Recursive trigonometric interpolation algorithms

Proc. IMechE. // J. Systems and Control Engin. Part I. ,Volume 224, Number 1 / 2010, pp. 65-77Two new recursive algorithms for the calculation of the coefficients of the trigonometric polynomial that is fitted to measured data in the least-squares sense in a window of a sufficiently large size that is moving in time are proposed. Both algorithms use the strictly diagonally dominant property of the information matrix for a sufficiently large window size. The first one is based on a recursive inversion of the information matrix and the second one uses a priory estimate of the coefficients of the polynomial obtained from the Kaczmarz projection method. The algorithms are computationally suitable for selection of the order of a trigonometric polynomial in each step of a moving window in real-time applications. The results are verified by simulations.