Brandon Jones, University of Texas at Austin; Emmanuel Delande, The University of Texas at Austin; Enrico Zucchelli, University of Texas at Austin; Moriba Jah, University of Texas at Austin
Keywords: Astrodynamics, Propagation, Uncertainty
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 our knowledge of an orbit state for each object in the catalog, and a refinement of such knowledge given new data. Typically, we represent such knowledge using a Probability Density Function (PDF), with known methods for optimal refinement via Bayesian filtering. Recently, the lead author of this paper presented a multi-fidelity approach to orbit uncertainty propagation that leverages a hierarchy of increasing fidelity force models. This enables a reduced runtime for both particle and Gaussian mixture representations of the orbit-state PDF, but at the cost of some accuracy in the propagation. The error in the approximation may be bounded, but no information on the underlying PDF for the error is available. This introduces a systematic uncertainty, and assuming a uniform PDF for the error biases our understanding of a space objects trajectory. A new representation of uncertainty based on Outer Probability Measures (OPMs), allows for representing systematic errors when only provided bounds on the error or probability of a value. This paper will present a combination of OPMs and multi-fidelity methods for uncertainty propagation to predict our knowledge of a spacecrafts trajectory.
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 and Gaussian Mixture Models when propagated via the unscented transform. Given a small number of additional high-fidelity propagations (on the order of 10-20 samples), we can bound the error of the surrogate for a given particle.
OPMs offer a more general representation of uncertain systems than probability measures, or their associated PDFs. They account for the epistemic or systematic uncertainty due to the limited information we possess on the studied system, as well as the aleatory or random uncertainty due to the inherent randomness of the system (if any). Like probability measures or PDFs, OPMs originate from measure theory; Bayesian inference rules can be developed for OPMs, and a Bayesian estimation framework exploiting uncertainvariables, a generalization of randomvariables accounting for systematic uncertainty, has been recently developed. Some of the authors have exploited OPMs and uncertain variables to model Two-Line Elements (TLEs) as a data source, and to propose an orbital propagator accounting for systematic uncertainty, in a single-object SDA tracking problem. Since the multi-fidelity uncertainty propagation induces a systematic error that we are able to bound but not characterize, an OPM-based formulation should provide an appropriate representation of a multi-fidelity orbital propagator in the context of filtering.
In this paper, we propose an OPM-based representation of a multi-fidelity orbital propagator and illustrate the concept and performance on a simulated scenario of a space object. Using OPMs to represent the systematic uncertainty introduced in the multi-fidelity approximation will improve accuracy of the propagated uncertainty, which has implications to estimation, data association, sensor tasking, and characterization. This paper focuses on the impacts to data association when correctly accounting for all sources of uncertainty in the computationally efficient multi-fidelity approach. Performance will be quantified by propagator runtime and accuracy of the resulting data association hypotheses.
Date of Conference: September 17-20, 2019
Track: Astrodynamics