Filtering of Quasi Periodic Stochastic Systems Using Robust Techniques - Vázquez-Olguín, Miguel A.; Andrade-Lucio, José A.; Zhao, Shunyi; Shmaliy, Yuriy S. (Journal of Electronics and Electrical Engineering, 2026)
The behavior of a periodic system becomes quasi-periodic when it is driven by noise or operates under perturbations (disturbances and/or uncertainties). If the perturbation is not Gaussian, a robust state estimator is required. In this paper, we consider a quasi-periodic conservative Llinear Time Invariant (LTI) stochastic system driven by white Gaussian noise, the measurement of which is carried out in the presence of unknown but norm-bounded measurement disturbance. Therefore, choosing a proper estimator is a challenging task in each special case. Based on real data of daily quasi-periodic and hourly averaged measurements of nitrogen oxide NOx contamination, the Kalman filter is shown to be the worst tracker of daily smoothed data. The best performance demonstrate the unbiased finite impulse response filter and the robust peak-to-peak L1 filter developed using the error-to-error transfer function (ERTF) approach. Other ERTF-based energy-to-peak GH2 and energy-to-energy H∞ filters provide in-between estimates.