Improved performance properties of the CISPRT algorithm for distributed sequential detection

In distributed sequential detection problems, local sensors observe raw local observations over time, and are allowed to communicate local information with their immediate neighborhood at each time step so that the sensors can work together to make a quick but accurate decision when testing binary hypotheses on the true raw sensor distributions. One interesting algorithm is the Consensus-Innovation Sequential Probability Ratio Test (CISPRT) algorithm proposed by Sahu and Kar (IEEE Trans. Signal Process., 2016). In this article, we present improved finite-sample properties on error probabilities and expected sample sizes of the CISPRT algorithm for Gaussian data in term of network connectivity, and more importantly, derive its sharp first-order asymptotic properties in the classical asymptotic regime when Type I and II error probabilities go to 0. The usefulness of our theoretical results are validated through numerical simulations.