Maximum Observation of a Target by a Slower Observer in Three Dimensions

What is it about?

In this work, we consider a two-agent scenario consisting of an observer and non-maneuvering target. In the scenario, the observer is considered to be maneuverable and slower than the target. The observer is endowed with a nonzero radius of observation within which he strives at keeping the target for as long as possible. Using the calculus of variations, we solve for the heading and flight path angle of the observer which maximizes the amount of time the target vehicle is contained within his observation radius. Using the optimal heading and flight path angle, the exposure time is computed, based upon the initial azimuth and elevation by which the target is captured by the observer. Presented, along with examples, are the zero-time of exposure conditions, maximum exposure time conditions, and proof that observation is persistent under the optimal observer strategy.

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