Aspects of vector-sensor processing

This dissertation explores some aspects of signal processing with acoustic, electric, and magnetic vector sensors. These sensors measure vector physical quantities such as the three-dimensional magnetic field, and are of interest because, unlike scalar or magnitude sensors, they preserve the structure of the field. We first compute fundamental limits on the number of plane-wave signals that a vector sensor can simultaneously identify. We then show how both vector sensors and diversely-oriented scalar sensors may be applied profitably to magnetoencephalography, where magnetic field measurements are used to locate electrical activity in the human brain.;Since the sensors' measurements are corrupted by noise, the analyses in this dissertation rely on statistical methods to derive their conclusions. One statistical method involves computing the Cramer-Rao lower bound on error covariance, the complexity of which can be prohibitive because of the large number of unknown parameters. We conclude with a way to reduce this complexity by circumventing computations involving so-called nuisance parameters. The complexity reduction is demonstrated on a vector-sensor model.