Hybrid Cramér-Rao bound of direction finding, using a triad of cardioid sensors that are perpendicularly oriented and spatially collocated.

Cardioid microphones/hydrophones are highly directional acoustical sensors, which enjoy easy availability via numerous commercial vendors for professional use. Collocating three such cardioids in orthogonal orientation to each other, the resulting triad would be sharply directional yet physically compact, while decoupling the incident signal's time-frequency dimensions from its azimuth-elevation directional dimensions, thereby simplifying signal-processing computations. This paper studies such a cardioid triad's azimuth-elevation direction-of-arrival estimation accuracy, which is characterized here by the hybrid Cramér-Rao bound.

A uniform circular array of isotropic sensors that stochastically dislocate in three dimensions-The hybrid Cramér-Rao bound of direction-of-arrival estimation.

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 Cramér-Rao bound (HCRB) in a closed form that is expressed explicitly in terms of the sensors' dislocation parameters.

Beamforming pointing error of a triaxial velocity sensor under gain uncertainties.

A "triaxial velocity sensor" consists of three uniaxial velocity sensors, which are nominally identical, orthogonally oriented among themselves, and co-centered at one point in space. A triaxial velocity sensor measures the acoustic particle velocity vector, by its three Cartesian components, individually component-by-component, thereby offering azimuth-elevation two-dimensional spatial directivity, despite the physical compactness that comes with the collocation of its three components. This sensing system's azimuth-elevation beam-pattern has been much analyzed in the open literature, but only for an idealized case of the three uniaxial velocity sensors being exactly identical in gain.