The advances in low-latency communications networks and the ever-growing amount of devices offering localization and navigation capabilities opened a number of opportunities to develop innovative network-based collaborative solutions to satisfy the increasing demand for positioning accuracy and precision. Recent research works indeed, have fostered the concept of networked Global Navigation Satellite System (GNSS) receivers supporting the sharing of raw measurements with other receivers within the same network. Such measurements (i.e. pseudorange and Doppler) can be processed through Differential GNSS (DGNSS) techniques to retrieve inter-agent distances which can be in turn integrated to improve positioning performance. This paper investigates an improved Bayesian estimation algorithm for a sensorless, tight-integration of DGNSS-based collaborative measurements through a modified Particle Filter (PF), namely Cognitive PF. Differently from Extended Kalman Filter and Uscented Kalman Filter indeed, a PF natively support the non-Gaussian noise distribution which characterizes DGNSS-based interagent distances. The proposed Cognitive PF is hence designed, implemented and optimized according to the architecture of a proprietary Inertial Navigation System (INS)-free Global Navigation Satellite System (GNSS) software receiver. Experimental tests performed through realistic radio-frequency GNSS signals showed a remarkable improvement in positioning accuracy w.r.t. reference PF and EKF architectures.