MMSE-Based Distributed Direct Position Determination in Single-Hop Sensor Networks

Distributed adaptive direct position determination (D-ADPD) is a time-difference-of-arrival (TDOA)-based localization algorithm designed for single-hop sensor networks. The algorithm is iterative and typically initialized by using two-step methods. However, the obtained initial values and the convergence performance of the D-ADPD are poor in low signal-to-noise ratio (SNR) environments, resulting in significant positioning errors. The algorithm also fails when channel propagation induces phase offsets. To address these issues, this paper proposes a distributed direct position determination algorithm with single-hop transmission. The proposed algorithm consists of three steps: First, a distributed frequency domain detection method is proposed to identify the radiated signal's frequency components. A cost function is then formulated based on these detected frequency components with the minimum mean square error (MMSE) criterion to eliminate the influence of out-of-band noise. Second, a coarse positioning method is introduced to provide reliable initial values for subsequent iteration. Finally, the algorithm iteratively estimates target positions and compensates for phase offsets using the diffusion strategy and the gradient method. Simulation results demonstrate that the proposed algorithm outperforms the D-ADPD and other similar methods in low SNR environments. When the SNR is between -15 dB and 10 dB, the root mean square error of the proposed positioning algorithm is approximately 5 dB lower than other distributed direct localization methods and about 10 dB lower than that of the classical distributed two-step method. Furthermore, it is insensitive to the channel-induced phase offset, exhibiting greater robustness than the D-ADPD.