Optimal N-P detection for multisensor system without high-dimensional integral

Consider detection problem for multisensor system with Gaussian measurements. According to the Neyman-Pearson criterion, the detection probability was maximized subject to an upper limit on the probability of false alarm. In this case, it is well known that the optimal test admits the likelihood-ratio test (LRT) form. However the threshold computation of LRT is generally computationally intractable because of the high-dimensional integral caused by the multisensor measurements. In this paper, we equivalently transform the LRT into semidefinite positive quadratic form, whose distribution can be obtained by recursive formula of a series. More importantly, using such technique, the high-dimensional integral computation can be reduced to one dimensional iterative computation. Therefore, our method can greatly reduce computational burden. Numerical examples support the above analysis.