Efficient and Robust EM Algorithm for Multiple Wideband Source Localization

Source-localization techniques are crucial in transportation applications such as navigation or Global Positioning Systems (GPS). A computationally efficient technique for multiple wideband source localization is presented in this paper using the expectation–maximization (EM) algorithm in the near field of a sensor array/area. Our basic idea is to decompose the recorded sensor data, which is a superimposition of multiple sources, into individual components in the frequency domain and then separately estimate the corresponding location parameters associated with each source. Instead of the conventional alternating projection (AP) method, we propose to adopt the EM algorithm in this paper; our method involves two steps, namely, Expectation (E-step) and Maximization (M-step). In the E-step, the individual incident source waveforms are estimated. Then, in the M-step, the maximum-likelihood (ML) estimates of the source-location parameters are obtained. These two steps are iteratively and alternatively executed until the user's predefined convergence is reached. The computational complexity comparison between our proposed EM algorithm and the existing AP scheme is also investigated. Provably, it is shown through Monte Carlo simulations that the computational complexity of the proposed EM algorithm is significantly lower than that of the conventional AP scheme. We also derive the Cramer–Rao lower bound (CRLB) for the source-location estimates.