DOI: 
10.22389/0016-7126-2022-982-4-2-8
1 Padve V.A.
2 Kosarev N.S.
Year: 
№: 
982
Pages: 
2-8

Siberian State University of Geosystems and Technologies

1, 

Research Institute of Geodesy, Topography and Cartography

2, 
Abstract:
An algorithm for averaging part of GNSS measurements information obtained at different times and belonging to the same baseline is given. The averaging extends to the increments of such lines’ coordinates and the accompanying covariance matrix of the increments. It is implemented using the algorithm of the classic parametric version of data LS-optimization. The design matrix of the measured increasing is built with positive single blocks size 3×3; their total number is equal to that of the baseline observation sessions. Solving the system of relevant normal equations through the method of conversion, size 3×3, gives the vector of average increments of the base line coordinates. The reverse matrix of its normal equation ratios is an averaged covariance one of average increments (system roots). Processing observational materials is carried out in the Excel electronic computational table using a synthesized version of the parametric one of the data LS-optimization, taking into account the errors of the reference points’ coordinates. The two-way processing-determined coordinates and their RMSE (root mean square error) were identical both before and after averaging.
References: 
1.   Astapovich A. V., Kolesnikov D. D. Obosnovanie metoda sovmestnogo uravnivaniya sputnikovykh i nazemnykh izmerenii. Tr. voenno-kosmich. akad. imeni A. F. Mozhaiskogo, 2020, no. 672, pp. 158–168.
2.   Gerasimov A.P. Sputnikovye geodezicheskie seti. M.: Prospekt, 2012, 176 p.
3.   Glushkov V.V., Nasretdinov K.K., Sharavin A.A. Kosmicheskaya geodeziya: metody i perspektivy razvitiya. M.: Nacional'naya kartograficheskaya korporaciya, 2002, 448 p.
4.   Kosarev N. S., Padve V. A., Sergeev S. A., Dudarev V. I. Ispol'zovanie sintezirovannogo varianta algoritma parametricheskoi versii MNK-optimizatsii rezul'tatov GNSS-izmerenii dlya ikh sravnitel'nogo analiza. Vestnik SSUGT, 2018, Vol. 23, no. 3, pp. 30–45.
5.   Kougiya V.A. Izbrannye trudy: Monografiya [Selected works: the monograph]. Под ред. М. Я. Брыня. SPb.: Peterburgskij gos. un-t putej soobshcheniya, 2012, 448 p.
6.   Markuze Yu. I., Khoang N. Kh. Uravnivanie prostranstvennykh nazemnykh i sputnikovykh geodezicheskikh setei. Moskva: Nedra, 1991, 274 p.
7.   Mashimov M. M. Uravnivanie geodezicheskikh setei. 2-e izdanie, pererabotannoe i dopolnennoe. Moskva: Nedra, 1989, 280 p.
8.   Mustafin M. G., Chan Shon Than' Ispol'zovanie topotsentricheskoj pryamougol'noj sistemy koordinat pri reshenii inzhenerno-geodezicheskih zadach. Vestnik SGUGiT, 2018, Vol. 23, no. 3, pp. 61–73.
9.   Padve V. A. Matematicheskaya obrabotka i analiz rezul'tatov geodezicheskikh izmerenii: Monografiya. V 2 ch. – Ch. 2: Sintezirovannye i kombinirovannye algoritmy tochnostnoi MNK-optimizatsii i analiza rezul'tatov izmerenii. Novosibirsk: SGUGiT, 2018, 134 p.
10.   Bhatta B. (2021) Global Navigation Satellite Systems. New Technologies and Applications. 2nd ed. CRC Press, London, 386 p. DOI: 10.1201/9781003148753.
11.   Fotiou A., Pikridas C., Rossikopoulos D., Chatzinikos M. (2009) The effect of independent and trivial GPS baselines on the adjustment of networks in everyday engineering practice. Proceeding of International symposium on modern technologies, education and professional practice in geodesy and related fields, 05-09 November, Sofia, pp. 201–212. URL: clck.ru/36ymH7 (accessed: 15.02.2023).
12.   Gargula T. (2021) Adjustment of an Integrated Geodetic Network Composed of GNSS Vectors and Classical Terrestrial Linear Pseudo-Observations. Appl. Sci, no. 11, pp. 43–52. DOI: 10.3390/app11104352.
13.   Ghilani C. D. (2018) Adjustment Computations: Spatial Data Analysis. John Wiley and Sons, 720 p.
14.   Kaplan E., Hegarty C. (2017) Understanding GPS/GNSS: Principles and Applications. Artech. 1002 p.
15.   Leick A., Rapoport L., Tatarnikov D. (2015) GPS Satellite Surveying. A Willey-Interscience Publication, New York, 836 p.
16.   Nguyen D. H., Lee H., Yun S. (2020) A Study on Simultaneous Adjustment of GNSS Baseline Vectors and Terrestrial Measurements. Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography, no. 38, 5, pp. 415–423. DOI: 10.7848/ksgpc.2020.38.5.415.
17.   Sickle J. V. (2015) GPS for land surveyors. Taylor and Francis, N. Y., London, 350 p.
18.   Strang G., Borre K. (1997) Linear Algebra, Geodesy and GPS. Wellesley-Cambridge Press, 644 p.
19.   Teunissen P. J. G., Montenbruck O. (eds.) (2017) Springer Handbook of Global Navigation Satellite Systems. Springer International Publishing AG, 1272 p.
20.   Zahraa H. (2019) GNSS Geodetic Network Design using Least Squares Adjustment Method. LAP LAMBERT Academic Publishing, 168 p.
Citation:
Padve V.A., 
Kosarev N.S., 
(2022) Algorithm for averaging the increments of coordinates and their covariance matrices of repeated GNSS measurements. Geodesy and cartography = Geodezia i Kartografia, 83(4), pp. 2-8. (In Russian). DOI: 10.22389/0016-7126-2022-982-4-2-8
Publication History
Received: 13.10.2021
Accepted: 08.04.2022
Published: 20.05.2022

Content

2022 April DOI:
10.22389/0016-7126-2022-982-4

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