A novel methodology for measured data fitting

This paper presents a novel methodology for data fitting using a piecewise rational function. That function is able to satisfy any regularity conditions through the direct setting of some free parameters. Moreover, in any grid point of a defined grid we can impose simultaneous interpolation conditions of both the samples and their derivatives. The value of the interpolation function in any point of the input domain depends only on the closest four grid points in its neighborhood. This property bounds the uncertainty propagation in the case of noisy data. A suitable procedure permits to extend the grid beyond the convex hull, so keeping the described properties of the interpolation without affecting the function in the other regions

1. Introduction

THE characterization of a certain phenomenon can be divided into two different phases. The first one concerns the acquisition of a set of measurements. The second one deals with the construction of a function matching the given data as best as possible. This interpolation function can be used to extract the data values in the convex-hull of the input domain. Moreover, in some applications it is necessary to extend the valid domain of this interpolation function outside the given data boundary. This procedure is often called extrapolation. That approach allows us to describe the phenomenon behavior in those regions where no information are available. Owing to the cause of the data lacking, we can point out different cases. For example we cannot acquire the measurements in a direct way [1], or the measured values are unreliable or missing [2], or an interrupted data collection could occur [3]. All these cases frequently happen in aerospace missions. The whole procedure, consisting of both interpolation and extrapolation, is usually referred as data fitting.