Uncertainties in a direction-finding sensor affect the determined orbit. In a radio-frequency interferometer, modeling only phase difference (timing) uncertaintywith a normal distribution, the posterior probability density function ofthe direction is multimodal. We show that by treating the probability densityfunction of the direction cosine as a discrete set of disconnected regions, orsegments, corresponding to each mode, and computing within each mode aconventional mean and standard deviation, we can retain information thatwould be lost given a conventional treatment which is optimized for aunimodal result. With a corresponding generalization in other parts of the calculation,such as observation association and orbit determination, we may obtainnot only improvement of results from a conventional antenna array, butthe possibility that a less expensive, simplified array, that can still contributevaluable orbital knowledge, and, due to its lower cost, could enjoy more widespreaddeployment. We introduce and explain the notion of Multiple ModeCombinatorial Hypothesis Least Squares (MMCHLS), graphing the results obtainedfrom synthesized observations, comparing with the known correct result,as an idea of how that generalization might proceed.
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