Real-time identification of linear continuous-time systems with slowly time-varying parameters

Long-memory recursive prediction error method for identification of continuous-time fractional models

“…It has been shown in [5] that the cut-off frequency ω f may have an influence on the convergence rate of the algorithm, as well as sampling time and input. This frequency is typically chosen to be somewhat larger to the system bandwidth [33]. This means that a priori estimation or tuning of the system bandwidth may be required to get better results.…”

“…Recursive prediction-error methods are also available in literature [19]. Padilla [33] provides a recursive versions of LSSVF and RIVC for integer-order systems. By starting from Le Lay's method and online estimation concepts, a method to estimate coefficients of a fractional order transfer function was proposed in [6].…”

Identification of continuous-time models with slowly time-varying parameters

“…This alternative is evaluated in an example in Section 7.3. A third option is to use the SVF (24), yielding the recursive instrumental variable state variable filter (RIVSVF) algorithm. RIVSVF is then given by (38), but with y (na) f (t k ) and ϕ f (t k ) defined in (28) and (30), respectively.…”

“…a first guess for λ svf can be obtained using (47) and ω b,max = ω b . For LTV systems with relatively large bandwidth variations, the specification of λ svf can be critical since the system bandwidth is time-varying (see the numerical example in [24]). In practice, some prior guidance on the selection of the cut-off frequency for the SVF, λ svf , can be obtained by estimating local LTI models on segments of the training data using RIVC, SRIVC or LSSVF.…”

“…In [3], only some comments about the recursive on-line version of SRIVC (RSRIVC) are given. More recently, the RSRIVC approach, which exploits the KF version of the algorithm as an adaptation mechanism, has been developed for the estimation of CT LTV models in [24].…”