Comparisons of Split-linear Fitting of Wind Curves

The detection of slope change points in wind curves depends on linear curve-fitting. Hall and Titterington's algorithm based on smooth- ing is adapted and compared to a Bayesian method of curve-fitting. After prior spline smoothing of the data, the algorithms are tested and the er- rors between the split-linear fitted wind and the real one are estimated. In our case, the adaptation of the edge-preserving smoothing algorithm gives the same good performance as automatic Bayesian curve-fitting based on a Monte Carlo Markov chain algorithm yet saves computation time. This study is aimed at the improvement of the aircraft autopilot concep- tion process. The autopilot allows landings in bad weather conditions and must guarantee passengers safety, touchdown comfort, and precision. We study in par- ticular the influence of wind during automatic landing. We focus on the effect of the linear wind components in the last 30 seconds to show that they are a decisive factor in touchdown precision. This is achieved by comparing simulated landings with either a real wind or its piecewise linear approximation. This has led us to develop a method of split-linear fitting based on slope change detection adapted to our data. This method is similar to those proposed by Jones (1998) which aim at predicting the influence of discrete gusts on linear systems. Slope change detection is associated with edge and peak detection. Two kinds of method can be adapted : a classic one, based on smoothing and a Bayesian one based on Monte Carlo Markov Chains. Hall and Titterington (1992) pro- posed an edge-preserving smoothing algorithm. It is based on edge detection by comparisons of three smoothings. The aim of this method is to compute, for each given point, three smoothed estimates of the function, based on the data to the right, to the left and on both sides of the point. Each discontinuity is asso- ciated with a local maximum of the difference between the three fits. Wu and Chu (1993) took this algorithm and modified it using kernel smoothing instead