Computing Meaningful Integrity Bounds of a Low-cost Kalman-filtered Navigation Solution in Urban Environments

Accurate and reliable positioning, navigation and timing in harsh environments are key enablers for an increasing number of applications. Specifically, a wide range of so-called liability-critical applications like on-street parking pricing or road user charging are waiting for technological readiness of a suitable solution which fulfils their demanding requirements in terms of accuracy, integrity, availability and cost-efficiency. Attempts to use Satellite Based Augmentation Systems (SBAS) integrity such as EGNOS for land users have revealed major shortages, given that SBAS integrity has been conceived for use in open sky and clean operation scenarios as it is the case of aviation users. As a result, a lot of effort is being devoted to the investigation of autonomous techniques for determining the integrity of the navigation solution. In particular, the authors have contributed to that effort over the years with a number of those techniques, the most successful of which so far has been so-called Isotropy-Based Protection Level (IBPL). The IBPL method assumes basically no a priori knowledge on either the size or the pointing direction of the vector of measurement errors, which leads to the so-called isotropy assumption that all possible pointing directions are equally probable. IBPL has proven highly reliable in all kinds of environments thanks to the simplicity of its assumptions, although its application is limited to the navigation solutions based on least-squares. Kalman filtering, which, incidentally, is what most GNSS devices do to compute their navigation solutions, improves accuracy by effectively incorporating extra information. Therefore it seems natural to expect that the bounds will also improve when applied to a Kalman-filtered solution, provided that the IBPL, which was initially conceived for least squares positioning, can be properly adapted to Kalman filters. What is presented here is a solution to this challenge. Namely, we present an evolution of IBPL for Kalman-filtered solutions which successfully addresses the problems just mentioned. This evolution has been successfully applied to GNSS-standalone as well as to hybrid GNSS/INS navigation systems, showing the same levels of robustness and versatility of the original IBPL concept, in particular being able to provide tight integrity bounds in all kinds of environments for virtually any desired confidence level. In addition to discussing the key concepts and ideas behind the proposed algorithm, the results of an extensive validation campaign carried out in the center of Madrid (Spain) are presented, paying attention to the levels of integrity achieved as well as to other key performance figures such as the size of the integrity bounds obtained.