The practical efficiency of using the apparatus of cubic B-splines for approximating time series of trajectory measurements is analyzed. The approximating function is represented as a linear combination of basis splines providing a minimum of the sum of squares of the residuals of measurements. The possibility of approximation of series with different degree of smoothness, consistent approximation of the coordinate series and the corresponding series of speeds, interpolation of the approximated data between nodes of the original grid. Filling in the gaps in the measurements is carried out using a linear model. Detection of intervals with anomalous measurements and their correction at these intervals is carried out by median processing of the initial series, followed by smoothing using the Hanning filter. To assess the practical effectiveness of the proposed approach to the approximation of trajectory measurements, the calculation algorithms were implemented in the MATLAB software package and a series of computational experiments with different sets of real data was carried out.

Authors: V. E. Hertzman, A.-V. I. Sereda

Direction: Informatics, Computer Technologies And Control

Keywords: Time series, cubic B-splines, approximation, interpolation

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