A 2-SPRT Based Approach to Multiple-Model Hypothesis Testing for Multi-Distribution Detection

This paper presents an approach to multiple-model hypothesis testing (MMHT) based on 2-SPRT (2-MMSRPT) for detecting unknown events that may have multiple possible distributions. The sequential probability ratio test (SPRT) based MMHT method (MMSPRT) is promising because of its efficiency and theoretical validity. However, it may suffer from SPRT's lack of an upper bound on its stopping time, especially in the mis-specified case. The proposed 2-MMSPRT algorithm not only copes with this problem, but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints. Specifically, we prove the theoretical validity of 2-SPRT for the problem of testing hypotheses with multivariate normal densities. Moreover, we present a technique of forced independence and identical distribution (i.i.d.) to map the non-i.i.d. likelihood ratio sequence to an i.i.d. one, which enables us to apply the SPRT and 2-SPRT effectively to the dynamic case (under the linear-Gaussian assumption) with a non-identical distribution. Also, 2-MMSPRT's detection efficiency under some assumptions/approximations is verified. Performance of 2-MMSPRT is evaluated for signal detection and model-set selection problems in several scenarios. Simulation results demonstrate the detection efficiency of the proposed 2-MMSPRT compared with the MMSPRT and some traditional tests.