Filtering of Quasi Periodic Stochastic Systems Using Robust Techniques

Abstract

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 NO_x 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.