine signal, all the methods should produce the same results. However, for irregularly spaced signals with a complicated structure, e.g. a sum of different components, different methods may produce significantly different results. The basic approach is based on classical method of the least squares (1994OAP.....7...49A). However, contrary to common step-by-step methods of removal important components (e.g. mean, trend (detrending), sine wave (prewhitening), where covariations between different components are ignored, i.e. erroneously assumed to be zero, we use complete mathematical models. Some of the methods are illustrated on the observations of the semi-regular pulsating variable RY UMa. The star shows a drastic cyclic change of semi-amplitude of pulsations between 0.01 to 0.37mag, which is interpreted as a bias between the waves with close periods and a beat period of 4000d (11yr). The dominating period has changed from 307.35(8)d before 1993 to 285.26(6)d after 1993. The initial epoch of the maximum brightness for the recent interval is 2454008.8(5). It is suggested that the apparent period switch is due to variability of amplitudes of these two waves and an occasional swap of the dominating wave.
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