Abstract In this paper we derive and test a probability-based weighting that can balance residuals of different types in spline fitting. In contrast to previous formulations, the proposed spline error weighting scheme also incorporates a prediction of the approximation error of the spline fit. We demonstrate the effectiveness of the prediction in a synthetic experiment, and apply it to visual-inertial fusion on rolling shutter cameras. This results in a method that can estimate 3D structure with metric scale on generic first-person videos. We also propose a quality measure for spline fitting, that can be used to automatically select the knot spacing. Experiments verify that the obtained trajectory quality corresponds well with the requested quality. Finally, by linearly scaling the weights, we show that the proposed spline error weighting minimizes the estimation errors on real sequences, in terms of scale and end-point errors.