This paper presents a source localization algorithm based on the source signal's time-of-arrival (TOA) at sensors that are not synchronized with one another or the source. The proposed algorithm estimates source positions using a window of TOA measurements which, in effect, creates a virtual sensor array. Based on a Gaussian noise model, maximum likelihood estimates (MLE) for the source position and displacement are obtained. Performance issues are addressed by evaluating the Cramer-Rao lower bound and considering the virtual sensor array's geometric properties. To track the source trajectory from the TOA measurement, which is a nonlinear function of source position and displacement, this localization algorithm is combined with the extended Kalman filter (EKF) and the unscented Kalman filter, resulting in good tracking performance
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Li et al. (2006) studied this question.
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