New Bounds on the Horizontal Protection Level for the Non-Zero Mean Case

Steven Langel

Abstract:	This paper presents a new method to compute horizontal protection levels (HPLs) when the position estimate error vector is a non-zero mean Gaussian random vector. A closed form expression does not exist for HPL in the general case of non-zero mean estimate errors, and numerical methods must be used to determine an approximate protection level. For navigation applications, a computed HPL that upper bounds the true HPL is often desired. Current methods either do not guarantee that this condition is met or do not allow control over the tightness of the bound. In response, we derive a new approach for computing an upper bound on the true HPL that is simple to implement and is guaranteed to achieve a predefined relative error tolerance. The bound is obtained by approximating the circular integration region that defines HPL with rectangular elements. An analytical expression is derived that allows one to determine, a priori, the minimum number of rectangles needed to achieve the desired error tolerance, thereby minimizing the amount of computational effort required to compute the bound. Simulation results for a simple example validate the theoretical results in the paper, and MATLAB source code for the new method is provided.
Published in:	Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021) September 20 - 24, 2021 Union Station Hotel St. Louis, Missouri
Pages:	1565 - 1576
Cite this article:	Langel, Steven, "New Bounds on the Horizontal Protection Level for the Non-Zero Mean Case," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 1565-1576. https://doi.org/10.33012/2021.17888
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In