Effects of sensor placement on acoustic vector-sensor array performance

We consider the role played by the sensor locations in the optimal performance of an array of acoustic vector sensors. First we derive an expression for the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous wholespace and show that it has a block diagonal structure, i.e., the source location parameters are uncoupled from the signal and noise strength parameters. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled from each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or "canonical" location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptotic normalization, which are useful measures in three-dimensional bearing estimation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations, We then show that our previously derived geometrical conditions are also sufficient to ensure that this bound is independent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic.