Density Estimation for Entry Guidance Problems using Deep Learning

The accuracy of predictor–corrector entry guidance algorithms relies heavily on the accuracy of the onboard atmospheric density model. Existing approaches, such as fading-memory filters, assume a constant bias in the density profile from the current state in the entry trajectory to the terminal condition which does not capture the geospatial variation of atmospheric density. In this work, a deep-learning approach to estimate atmospheric density profiles for use in planetary entry guidance problems is developed. A long short-term memory (LSTM) neural network is trained to learn the mapping between measurements available onboard an entry vehicle and the density profile through which it is flying. Measurements include the spherical state representation, Cartesian sensed acceleration components, and a surface-pressure measurement. Training data for the network are initially generated by performing a Monte Carlo analysis of an entry mission at Mars using the fully numerical predictor–corrector guidance (FNPEG) algorithm that uses an exponential density model, while the truth density profiles are sampled from MarsGRAM. An iterative curriculum-learning procedure is developed to refine the LSTM network’s predictions for integration within the FNPEG algorithm. The trained LSTM is capable of accurately predicting both the density profile through which the vehicle will fly and reconstructing the density profile through which it has already flown. The performance of the FNPEG algorithm is assessed for three different density estimation techniques: an exponential model, an exponential model augmented with a first-order fading-memory filter, and the LSTM network. Results demonstrate that using the LSTM model results in an order of magnitude increase in terminal accuracy compared to the other two techniques when considering both noisy and noiseless measurements.