Joint maximum-likelihood source localization and unknown sensor location estimation for near-field wideband signals

In this paper, we derive the maximum-likelihood (NIL) location estimator for wideband sources in the near-field of a passive array. The parameters of interest are expanded to include the source range in addition to the angles in the far-field case. The NIL estimator is optimized in a single step as opposed to many that are optimized separately in relative time-delay and source location estimations. The ML method is capable of estimating multiple source locations, while such case is rather difficult for the time-delay methods. To avoid a multi-dimensional search in the ML metric, we propose an efficient alternating projection procedure that is based on sequential iterative search on single source parameters. In the single source case. the ML estimator is shown to be equivalent to maximizing the sum of the weighted cross-correlations between time shifted sensor data. Furthermore. the NIL formulation can expand the parameters to include the distance of a source to a sensor with unknown location. This provides inputs to our online unknown sensor location estimator. which is based on a least-squares fit to observations from multiple sources. The proposed algorithm has been shown to yield superior performance over other suboptimal techniques, and is efficient with respect to the derived Cramer-Rao bound. From the Cramer-Rao bound analyses, we find that better source location estimates can be obtained for high frequency signals than low frequency signals. In addition, large range estimation error results when the source signal is unknown, but such unknown parameter does not have much impact on angle estimation.