A sequential maximum-likelihood multiple source tracker and the relation of phased-locked loop theory to eigenstructure methods

The multiple-source location methods that utilize multiple-sensor data eigenstructure, in particular the MUSIC and minimum-norm algorithms, have similarities to phase-locked loop (PLL) theory. The author derives a phase-lock type bearing solution from maximum-likelihood considerations assuming uncorrelated sources and shows the effects of other sources in the equivalent bandwidth. This version effectively normalizes input signal power and excludes the need for estimation of either the source power or random phase variations. Noise analysis leads to the determination of error variance, probability of detection and resolution. The derivations shed considerable light on the eigenstructure methodologies. Optimum weights on the noise-space eigenvectors are obtained, and simulations show a significant resolution improvement over MUSIC