dr inż. Marcin Ciołek | Politechnika Gdańska

Savitzky–Golay (SG) filtering is a classical signal smoothing technique based on the local least squares approximation of the analyzed signal by a linear combination of known functions of time (originally — powers of time, which corresponds to polynomial approximation). It is shown that the regularized version of the SG algorithm can be successfully applied to identification of time-varying finite impulse response (FIR) systems....

When system parameters vary at a fast rate, identification schemes based on model-free local estimation approaches do not yield satisfactory results. In cases like this, more sophisticated parameter tracking procedures must be used, based on explicit models of parameter variation (often referred to as hypermodels), either deterministic or stochastic. Kalman filter trackers, which belong to the second category, are seldom used in...

The problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide...

The paper presents a new, two-stage approach to identification of linear time-varying stochastic systems, based on the concepts of preestimation and postfiltering. The proposed preestimated parameter trajectories are unbiased but have large variability. Hence, to obtain reliable estimates of system parameters, the preestimated trajectories must be further filtered (postfiltered). It is shown how one can design and optimize such...

The paper shows that the problem of noncausal identification of a time-varying FIR (finite impulse response) sys- tem can be reformulated, and solved, as a problem of smoothing of the preestimated parameter trajectories. Characteristics of the smoothing filter should be chosen so as to provide the best trade- off between the bias and variance of the resulting estimates. It is shown that optimization of the smoothing operation can...