With the continuous development of the mobile positioning technology and the Internet, spatio-temporal query processing has drawn more and more attention. In the real situation, the directions and trajectories of mobile objects are usually restricted by an underlying spatial network, and the position information is usually uncertain. Based on the general probability distribution function (PDF) used to represent the uncertainty of the positions, incremental processing model and optimization methods for probabilistic query based on split intervals are proposed. By taking the probability distribution approximate center as the estimated position of the target objects, the general position uncertainty problem is solved and the efficiency is improved with a minor cost of accuracy. Finally, based on the real-life road network dataset and synthetic object distribution, the accuracy and efficiency of the proposed models and algorithms are verified.