In the sharing of user trajectory data of road networks, privacy leakage emerges to be a major concern because attackers may make aggressive reasoning and analysis based on the published trajectory data with certain background knowledge to obtain the privacy information (e.g. location) associated with individuals. Most existing trajectory privacy-preserving methods require special assumptions about the types of attacks and their associated background knowledge, are therefore unable to achieve the required strength for privacy protection. This paper proposes a novel algorithm of differential privacy preserving trajectory data publishing for road networks by spatial coupling of ambiguity using a noisy R-tree (Cons-XRT), which can resist attacks with arbitrary background knowledge even in the case of sparse trajectories. Our algorithm first blurs the spatial trajectory locations using an R-tree index of the trajectory data to form a noisy R-tree of the trajectory that satisfies the differential privacy preserving condition. It then generates trajectory count values to hide the relative changes of the statistical data of adjacent sections in adjacent periods, and eliminate the fluctuations of statistical data. Finally, it deploys a fast query algorithm for spatial range count query which uses the noise counts in the noisy R-tree index nodes to quickly return the number of moving objects satisfying differential privacy. Extensive experiments on real public transport vehicle trajectory datasets of Guangdong Province show that our Cons-XRT method achieves differential privacy trajectory protection which can resist the attacks with maximum background knowledge.