Systems and methods are described for implementing a catheter model to estimate shape of a deformable catheter in a three-dimensional space. The catheter model includes two or more model segments that correspond to two or more segments of the deformable catheter. Each model segment includes a length and location of model electrode(s) and/or model magnetic sensor(s) corresponding electrodes and/or magnetic sensors of the deformable catheter. Variable shape parameter define a curvature of the segment. Varying the shape parameters generates a plurality of potential catheter shapes. In conjunction with generating the potential catheter shapes, impedance and/or magnetic responses (e.g., measured responses) are obtained for the physical electrodes and/or physical magnetic sensors of the deformable catheter. Using a selected one (e.g., most likely) of the potential catheter shapes and the measured responses, the shape parameters are updated and a catheter shape is generated and displayed.