Passive systems theory with narrow-band and linear constraints: Part II -- Temporal diversity

This paper is part of a series of three papers studying passive tracking problems arising in navigation and positioning applications. The basic question here lies with the determination of the position and dynamics of a point source being tracked by an omnidirectional observer, through demodulation of the Doppler effect induced on the radiated signals by the relative motions. A simple model, fitting a finite parameter nonlinear estimation context, is developed, the receiver designed, and its mean-square error performance studied. It is shown that, besides the speed and angle estimation, simultaneous global range passive tracking is possible. The signal model precludes range acquisition from synchronous measurement of the absolute phase reference: the global range estimation is attained by processing the higher order temporal modulations (varying Doppler). Quantifying the statistical and geometric performance tradeoffs, the work presents simple expressions and graphical displays that can be used as design tools in practical passive tracking problems. A subsequent paper considers the space/ time coupling issues, generalizing the study to the context where a moving source is tracked by a directional array.