A Mixed-Integer Solution for TDOA Based Direct Positioning of Digital Modulation Signal

This paper proposes a direct position determination (DPD) method for a digital modulation signal based on time difference of arrival (TDOA) measurements. Unlike the two-step positioning process, the measurements are used to directly estimate the source position. Fully utilizing information in a transmitted waveform can improve the accuracy of source localization in a single-step method. Based on maximum likelihood (ML) estimates, when the digital modulation scheme is known to the location system, an alternating iterative DPD method is developed to locate the emitter. The objective function of the proposed algorithm takes into account the source position and transmitted symbol sequence, which makes it a mixed-integer optimization problem. In particular, ML sequence estimation is adopted and the complex envelope is restored using a genetic algorithm. Then, based on Newton’s method, an alternating iterative algorithm is proposed to update the position and symbol sequence results. Compared with the existing DPD method, the proposed algorithm gives more accurate location results for unknown waveforms. In addition, the proposed algorithm can reach the Cramér-Rao bound (CRB) for known signal waveforms, as verified using comprehensive simulations.