Bayesian mapping with probabilistic cubic splines

This proposal presents the integration of interpolating global cubic splines into a general function regression framework to approximate curved functions or more dimensional curves based on noisy observations. We rearrange the iterative process of spline parameter calculation and obtain a practical linear matrix formulation. Then we employ Bayesian techniques to estimate spline model parameters and to perform model selection. While the number of basis functions is equal to the number of spline supporting points, this regularizer is automatically adapted towards an optimal trade-off between model complexity and model predicting performance, when Bayesian model selection is performed. Finally, we apply the proposed method within a robotic mapping scenario and learn geometric shapes of roads from noisy GPS positions measurements.