Do we know how big the rock is for certain?

Maybe we could anchor one end of your tether to the rock, and then have a ion drive powered anchor at the other end of the tether.

The ion drive would proceed to encircle the asteroid over and over until there was no more tether left, at which point it too would anchor itself to the asteroid.

There could be various instruments a points along the tether that would offer many different methods for tracking the asteriod. (radio beakons, radio recievers, light beackons, and light recievers, photovoltaic cells, reflecting mirrors, and mylar stramers.

The tether could serve as a bus-cable tieing all of the instruments and other devices together.

A processor could be located at both ends of the tether giving it redundancy just in case one part of the tether is destroy or the tether breaks somehow...