Abstract:
An array’s constituent sensors could be spatially dislocated from their nominal positions. This
paper investigates how such sensor dislocation would degrade a uniform circular array (UCA) of
isotropic sensors (like pressure sensors) in their direction-finding precision. This paper analytically
derives this direction finding’s hybrid Cram er-Rao bound (HCRB) in a closed form that is
expressed explicitly in terms of the sensors’ dislocation parameters. In the open literature on UCA
direction finding, this paper is the first to be three-dimensional in modeling the sensors’ dislocation.
Perhaps unexpectedly to some readers, sensor dislocation could improve and not necessarily
degrade the HCRB; these opposing effects depend on the dislocation variances, the incident
source’s arrival angle, and the signal-to-noise power ratio—all analyzed rigorously in this paper.
Interesting insights are thereby obtained: (a) The HCRB is enhanced for the impinging source’s
polar arrival angle as the sensors become more dislocated along the impinging wavefront due to
aperture enlargement over the stochastic dislocation’s probability space. (b) Likewise, the HCRB is
improved for the azimuth arrival angle as the sensors become more dislocated on the circular
array’s plane, also due to aperture enlargement. (c) In contrast, sensor dislocation along the incident
signal’s propagation direction can only worsen the HRCBs due to nuisance-parameter effects
in the Fisher information. (d) Sensor dislocation orthogonal to the array plane must degrade the
HCRB for the azimuth arrival angle but could improve the HCRB for the polar arrival angle.
