The Rao Detection of Weak Signal in Gaussian Mixture Noise

The expectation maximization (EM) algorithm is available for Gaussian mixture density estimation. However, if there is not an appropriate initialization, the iterative computation will stop at initialization trap and lead to improper estimation. In this paper, the moment-EM algorithm is proposed to overcome the problem. It means to compute the moment-estimation of parameter and initialize parameter with moment-estimation firstly, and then amend the estimation through EM algorithm. In succession, with the Gaussian filter based on estimated parameter, the paper presents the Rao decision rule of the weak signal with unknown amplitude under Gaussian mixture noise environment. Simulation results indicate that moment-EM algorithm can estimate parameter accurately and the detection performance of Rao test based on moment-EM Algorithm outperforms that of Rao test based on EM Algorithm