Vertical Protection Level Estimation for Direct Positioning Using a Bayesian Approach

Abstract

GPS integrity monitoring is essential to ensure the safety of critical infrastructures, such as power grid, banking, and transportation systems. The integrity of a system is assessed using protection levels (PLs). PLs overbound positioning and timing errors using error models. Positioning errors have multi-modal Gaussian distribution due to changing environmental conditions. The number of modes present in the multi-modal distribution is not known and poses a challenge in overbounding errors using a multi-modal distribution. Direct positioning (DP) is an unconventional GPS receiver architecture that utilizes signal-in-space and provides position, velocity and time (PVT) solution in a single step. DP is robust against errors that arise due to multipath or signal blockage. In this work, we propose a Bayesian algorithm to estimate PLs for DP. We model the positioning error with a time-varying Gaussian distribution to capture the multi-modal behavior. Our Bayesian algorithm use DP likelihood manifold to estimate PLs. The effect of changing environmental conditions is captured by DP likelihood manifold, which is a function of timevarying variance. In this paper, we focus on overbounding vertical positioning errors of DP using our Bayesian algorithm. We generate 24 hours of stationary GPS data using a high fidelity GPS simulator. We show that the vertical positioning error distribution for DP is multi-modal. We further validate that our estimated VPL bounds vertical errors for DP.