Nonlinear Expectation Maximization Estimator for TDOA Localization

Time-difference-of-arrival (TDOA) techniques are widely used in high-accuracy positioning systems. The weighted nonlinear least squares (NLLS) algorithm can be used in such systems to estimate the target position. If the range measurement errors can be modeled as additive white Gaussian noise (AWGN), the performance of the weighted NLLS algorithm approaches the Cramér-Rao lower bound (CRLB). However, TDOA with weighted NLLS is complex to implement because the covariance matrix of the range measurements is non-diagonal, which requires matrix multiplication and inversion. In this paper, we develop a low-complexity nonlinear expectation maximization localization algorithm. The proposed algorithm is much simpler to implement than the weighted NLLS method since no matrix manipulation is required, while their performances are similar, both approaching the CRLB.