Onboard Density Modeling for Planetary Entry via Karhunen-Loeve Expansion

Onboard density models are a key aspect of autonomous closed-loop guidance systems for hypersonic flight. Traditional approaches model density as a deterministic function of altitude, but a recent drive toward stochastic guidance approaches motivates onboard uncertainty propagation. Existing solutions for efficient uncertainty propagation generally treat density as an exponential function of altitude, but this approach is limited in its ability to capture relevant dispersions. This work models density as a Gaussian random field that is approximated by a Karhunen-Lo`eve expansion, enabling a relatively high-fidelity, finite-dimensional parametric representation. Various normalization schemes are presented and compared by their efficiency in capturing density variability in a limited number of terms, and normalization by reference dynamic pressure is shown to be the most compact approach. The model alternatives are compared both by their approximations of density itself and their predictions of peak heat flux for dispersed direct-entry and aerocapture trajectories. An extension of this approach for modeling density as a function of multiple independent variables is also presented and demonstrated. Finally, it is shown that the density model can be sequentially updated according to noisy density observations by formulating the problem as a Kalman measurement function.