Brandon Jones, University of Texas at Austin
Keywords: Orbit determination, uncertainty propagation, multi-fidelity methods
Abstract:
Space domain awareness (SDA) requires the prediction of a space-object catalog to identify risks to existing missions, update the orbit state estimates for each object, and enable sensor tasking. This prediction requires the propagation of an orbit state Probability Density Function (PDF) for each object in the catalog and a refinement of the PDF given new information via Bayes rule. Prediction of the PDF requires two important elements: a tractable approximation of the PDF, and selection of dynamic models employed to describe propagation. The measurement update requires a similar process to produce a likelihood function using the prior information. Several approximations of a PDF have been proposed in the literature, but little research exists to adaptively select the force- and measurement-model fidelity required for orbit-state PDF propagation and update. Higher-fidelity models require increased computational complexity for their evaluation, but not all orbit regimes require the same models due to, for example, distances from the central body and perturbing third bodies. Recently, the author of this paper presented a multi-fidelity approach to orbit uncertainty propagation that can leverage a hierarchy of increasing fidelity force models. This enables a reduced runtime for both particle and Gaussian mixture representations of the orbit-state PDF. This paper leverages this method to reduce the computation cost of orbit determination.
The multi-fidelity uncertainty propagation approach leverages a hierarchy of orbit force model fidelities to correct a large ensemble of low-fidelity propagations. Using the subspace spanned by the low-fidelity samples, a set of points are selected for high-fidelity propagation. In this context, low-fidelity may be described by force model truncation, propagation via general perturbations, or numeric integration with an increased step size. A bi-fidelity approach combines the low-fidelity propagated states with a small number of samples (on the order of 10) using the highest-fidelity model, and generates a corrected stochastic collocation surrogate for propagating all samples. This method provides a reduced computational burden for the prediction step of Sequential Monte Carlo (SMC) and Gaussian Mixture Models (GMMs) when propagated via the unscented transform.
The goal of this effort is to reduce the computation burden of nonlinear filtering with applications to SDA, and this paper leverages the new approach to enable multi-fidelity orbit determination via SMC-based estimation. Recent efforts in nonlinear estimation for space objects focus on GMM filters for the sake of tractability. A potential boon to space-object tracking is the use of SMC-based filters, but at the cost of increased runtime. While not their only advantage, such SMC approaches enable improved models for detection and survival probability, both of which are greatly simplified or require heuristic approaches to allow for their use in GMM filters. For cases where many low-fidelity propagations may be performed, the multi-fidelity approach makes SMC methods tractable with a reduced computation load. For example, thousands of low-fidelity propagations (e.g., two-body and J2 perturbations) may be achieved via parallelization on a Graphical Processing Unit (GPU). This reduced runtime mitigates the existing limitations on SMC filters required for multi-target tracking. In theory, the approach also allows for multi-fidelity sensor models to be employed in the filter to approximate the measurement likelihood function, which will be developed in this work.
This paper presents the framework for multi-fidelity orbit determination via SMC methods, and demonstrates the efficacy of the approach with simulated observations. We focus on single-target tracking via a Bayes-optimal Bernoulli filter, which allows for incorporating clutter, missed detections, and target survival into a mathematically rigorous framework. Demonstrations of the proposed method employ probability of detection models not feasible in GMM filters. Performance of the approach will be quantified via estimated state accuracy, filter consistency, and runtime.
Date of Conference: September 11-14, 2018
Track: Astrodynamics