The present disclosure provides systems and methods for generating smoothed images of an elongate medical device including a plurality of position sensors. The system includes a model construction system configured to be coupled to the medical device and acquire data points corresponding to positions of the position sensors. The computer-based model construction system is further configured to establish a coordinate system, calculate a coordinate for each position sensor, estimate a set of true parameters describing the medical device including a curvature term and a torsion term, calculate a measurement error for each position sensor based on a stiffness parameter, compute smoothed data points for the position sensors based on (i) a function of the estimated set of true parameters and the coordinates of the position sensors, and (ii) a weighting of the measurement error, generate an image of the medical device using the smoothed data points, and display the image.