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Low-Complexity Hyperbolic Source Localization With A Linear Sensor Array

We develop linear equations for low-complexity source localization, based on time difference of arrival (TDOA) measurements at a linear sensor array. The derivation comes from hyperbolic geometry in Cartesian coordinates, and the algorithm is valid for (possibly wideband) sources in the near or far field. An error analysis is used to predict bias and mean-square error, as well as provide optimal weighting for a low-complexity noniterative weighted least squares solution. A connection is made with an algorithm for arbitrary array geometry. Simulation results show that the proposed algorithm achieves maximum-likelihood performance and the CramrRao bound at medium to low TDOA measurement noise level.