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We have assumed δtr0 ≈ 0: (1:57) If the error δtr0 cannot be assumed to be negligibly small, then the equations cannot be linearized, because errors in satellite positioning can become prohibitive: dx ¼ xsi ðtrS Þ À xsi ðtSS Þ: (1:58) An average velocity of a GPS satellite is about four kilometers per second and up to about 800 meters per second along the line of sight (LOS). 1 second will result in satellite position error of 400 meters and 80 meters in LOS direction. These errors will be magnified by constellation geometry (DOP).

Van Brummelen (editors), Berlin/Heidelberg, Springer, 2005. 36 Methods of positioning with navigation satellites [13] P. McDonnel, Introduction to Map Projections, 2nd edition, Rancho Cordova, CA, Landmark Enterprises, 1991. [14] C. Audoin and B. Guinot, The Measurement of Time. Time, Frequency and the Atomic Clock, Cambridge, Cambridge University Press, 2001. [15] S. Bancroft, An algebraic solution of the GPS equations, IEEE Transactions on Aerospace and Electronic Systems, 21, 1985, 56–59. [16] R.

Claudius Ptolemy, Almagest, Book 1–7. In order to use GNSS for almost any practical application or to simulate a GNSS signal, we need to be able to define satellite coordinates at any moment of time. In this chapter we look at GNSS satellite orbits. We consider their mathematical presentations and requirements of constellation design. 1 Claudius Ptolemy. Development of models for celestial body movements from Ptolemy to Einstein Movement of satellites around the Earth is described using mathematical instruments and models which were developed for describing the movement of the planets.

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