Robust Beamforming in GPS Arrays

Robert G. Lorenz and Stephen P. Boyd

Abstract:	Multipath frequently limits the performance of carrier phase-based relative positioning and precision navigation techniques. Multipath mitigation techniques that discriminate between the direct signal path and reflections based on differences in time-of-arrival are of little utility in combating close-in multipath. In this paper, we describe an antenna array for mitigating multipath based on angle-of-arrival differences. We also describe signal processing algorithms for combining the output of the array elements to minimize the effect of interferences and multipath. This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the assumed array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncertainty in the array manifold is modeled explicitly via an uncertainty ellipsoid that gives the possible values of the array for a particular look direction. We choose weights that minimize the total weighted power output of the array, subject to the constraint that the gain exceeds unity for all array responses in this uncertainty ellipsoid. Hence, we can guarantee performance of the robust method in the presence of uncertainties. We show that the robust weights can be computed very e±ciently. These methods extend naturally to the case where the aggregate uncertainty arises from more than one component in the signal path, e.g., the array manifold, the radio frequency (RF) electronics, etc. These methods are shown to be directly applicable to antenna arrays with non-uniform responses, e.g., closely-spaced arrays in which the coupling between elements is significant. Measurements taken from a vertically-stacked turnstile array are presented.
Published in:	Proceedings of the 2002 National Technical Meeting of The Institute of Navigation January 28 - 30, 2002 The Catamaran Resort Hotel San Diego, CA
Pages:	409 - 427
Cite this article:	Lorenz, Robert G., Boyd, Stephen P., "Robust Beamforming in GPS Arrays," Proceedings of the 2002 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2002, pp. 409-427.
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