Juan Gutierrez, KBR; Waqar Zaidi, L3Harris
Keywords: Statistical Distance, Consensus, Implicit, Divergence, Centroid, Gaussian Mixture Model, Space Traffic Management, Space Situational Awareness
Abstract:
This paper explores the concept of consensus between implicitly updated decentralized probability distribution functions (PDFs). A prior PDF tied to an angles-only optical observation of a space object is formed using a probabilistic method of admissible regions. This PDF is then implicitly updated at a time of three decentralized radar measurements using a closed-form solution derived from conservation equations. The implicit update produces three independent bimodal PDFs where one mode is eliminated based on the sensor field of view. We then apply a Gaussian Mixture Model (GMM) to the second non-Gaussian mode of each PDF and study information divergence between the components of PDF’s GMM representation. Specifically, the Burbea-Rao and Bhattacharyya centroids are utilized to understand difference in distributions as well as perform a fusion step between GMM components to produce a new mean and covariance. In verifying the statistical distances from selection of GMM components establishes a consensus approach to obtain distributions closer to truth state.
Date of Conference: September 14-17, 2021
Track: Astrodynamics