Estimation and detection of a weak magnetic dipole signal with a latent variable based on a non-probability-distribution EM algorithm

Abstract

The estimation and detection of a weak magnetic dipole signal is a critical problem in magnetic target detection. The difficulty arises due to a latent variable in the model, which affects the estimation and detection performance, especially at low signal-to-noise ratios (SNRs). A non-probability-distribution expectation maximization (NPD-EM) algorithm is proposed to estimate the magnetic dipole signal with the latent variable at low SNRs. A reasonable value of an intermediate variable instead of the optimal one is determined without any probability information in the iteration of the NPD-EM algorithm, which overcomes an unknown probability distribution appearing in the traditional expectation maximization (EM) algorithm and reduces the calculated amount by 3 orders of magnitude compared with the traditional EM algorithm. A statistic based on the NPD-EM algorithm representing an unbiased estimator of the target signal energy is constructed to detect the magnetic dipole signal at low SNRs, and an innovative compensation in the detector is introduced so as to reduce the noise influence on the statistic. The experiment results show that, the constructed detector is comparable to the ideal matching filter due to the attractive performance of the NPD-EM algorithm and the outstanding statistic.