Hybrid RSS/TDOA Target Localization With Unknown Model Parameters: A Factor Graph Approach

This paper develops low-complexity hybrid received signal strength (RSS) and time difference of arrival (TDOA) localization algorithms for wireless sensor networks (WSNs) using factor graph and message passing techniques, addressing the critical challenge of high-dimensional integration in scenarios with unknown model parameters, i.e., the transmit power (TP) of a target node and the path loss exponent (PLE) of wireless channels. The existing hybrid RSS/TDOA localization algorithms require the knowledge of these model parameters, and have high complexity for minimizing the weighted summation of cost functions of RSS and TDOA measurements. Departing from conventional approaches, the proposed method constructs a factor graph framework to obtain the belief information of target location with RSS and TDOA measurements separately, and decouple the nonlinear relationship between PLE and target location through Taylor series linearization. An alternating maximization strategy is employed to iteratively update parameters, enabling joint estimation of target position and model parameters. The framework supports four practical cases with varying combinations of known/unknown parameters, significantly reducing computational complexity. Simulation results demonstrate that our proposed algorithms achieve localization accuracy close to the Cramer-Rao Lower Bound (CRLB) with diverse noise conditions and sensor densities, outperforming state-of-the-art methods including weighted least squares (WLS) and semidefinite programming (SDP). Remarkably, its computational time is only 10%–30% of existing techniques while maintaining robustness in parameter-unknown scenarios. This work provides an efficient solution for real-time localization in resource-constrained WSNs, particularly where prior knowledge of propagation parameters is unavailable.