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A Basis Function Approach to Position Estimation Using Microwave Arrays
Author(s) -
Webb Andrew R.,
Garner Philip N.
Publication year - 1999
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/1467-9876.00149
Subject(s) - detector , basis function , estimator , inverse problem , regularization (linguistics) , basis (linear algebra) , position (finance) , radar , radial basis function , optics , algorithm , computer science , mathematics , physics , mathematical analysis , artificial neural network , telecommunications , artificial intelligence , statistics , geometry , finance , economics
We consider the problem of estimating the bearing of a remote object given measurements on a particular type of non‐scanning radar, namely a focal‐plane array. Such a system focuses incoming radiation through a lens onto an array of detectors. The problem is to estimate the angular position of the radiation source given measurements on the array of detectors and knowledge of the properties of the lens. The training data are essentially noiseless, and an estimator is derived for noisy test conditions. An approach based on kernel basis functions is developed. The estimate of the basis function weights is achieved through a regularization or roughness penalty approach. Choosing the regularization parameter to be proportional to the inverse of the input signal‐to‐noise ratio leads to a minimum prediction error. Experimental results for a 12‐element detector array support the theoretical predictions.