In favorable cases a satellite may allow simultaneous distance and angle measurements yielding directly the satellite's three-dimensional position relative to the ground station. Accounting for the known station location, these measurements can be converted to the position with respect to the center of the Earth. Only two of these position vectors (corresponding to six independent measurements) are then required to determine all six orbital elements in a unique way. The method described in the following comes from Gauss, and provides an efficient and robust way of solving the orbit determination problem for two given position vectors. Further methods like the Lambert-Euler method, the p-iteration and the use of f and g series are discussed in Escobal (1965) and Bate (1971).
Escobal P. R.; Methods ofOrbit Determination; John Wiley & Sons, Inc., New York (1965)_ Reprint: Krieger Publishing Company, Malabar, Florida (1976).
Bate R. R., Mueller D. D., White J. E.; Fundamentals of Astrodynamics; Dover Publieations, Ine., New York (1971).
Montenbruck O., Pfleger T.; Astronomy on the Personal Computer; Springer Verlag, Heidelberg; 4th edition (2000).
Vallado D. A; Fundamentals of Astrodynamics and Applications; McGraw-Hill, New York; 4th edition (2013).
Meysam Mahooti (2021). Initial orbit determination (https://www.mathworks.com/matlabcentral/fileexchange/77362-initial-orbit-determination), MATLAB Central File Exchange. Retrieved .
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