  Trajectory planning under uncertainty is an active research topic. Previous
works predict state and state estimation uncertainties along trajectories to
check for collision safety. They assume either stochastic or bounded sensing
uncertainties. However, GNSS pseudoranges are typically modeled to contain
stochastic uncertainties with additional biases in urban environments. Thus,
given bounds for the bias, the planner needs to account for both stochastic and
bounded sensing uncertainties. In our prior work we presented a reachability
analysis to predict state and state estimation uncertainties under stochastic
and bounded uncertainties. However, we ignored the correlation between these
uncertainties, leading to an imperfect approximation of the state uncertainty.
In this paper we improve our reachability analysis by predicting state
uncertainty as a function of independent quantities. We design a metric for the
predicted uncertainty to compare candidate trajectories during planning.
Finally, we validate the planner for GNSS-based urban navigation of fixed-wing
UAS.
