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This paper presents a robust method to estimate the relative distance and speed with the approaching vehicles in side and rear blind region of the vehicle for a BSDS with a vision system. Because the vehicle with same relative distance can be represented at different pixel position on the image frame according to the road curvature, a Perception Action Network has been designed based upon the lane model and the vehicle dynamics in order to recognize the rear side lanes and its curvature under ill conditioned background image. Through the various simulation studies for the proposed BSDS by using MATLAB and PRESCAN, it has been concluded that the proposed method can provide the accurate estimations of the relative distance and speed between the vehicles during lane change with satisfied error tolerance.