Target tracking among obstacles is an interesting class of motion planning problems that combine the usual motion constraints with robot sensors' visibility constraints. In this paper, we introduce the notion of vantage time and use it to formulate a risk function that evaluates the robot's advantage in maintaining the visibility constraint against the target. Local minimization of the risk function leads to a greedy tracking strategy. We also use simple velocity prediction on the target to further improve tracking performance. We compared our new strategy with earlier work in extensive simulation experiments and obtained much improved results