Spectral observers for unevenly sampled data

This paper investigates the problem of spectral observation in case of unevenly sampled input data. In [1] Hostetter proposed a dead-beat observer structure and an algorithm to calculate the observer gain values online. In this paper we give a formal proof of correctness of this algorithm and we also propose an efficient numerical method to reduce the amount of computations required by the algorithm. Moreover, we show a significantly more efficient solution of spectral observation for a special case of uneven sampling, namely when the sampling time instants are uneven but periodic.