Optimization of a Vertical Protection Level Equation for Dual Frequency SBAS

The advent of dual frequency Satellite Based Augmentation Systems (SBAS) will allow the aviation community to address some of the shortcomings of the current SBAS Minimum Operational Performance Standards (MOPS), in particular of the Vertical Protection Level (VPL), and also to adapt it to threats for a dual frequency user. First, satellite faults will become the dominant source of error – because the ionospheric delay threat is canceled. Second, it was discovered that there are nominal biases that cannot be corrected by the ground and that cause the current VPL to be inflated. Finally, actual data collected in support of system performance has shown that the statistics exhibit non-gaussian behavior. A Vertical Protection Level equation that addresses these points was proposed in [1]. This equation accounts explicitly for possible nominal biases and for the fact that the position error bound is dominated by one possible fault at a given time. The equation was evaluated using a Service Volume analysis tool and it was shown that it could provide significant benefits over the current equation. These simulations computed user coefficients (the coefficients that project the pseudorange onto the user position) based on a Least Squares (LS) approach. The LS approach is not optimal for the proposed VPL equation. In this paper we show that choosing optimally the coefficients that project the pseudoranges onto the position domain could significantly increase the performance of an SBAS based on the equation described in [1]. To this purpose, we will describe an algorithm that minimizes the Vertical Protection Level. Then, we will evaluate the availability benefits that can be obtained using the optimal algorithm using a Service Volume Analysis tool.