Simultaneous Localization and Mapping (SLAM) is one of the enabling technologies for autonomous navigation of robot. In this paper is to estimate- actual, predicted and optimized pose of robot which is equipped with IMU and non visual sensors using curved features as landmarks. Extended Kalman Filter based SLAM algorithm is applied with Bezier/ B Spline curve parametric algorithm using blending functions to make computations more stable. After conducting 160 runs it has been seen that the deviation is in decrease trends from Extended kalman Filter to Extended kalman Filter with Bezier curve and Extended kalman Filter B Spline along with mathematical modeling