This paper considers the problem of time-difference-of-arrival (TDOA) source localization using possibly unreliable data collected by the Internet of Things (IoT) sensors in the error-prone environments. The Welsch loss function is integrated into a hardware realizable projection-type neural network (PNN) model, in order to enhance the robustness of location estimator to the erroneous measurements. For statistical efficiency, the formulation here is derived upon the underlying time-of-arrival composition via joint estimation of the source position and onset time, instead of the TDOA counterpart generated in the postprocessing of sensor-collected timestamps. The local stability conditions and implementation complexity of the proposed PNN model are also analyzed in detail. Simulation investigations demonstrate that our neurodynamic TDOA localization solution is capable of outperforming several existing schemes in terms of localization accuracy and computational efficiency.