How I would do a track and trail kind of thing:
1) Set up a barrier search across a choke point. I can gauge the effectiveness of my barrier by making some assumptions about my target's transit speed and my own sensor range. There exist various formulas I can plug those numbers into. They all come from the same idea, just figuring out the fractional area covered by a searcher in a reference frame where the target is stationary. It's more Koopman geeking, basically. Naval Operations Analysis by Wagner explains a lot of it.
A good scenario like this should begin with at least the initial position of the target uncertain. The speed is another variable to play with. This is one of those scenarios where the outcome depends on geometry that I keep harping about.
2) Once I detect and localize my target, it depends on how quickly he's moving. A faster target will be more difficult to maneuver close to, even though he'll be easier to detect. Once I make my decisions about how to navigate close to him, i figure I'll just close until I get broadband on the sphere. From that point on I'd just keep my weapons ready to go.
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