On Directional Measurement Representation in Orbit Determination
U.S. Naval Research Laboratory Washington United States
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Precision Orbit Determination OD is often critical for successful satellite operations supporting a wide variety of missions. Directional or angles only measurements of a satellite are typically represented in spherical coordinates on the observers celestial sphere e.g. azimuth and elevation or right ascension and declination. Computing residuals in these angular coordinates during the OD process can introduce errors in the same way an equirectangular projection distorts both distance and direction on a map. One technique is to weight the azimuth residuals by the cosine of the elevation, as in a sinusoidal projection. While this technique preserves the length of every parallel it still induces distortion in direction and distance. Therefore, it is proposed to use the angular distance between the computed and observed locations as the residual. This is similar to using an azimuthal equidistant projection with the observed location at the center. It is shown that this technique removes distortion present in the other two representations. The three techniques are then compared experimentally for a geostationary and a low Earth orbit satellite using simulated data to evaluate their differences. It is shown that using angular distance as the residual decreases the number iterations required for convergence and allows the OD process to more closely fit the observed data when there are observations near the pole of the spherical coordinate representation.