Chernoff test for arbitrary returns from a strong-or-weak target

The active management of the sensing stage in radar systems can provide substantial gains in performance. This concept is illustrated in the application of an active inference procedure due to Chernoff, to the operation of a cognitive radar system. A simple model for the radar returns from different targets is proposed, and Chernoff´s test is cast in a setting where the environment is sequentially probed by using a sequence of waveforms, each tailored to a specific target. An active multihypothesis test that approximates Chernoff´s optimal solution is then developed. The test is active in the sense that the radar can choose at each step which is the best waveform to emit, depending upon the past selections and the past radar returns, and it is prone to a simple physical interpretation. The resulting performance is evaluated in the limit of vanishingly small risk of miss detection, as well as for finite risk via computer simulations and analytical approximations.