Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models

Abstract

Seeking improvements in speed and accuracy in multiobject trajectory simulations, a solution methodology is presented that takes advantage of 1) new high-fidelity geopotential and third-body perturbation models that efficiently trade memory for speed, and 2) a graphics processing unit based integrator to achieve parallelism across multiple objects. The two methods combined lead to multiplicative speedups, making the tool three orders of magnitude faster, in some cases, compared to the same simulation performed in serial on a single central processing unit. The tool is capable of Monte Carlo simulations of a single object or of propagating the mean and covariance of all the objects in a space catalog. The tool performance is demonstrated for 1) a five-day Monte Carlo simulation of the state uncertainty point cloud modeled with over one million objects, and 2) a seven-day simulation of position and velocity states of a full space catalog with over 250,000 objects. The simulations required approximately 1 and 3 h of runtime, respectively, on a single desktop workstation using a single-core central processing unit and a single graphics processing unit. The solution method is applicable to a variety of space situational awareness applications, including orbit determination, catalog maintenance, uncertainty propagation, and conjunction analysis.

Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions

“…Parallelizing the computations on multiprocessor CPUs or on Graphics Processing Units (GPUs) reduces the runtime of the simulations significantly [7][8][9] at the cost of increasing the difficulty of implementation [10]. Reducing the number of sample points required for a result with satisfactory confidence bounds is sometimes possible through variance reduction techniques [11].…”

An Online Gravity Modeling Method Applied for High Precision Free-INS

“…To improve the efficiency of SHMs’ execution, 3D interpolation models perform more acceptably for the Earth’s application [12]. The modeling method, effectively a trade-off between speed and memory, stores nodal gravity field information on an equivalent spherical grid.…”

“…Recently, the developments of memory and processor technology applied for satellites have motivated more works on the 3D interpolation models. Interpolation methods, such as weighting functions, wavelets, B-splines and octrees, were employed in the models to reduce the computational complexity [12,15]. Efficient models, such as the cubed-sphere model and the fetch model, were established to balance accuracy with complexity.…”

A Novel Gravity Compensation Method for High Precision Free-INS Based on “Extreme Learning Machine”

“…However, the accuracy of these models cannot satisfy the requirements of high precision INS, especially in rough topography, such as mountains, plateaus and oceanic trenches [7]. The third way is to obtain the gravity disturbance using the interpolation method based on measured gravity data on the geoid, then to process the gravity disturbance to the height where INS has an upward continuation [4,8]. In recent years, the most popular interpolation methods used in the geodetic and geophysical communities have been the inverse distance weighted (IDW) interpolation method and the bilinear interpolation method [9,10].…”