Offline map matching involves aligning historical trajectories of mobile objects, which may have positional errors, with digital maps. This is essential for applications in intelligent transportation systems (ITS), such as route analysis and traffic pattern mining. Existing methods have two main limitations: (i) they assume a uniform Localization Error Distribution (LED) across urban areas, neglecting environmental factors that lead to suboptimal path search ranges, and (ii) they struggle to efficiently handle local non-shortest paths and detours. To address these issues, we propose a novel offline map matching method for sparse trajectories, called LNSP, which integrates LED modeling and non-shortest path detection. Key innovations include: (i) leveraging public transit trajectories with fixed routes to model LED in finer detail across different city regions, optimizing path search ranges, and (ii) scoring paths using sub-region dependency LED and a sliding window, which reduces global map matching errors. Experimental results using real-world bus and taxi trajectory datasets demonstrate that the LNSP algorithm significantly outperforms existing methods in both efficiency and matching accuracy.