  Spacecraft entering Mars require precise navigation algorithms capable of
accurately estimating the vehicle's position and velocity in dynamic and
uncertain atmospheric environments. Discrepancies between the true Martian
atmospheric density and the onboard density model can significantly impair the
performance of spacecraft entry navigation filters. This work introduces a new
approach to online filtering for Martian entry using a neural network to
estimate atmospheric density and employing a consider analysis to account for
the uncertainty in the estimate. The network is trained on an exponential
atmospheric density model, and its parameters are dynamically adapted in real
time to account for any mismatch between the true and estimated densities. The
adaptation of the network is formulated as a maximum likelihood problem by
leveraging the measurement innovations of the filter to identify optimal
network parameters. Within the context of the maximum likelihood approach,
incorporating a neural network enables the use of stochastic optimizers known
for their efficiency in the machine learning domain. Performance comparisons
are conducted against two online adaptive approaches, covariance matching and
state augmentation and correction, in various realistic Martian entry
navigation scenarios. The results show superior estimation accuracy compared to
other approaches, and precise alignment of the estimated density with a broad
selection of realistic Martian atmospheres sampled from perturbed Mars-GRAM
data.
