A Neural Network Approach to Localized Atmospheric Density Estimation for Orbit Determination
Kyri E. Barton, University of Kansas; Humberto C. Godinez, Los Alamos National Laboratory; Craig A. McLaughlin, University of Kansas
Alternate Number 3
Atmospheric density presents the largest uncertainties in the estimation of drag on satellites in Low Earth Orbit. This research uses artificial neural networks (ANN) to improve neutral density estimation along the orbits of the CHAllenging Minisatellite Payload (CHAMP), and the Gravity Recovery and Climate Experiment (GRACE) satellites. The Focused Time-Delay Neural Network (FTDNN), Nonlinear Autoregressive Network with Exogenous inputs (NARX), Gated Recurrent Unit (GRU), and Long-Short-Term-Memory (LSTM) network architectures are tested to capture the temporal and secular dynamic behavior exhibited while in orbit. The inputs to each network are the estimated neutral densities derived from multiple empirical and semi-empirical models, including CIRA-71, NRLMSISE-00, Jacchia-Bowman 2008, DTM-2013, and Precision Orbit Ephemerides (POE). The output is the estimated localized density at some point in the future along the orbit. Neutral densities derived from accelerometer data onboard each satellite are used to train the networks for multi-step-ahead prediction. The training data from two days within the tested time interval, January 2 and April 5 of 2010, were used for capturing the effects of high and low solar and geomagnetic activity on the local density. The prediction time intervals are varied from seconds to months for determining the performance using both long- and short-term time horizons. Case studies are done on each network to determine the optimal representation of the satellite orbit dynamics, including setting appropriate network parameters such as number of layers, number of neurons used in the hidden layer(s), number of time-delays and their location within the network structure. The networks are trained using the Levenberg-Marquardt algorithm, where the total input vectors and target vectors are randomly divided into three sets: 70% for total training, 15% for validation, and 15% for independent testing of the network. Performance of each network is evaluated by the mean squared error (MSE), giving the averaged squared distance between the outputs and the targets; the Pearson correlation coefficient of the targets to model outputs, showing the dependence relationship between outputs and targets; and root mean squared error (RMSE). Preliminary comparisons with the accelerometer data over the future specified time horizon reveals more accurate density estimation using the presented neural networks than the existing empirical atmospheric models. As expected, the accuracy decreases for a longer prediction time interval in all cases. Orbit propagation is performed on each satellite using the densities estimated by the neural networks to determine and compare the orbit error associated with each network. It is found that the networks presented reduce the orbit propagation error substantially. Additional research shows the presented neural networks provide improved neutral densities and reduced orbit propagation error when trained using inputs obtained from multiple empirical models when no accelerometer data are available. The case studies are still being conducted to determine which network architecture produces the least density estimation and orbit propagation error. This paper provides a novel and computationally efficient method of localized neutral density prediction for the purposes of autonomous orbit determination, maintenance, station-keeping, formation flying, collision avoidance, and other adaptive control applications seeking to increase space situational awareness.