Nonlinear Modeling of Gated Range Tracker Dynamics

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Nonlinear dynamic models for gated radar range trackers are developed and applied to the range resolution problem. Two common types of tracking loop dynamics, as well as the automatic gain control (AGC), are accounted for in the models. The null detector is formulated in a general way that encompasses many important error detector laws, including centroid and leading- edge. Both discrete-time and continuous-time dynamic models are presented for each class of tracking loop. The discrete-time models are derived using an analytical description of the pulse- to-pulse dynamics of the tracker. The continuous-time models are approximations of their discrete-time counterparts for sufficiently small values of the pulse repetition interval. Each of the models is analyzed for a deterministic target return condition. General criteria for asymptotic stability of equilibrium points of the models are obtained. The most striking of the stability criteria is a sign requirement on the slope of of a "range error curve". These criteria are used in a two- target example to draw conclusions on a tracker's ability to resolve closely spaced targets as a function of target separation. These conclusions are compared with previously reported conclusions on resolvability obtained using Woodward's "ambiguity function" approached.