This paper proposed a novel weighted multidimensional scaling (MDS) estimator for estimating the position of a stationary emitter with sensor position uncertainties using time-difference-of-arrival measurements. The solution is closed form and unbiased. It is shown analytically to achieve the Cramer-Rao lower bound performance in small noise region. Simulation results show that the proposed estimator offers smaller bias and mean square error than the two-step weighted least square approach and traditional MDS estimator ignoring sensor position uncertainties at moderate noise level. Additionally, the computation complexities of them are comparable.

The classic two-step approach for time difference of arrival (TDOA) geolocation is suboptimal since the TDOA measurements have not followed the constraint that all measurements should be consistent for a geolocation of a single emitter. In this study, the direct TDOA geolocation approach is proposed for frequency-hopping (FH) emitters. It makes use of the sparsity of the FH signals in frequency domain, and constructs a cross correlation function (CCF) matrix in frequency domain, then the location estimate is obtained by searching the maximum eigenvalue of the CCF matrix in a two dimensional grid. The Cramer-Rao lower bound has been derived. The resolution for a single FH signal geolocation is also analysed. Further, an extension of the new method for multiple FH emitters direct TDOA geolocation has been presented. The performance comparison between the direct approach and the conventional two-step method has been made by simulations. The results demonstrated that the proposed method outperforms the conventional two-step method. The simulations also demonstrated the effectiveness of the new method in locating multiple FH emitters.

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