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Precise Orbit Determination (POD) is an integral part for analyzing measurements from space geodetic techniques such as Satellite Laser Ranging (SLR) and Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS). In the last two decades, POD based on GPS data has furthermore been established as one of the standard techniques to derive trajectories of satellites in the low Earth orbit (LEO) with highest accuracy. Since the launch of dedicated gravity missions, GPS sensors are not only used as a key tracking system for LEO POD, but also for extracting the long wavelength part of the Earth’s gravity field (together with SLR to spherical satellites). This chapter introduces SLR and GNSS measurements collected by the terrestrial networks of the International Laser Ranging Service (ILRS) and the International GNSS Service (IGS) as the observational basis for the realization of a terrestrial reference frame from satellite data. On this foundation, the basic equations and mathematical methods of orbit determination are introduced and extensively discussed. Pseudo-stochastic orbit modeling techniques are eventually presented as a general and efficient concept to determine satellite trajectories of highest quality even in presence of deficient force models, covering the full range between dynamic and purely kinematic solutions. Selected results from the application of the discussed orbit determination techniques are highlighted for GPS LEO data. Special emphasis is also put to present orbit determination in the context of more general orbit determination problems, where satellite trajectories are simultaneously determined with other parameters encompassing (at maximum) all pillars of geodesy, i.e., the shape, rotation, and gravity field of the Earth.
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Usage: p = polyfit(x,y,n), where p are the coefficients of a polynomial p(x) of degree n, that is a best fit (in a least-squares sense) for the data in y. The coefficients in p are in descending powers, and the length of the array p is n + 1.
Please notice that this way of initial orbit determination is not what is usually done; there are much more elaborate approaches which lead to more accurate initial orbits.
You can solve the normal equation system by inverting the normal equation matrix (using the MATLAB command inv) and multiplying by the right hand side of the normal equation system. However, a faster and more robust way to solve a linear system is by using the command mldivide (matrix left division): x = mldivide(A,b) solves the linear system A*x = b. The abbreviation for mldivide is the backslash operator: x = A\b.
- Precise Orbit Determination
- Chapter 2
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