Error Bound Optimization Using Second Order Cone Programming

Juan Blanch, Todd Walter and Per Enge

Abstract:	In safety of life applications using satellite navigation, the Protection Level (PL) equation translates what is known about the pseudorange errors into a hard bound on the positioning error (the Protection Level). The current PL equations for Satellite Based Augmentation Systems are based on Gaussian statistics: all errors are characterized by a zero mean Gaussian distribution which is an upper bound of the true distribution. This approach is very practical: the calculations are simple and the receiver computing load is small. However, when the true distributions are far from Gaussian, such characterization forces an inflation of the protection levels that damages performance. Also, in the certification process, it is very difficult to agree on a given distribution when the statistics are gathered from a multitude of situations (like differing elevation angle in the case of multipath), or when the process involved has large deviations from a Gaussian model (stormy ionospheric behavior). With the development of new optimization methods and the increasing computing power, it is worthwhile exploring new ways of calculating integrity error bounds. In this paper we present a way of computing optimal protection levels when the errors are characterized by a Gaussian random component and a bias that is linearly constrained. We show that the minimization of the protection level can be cast as a second order cone program (SOCP), and that this particular structure allows a quick computation. As an example, this algorithm is applied to a dual frequency Wide Area Augmentation System where biases are sent to the user (as well as the usual Gaussian terms).
Published in:	Proceedings of the 2005 National Technical Meeting of The Institute of Navigation January 24 - 26, 2005 The Catamaran Resort Hotel San Diego, CA
Pages:	1009 - 1013
Cite this article:	Blanch, Juan, Walter, Todd, Enge, Per, "Error Bound Optimization Using Second Order Cone Programming," Proceedings of the 2005 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2005, pp. 1009-1013.
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