Globally Valid Posterior Cramér-Rao Bound for Three-Dimensional Bearings-Only Filtering

, und . IEEE Transactions on Aerospace and Electronic Systems (2018)


This work addresses the problem of three-dimensional target motion analysis from bearing measurements. The established description of uncertain directional data involves azimuth and elevation angles with additive Gaussian noise. Investigation of this widely accepted representation in terms of the corresponding Fisher information matrices reveals that the underlying probability densities are only valid for small absolute elevation angles and precise measurements. Employing spherical statistics, an alternative representation is proposed that is sensible for the whole state space and arbitrarily imprecise bearing sensors. Based on this, a globally valid posterior Cramér-Rao lower bound is derived.

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