Passive systems theory with narrow-band and linear constraints: Part I--Spatial diversity

This paper studies passive problems where the receiver extracts from the source radiated signature information concerning the parameters defining the relative source/receiver geometry. A model encompassing the fundamental global and local characteristics for passive positioning and navigation is presented. It considers narrow-band signals, imposes linear constraints on the geometry, and exhibits explicitly the symmetry between the space and time aspects. The analysis concentrates on questions of global geometry identifiability, emphasizing the passive global range acquisition. The maximum-likelihood processor is analyzed by studying the ambiguity structure associated with inhomogeneous passive narrowband tracking. Bounds on the global and local mean-square error performance are studied and tested via Monte Carlo simulations. By considering two limiting geometries, a distant and a close observer, simple approximate expressions for the mean-square errors are presented and compared to the exact bounds. Herein the study is restricted to stationary geometries where the source is located by an extended array (spatial diversity). Subsequent papers generalize the study to moving sources (temporal diversity) and to coupled geometries.