On the Overdetermined Celestial Fix

Abstract

We present an algorithm for computing the best position fix (in the least-squares sense) from a sequence of observations of any number of celestial bodies. This algorithm has several advantages, most notably that it does not rely on an initial guess of the position, is computationally expedient, and is simple enough to program on the more sophisticated hand-held calculators. We present the mathematical background for this algorithm, a description of its implementation, examples of its use on both simulated and “real” data, and an estimate of the error on the derived position.

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