D-ary Sequential Tests of Circular Error Probability

In the context of evaluating a system’s precision quality, one wants to utilize observed two-dimensional data to quickly test the hypotheses on the circular error probability (CEP) or the probability of nonconforming, which refer to the chance of the system hitting or missing a pre-specified disk target, respectively. We propose to develop efficient sequential tests based on the D-ary quantization of the observed two-dimensional data. We not only analyze the asymptotic performance limits of non-stationary D-ary quantization in the CEP context, but also investigate the optimal stationary D-ary quantizers from both theoretical and practical viewpoints. Our results suggest that the sequential probability ratio test (SPRT) based on the stationary triplet quantization is often efficient and makes operational sense in practice.