A closed-form formula for GPS GDOP computation

Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision. An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that increasing the number of satellites for positioning will always reduce the GDOP. Since most GPS receivers today can receive signals from more than four satellites, it is desirable to compute GDOP efficiently for the general case. Previous studies have partially solved this problem with artificial neural network (ANN). Though ANN is a powerful function approximation technique, it needs costly training and the trained model may not be applicable to data deviating too much from the training data. Using Newton's identities from the theory of symmetric polynomials, this paper presents a simple closed-form formula for computing GDOP with the inputs used in previous studies. These inputs include traces of the measurement matrix and its second and third powers, and the determinant of the matrix.