Direct discrete variational curve reconstruction from derivatives and its application to track subsidence measurements

This paper presents a new direct discrete variational solution to curve reconstruction from derivatives. The formulation of basis functions and the variational problem in terms of matrix algebra has simplified many proofs; including the χ² confidence interval surrounding the reconstructed curve. Simultaneous spatial reconstruction and temporal filtering is implemented. The Method is verified via Monte-Carlo simulations and also applied to the real-time monitoring of rail-track subsidence. In this application a string of inclinometers are mounted along the stretch of track where it will be monitored. The curve representing the form of the track is reconstructed from the measured derivatives.