|Minimax Lower Bounds for Circular Source Localization
|Aolin Xu, *, United States; Todd Coleman, UCSD, United States
|E.4: Estimation and Applications
|Detection and Estimation
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|We consider the problem of estimating the unknown location of a spatial signal defined on a circular interval from noisy measurements. Lower bounds are derived for the minimax risk of the localization error defined by the circular distance. The lower bounds reveal the fundamental dependence of the localization error on various problem parameters, including the shape of the signal, the noise level, the length of the interval, the number of sensors, and the number of measurement trials. Le Cam's method and Fano's method are used for the derivation. All lower bounds are non-asymptotic, and different lower bounds are tight in different problem parameters. We also derive a Bayesian Cramer-Rao lower bound for the problem of linear source localization, which helps us understand the tightness of the lower bounds for the circular source in some asymptotic situations as well.