Robust Semidefinite Relaxation Method for Energy-Based Source Localization: Known and Unknown Decay Factor Cases

Acoustic energy-based source localization has aroused many researchers' interest because of its low cost and easy implementation. In this paper, we focus on the centralized energy-based source localization problem. For the case of known decay factor, a highly nonlinear and non-convex weighted least squares (WLS) problem is formulated. By taking the ratio of received energy and using the first-order Taylor-series expansion, the original WLS problem can be converted to an approximate WLS problem. Then, the semidefinite relaxation (SDR) technique is leveraged to obtain a convex semidefinite program, which can be efficiently solved. For the case of unknown decay factor, a new iterative method is proposed to jointly estimate the source location and the decay factor. In each iteration, a robust weighted least squares (RWLS) problem is formulated and solved to alleviate the model uncertainties introduced by the unknown decay factor. By doing so, the newly proposed iterative method is shown to be robust to the inaccurate initial decay factor estimate. Simulations are conducted to test the performance of the proposed method in both cases, and the results indicate that the proposed method delivers superior performance over several existing methods.