Frequency-domain instrumental variable based method for wide band system identification

Abstract

The aim of this paper is to propose an instrumental variable (IV) solution for wide-band frequency domain identification. The focus is first on the extension of the refined IV method for continuous-time model identification to the frequency domain. Then, an iterative IV scheme coupled with an appropriate frequency localising basis function is developed to provide consistent results in the case of highly resonant wide-band systems. Finally, to illustrate the performance of the proposed approach, a representative Monte Carlo simulation as well as a practical case are presented.

Refined instrumental variable estimation: Maximum likelihood optimization of a unified Box–Jenkins model

“…The paper has not described various additional RIV al-gorithms that have been developed and are available in the CAPTAIN and CONTSID Toolboxes. These include multiple input models with either a common denominator in all constituent transfer functions or different denominators [15,9], where the former is a trivial extension of the single input case described in the present paper; models within a feedback system [47,11]; Linear Parameter Varying (LPV) models [21]; State Dependent Parameter (SDP) nonlinear models [54]; and frequency-domain formulations [13]. Except for the latter approach, these are described in [48], and the prior references therein.…”

“…Alternative IV approaches formulated in the frequency domain (see e.g. [30]) have received much less attention, although recent research [13] is moving in this direction.…”

On numerically reliable frequency-domain system identification: new connections and a comparison of methods

“…First, the IV based methods converge to a lower value of the cost function than the SK based methods. Second, the IV-FLBF method as proposed by Gilson et al (2013), on average, converges to a higher value of the cost function than the other IV based methods. This can be explained from the earlier observation that the IV-FLBF method solves a weighted version of the optimal IV criterion (7) , meaning that, the IV-FLBF method does not converge to a local minimum of the cost function (1).…”

“…To further reduce the effects of the a priori unknown weighting introduced in this method, Gilson et al (2013) proposed to use an iterative IV algorithm. However, this IV algorithm is still applied to the linearised problem which is weighted with D(s k , θ).…”

“…As a result, this routine does not converge to a minimum of the original cost function (1), as will be seen in the benchmark results. The IV algorithm of Gilson et al (2013) is referred to as FLBF-IV in the present paper.…”