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Traffic congestion is a widespread problem. Dynamic traffic routing systems and congestion pricing are getting importance in recent research. Lane prediction and vehicle density estimation is an important component of such systems. We introduce a novel problem of vehicle self-positioning which involves predicting the number of lanes on the road and vehicle's position in those lanes using videos captured by a dashboard camera. We propose an integrated closed-loop approach where we use the presence of vehicles to aid the task of self-positioning and vice-versa. To incorporate multiple factors and high-level semantic knowledge into the solution, we formulate this problem as a Bayesian framework. In the framework, the number of lanes, the vehicle's position in those lanes and the presence of other vehicles are considered as parameters. We also propose a bounding box selection scheme to reduce the number of false detections and increase the computational efficiency. We show that the number of box proposals decreases by a factor of 6 using the selection approach. It also results in large reduction in the number of false detections. The entire approach is tested on real-world videos and is found to give acceptable results.