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As one part of ITS (intelligent transportation system), IRS (intelligent road system) focus on improving the road safety and operation efficiency of highway system based on the idea of cooperation between road infrastructure and vehicles. Many IRS applications such as collision avoidance, automatic lane changing and others are principally based on the knowledge of the accurate geographical locations of interrelated vehicles nearby. Based on the state-space approach, this paper addresses the distributed position estimation problem. Specially, the state transfer matrix and measure matrix of the vehicle are established. And based on vehicle dynamics and Kalman filtering, the model of the position state estimation and prediction are formulated. Finally, we found that this approach can get more accurate results by the simulation under condition that the cooperative vehicle communication is available.