Passive systems theory with narrow-band and linear constraints: Part III -- Spatial/Temporal diversity

This is the last of a series of three papers studying the theory of passive systems. The model assumes that i) the narrow-band signals are transmitted through a Rayleigh channel, ii) the observing array is geometrically linear, and iii) the source motion is deterministic. Ranging techniques based on synchronized measurements of the travel time delay are precluded by the incoherent phase model considered. The paper explores alternative methods that process the phase modulations induced on the signal by the extended geometry and relative dynamics. The present work applies maximum likelihood theory to design the receiver, being concerned with the global identifiability of all parameters defining the relative source/receiver geometry and dynamics. The emphasis is placed on the passive range global acquisition. In contradistinction with the previous papers, where the time stationarity (Part I) or the space homogeneity (Part II) lead to a one-dimensional processor, here the receiver involves processing over both domains. The paper considers the issues of space/time factorability and coupling arising in nonhomogeneous passive tracking. The cross coupling, resulting in more complex filters, improves the receiver acquisition capability. Resorting to Taylor's series type studies, the paper quantifies these improvements, as well as the receiver's mean square error performance, in terms of intuitively satisfying analytical expressions.