Submillimetric GPS distance measurement over short baselines: case study in inner consistency

Distance determination in the open air with submillimetric accuracy is a challenging task usually carried out with the use of submillimetric distancemeters and costly observation campaigns. The present paper represents a first step in the research of the potential use of GPS for submillimetric distance determination for distances up to a few hundred metres consisting in the evaluation of GPS distance determination reproducibility. As will be concluded, reliable submillimetric precision is attainable after some hours of observation if the same equipment in both baseline ends is used, even considering that there still remain some long-term systematic effects of a few tenths of a millimetre. The need for precise absolute antenna calibration values is also shown to be critical for submillimetric distance reproducibility.This research is funded by the Spanish Ministry of Science and Innovation (AYA2011-23232). The authors are grateful to the editor and the anonymous reviewers for their valuable suggestions, corrections and comments that helped improve the original manuscript.Baselga Moreno, S.; García-Asenjo Villamayor, L.; Garrigues Talens, P. (2013). Submillimetric GPS distance measurement over short baselines: case study in inner consistency. Measurement Science and Technology. 24(7):750011-750018. https://doi.org/10.1088/0957-0233/24/7/075001S750011750018247Amiri-Simkooei, A. R., & Tiberius, C. C. J. M. (2006). Assessing receiver noise using GPS short baseline time series. GPS Solutions, 11(1), 21-35. doi:10.1007/s10291-006-0026-8Bruyninx, C., Altamimi, Z., Boucher, C., Brockmann, E., Caporali, A., Gurtner, W., … Weber, G. (2009). The European Reference Frame: Maintenance and Products. International Association of Geodesy Symposia, 131-136. doi:10.1007/978-3-642-00860-3_20Doloca, N. R., Meiners-Hagen, K., Wedde, M., Pollinger, F., & Abou-Zeid, A. (2010). Absolute distance measurement system using a femtosecond laser as a modulator. Measurement Science and Technology, 21(11), 115302. doi:10.1088/0957-0233/21/11/115302Dow, J. M., Neilan, R. E., & Rizos, C. (2009). The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. Journal of Geodesy, 83(3-4), 191-198. doi:10.1007/s00190-008-0300-3Firuzabadì, D., & King, R. W. (2011). GPS precision as a function of session duration and reference frame using multi-point software. GPS Solutions, 16(2), 191-196. doi:10.1007/s10291-011-0218-8Hyun, S., Kim, Y.-J., Kim, Y., Jin, J., & Kim, S.-W. (2009). Absolute length measurement with the frequency comb of a femtosecond laser. Measurement Science and Technology, 20(9), 095302. doi:10.1088/0957-0233/20/9/095302Koivula, H., Häkli, P., Jokela, J., Buga, A., & Putrimas, R. (2011). GPS Metrology: Bringing Traceable Scale to a Local Crustal Deformation GPS Network. International Association of Geodesy Symposia, 105-112. doi:10.1007/978-3-642-20338-1_13Ray, J., Altamimi, Z., Collilieux, X., & van Dam, T. (2007). Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions, 12(1), 55-64. doi:10.1007/s10291-007-0067-7Schuhler, N., Salvadé, Y., Lévêque, S., Dändliker, R., & Holzwarth, R. (2006). Frequency-comb-referenced two-wavelength source for absolute distance measurement. Optics Letters, 31(21), 3101. doi:10.1364/ol.31.003101Snay, R. A., & Soler, T. (2008). Continuously Operating Reference Station (CORS): History, Applications, and Future Enhancements. Journal of Surveying Engineering, 134(4), 95-104. doi:10.1061/(asce)0733-9453(2008)134:4(95

Least-squares variance component estimation

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE. We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected by the results of LS-VCE. Various examples are given to illustrate the theory.Delft Institute of Earth Observation and Space Systems (DEOS)Aerospace Engineerin

Least-squares variance component estimation

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE. We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected by the results of LS-VCE. Various examples are given to illustrate the theory.Delft Institute of Earth Observation and Space Systems (DEOS)Aerospace Engineerin