Anil Chaudhary (Applied Optimization, Inc.), Tamara Payne (Applied Optimization, Inc.), Keith Lucas (Applied Optimization, Inc.), Kimberly Kinateder (Wright State University), Phan Dao (Air Force Research Laboratory/RV Kirtland AFB, NM), Jeremy Murray-Krezan (Air Force Research Laboratory/RV Kirtland AFB, NM)
Keywords: Synoptic search, Markov chain, Bayes network, transition probability, directed graph, nominal or anomalous status, cross-tag
Abstract:
The objective of Bayesian belief propagation in this paper is to perform an interactive status assessment of geosynchronous satellites as each new data point for the photometric brightness becomes available during the synoptic search performed by a space-based sensor as a part of its routine metric mission. The calculations are performed by using a dimensionless ratio of observed photometric brightness to its predicted brightness. The brightness predictions can be obtained using any analytical model chosen by the user. The inference for a level of confidence in the statistical assessment is performed by making a differential comparison of error in the predictive performance of the model for cluster of satellites that are located within a close proximity to each other. This is meant to render the statistical assessment to be independent of assumptions and algorithms utilized in the analytical model; and to mitigate the effect of bias that could be introduced by the choice of analytical model. It considers that a model performs predictions based on the geometry of observation conditions and any information that could have been extracted by the inversion of prior data on its photometric brightness. Thus the model predictions are deemed invariant. The statistics of error in the model predictions for each satellite within a cluster of closely-spaced satellites is also deemed to be invariant. Thus, if there is a statistical change in the predictive error for a single satellite or a pair of satellites, while remaining unchanged for the rest, there is higher likelihood of anomaly in either the operational status of that satellite or an error in object correlation (i.e. cross-tag). The algorithm in this paper uses a first order Markov chain model to compute a conditional probability value for the satellite status to be nominal or anomalous (i.e., NOM or ANOM), given its latest photometry observation. This calculation is repeated as data for each new observation becomes available. Also, it is performed for each satellite (member) that belongs to a geosynchronous cluster (group). This provides a sequence of conditional probability values for each member in a group. This information is mapped to a tree-like directed graph (i.e. Bayesian network) of nodes. There is a node for each new data point and it represents a hypothesis if the member status is NOM or ANOM at the time of that observation. The conditional probability values for the status of each member in the group are utilized in order to compute the marginal probability (i.e. belief) that the status of an individual member is NOM or ANOM. The propagation of belief summarizes all preceding computations of belief in order to determine a level of confidence in the statistical assessment for its use by an analyst.
Date of Conference: September 9-12, 2014
Track: Non-Resolved Object Characterization