Three-dimensional dislocations in a uniform linear array's isotropic sensors-Direction finding's hybrid Cramér-Rao bound

Abstract

The linear array’sone-dimensional spatial geometry is simple but suffices forunivariate direction finding, i.e., isadequate for the estimation of an incident source’s direction-of-arrival relative to the linear array axis. However, thisnominalone-dimensional ideality could be often physically compromised in the real world, as the constituentsensors may dislocatethree-dimensionally from their nominal positions. For example, a towed array is subject toocean-surface waves and to oceanic currents [Tichavsky and Wong (2004). IEEE Trans. Sign. Process.52(1),36–47]. This paper analyzes how a nominally linear array’sone-dimensional direction-finding accuracy would bedegraded by thethree-dimensional random dislocation of the constituent sensors. This analysis derives the hybridCram er-Rao bound (HCRB) of the arrival-angle estimate in a closed form expressed in terms of the sensors’ disloca-tion statistics. Surprisingly, the sensors’ dislocation could improve and not necessarily degrade the HCRB, depend-ing on the dislocation variances but also on the incident source’s arrival angle and the signal-to-noise power ratio