Complexity-Reduced Solution for TDOA Source Localization in Large Equal Radius Scenario with Sensor Position Errors

This paper presents a new algebraic solution for source localization using time difference of arrival (TDOA) measurements in the large equal radius (LER) scenario when the known sensor positions have random errors. The proposed method utilizes the LER condition to directly approximate the true TDOAs so that the originally nonlinear TDOA equations can be recast into ones linearly related to the source position. This enables the use of the closed-form weighted least squares (WLS) technique for source localization and makes the proposed method have lower complexity than the existing technique. The approximate efficiency of the new algorithm is established analytically under strong LER condition. The associated approximation bias is also derived and it is shown numerically to be greater than that of the benchmark technique, especially when LER condition is weak. However, through iterating the proposed method once with bias correction, the proposed method yields comparable localization accuracy with reduced complexity. The theoretical developments are validated by computer simulations.