An Optimal Instrumental Variable Approach for Identifying Hybrid Continuous-Time Box-Jenkins Models

Abstract

The paper describes and evaluates an optimal instrumental variable method for identifying hybrid continuous-time transfer function models of the Box-Jenkins form from discrete-time sampled data, where the relationship between the measured input and output is a continuous-time transfer function, while the noise is represented as a discrete-time AR or ARMA process. The performance of the proposed hybrid parameter estimation scheme is evaluated by Monte Carlo simulation analysis.

Identification and Estimation of Continuous-Time Rainfall-Flow Models

“…Indeed, the results obtained here and in other studies we have carried out, suggest that SRIVC provides an excellent default algorithm for day-to-day applications of this kind. Of course, as illustrated in other simulation studies reported by Young et al (2006), the advantages of full RIVC estimation can be significant in the case of more severely coloured noise, particularly when the AR model has roots near to the unit circle. For example, the results shown in Table 1 were obtained by MCS analysis using a simulation model based on the SRIVC estimated parameters but with the noise process simulated as a first order AR process with denominator polynomial C(z −1 ) = 1 − 0.96z…”

“…This more sophisticated and statistically motivated RIVC method of CT identification and estimation is described and evaluated in Young et al (2006) in order to demonstrate the advantages of the stochastic model formulation. This evaluation is based on comprehensive Monte Carlo Simulation (MCS) analysis.…”

“…In the RIVC algorithm (Young et al, 2006) the relationship between the measured input and output is a continuous-time transfer function, while the noise is represented as a discretetime AR or ARMA process. This RIVC algorithm is a direct development of the Simplified Refined Instrumental Variable (SRIVC) method for continuous-time systems (Young and Jakeman, 1980) that has been used successfully for many years and has demonstrated the advantages of the stochastic formulation of the CT estimation problem over earlier deterministic methods.…”

“…This paper presents the results of direct continuous-time (CT) identification and estimation of a rainfall-flow model for the Canning, an ephemeral river in Western Australia, based on daily sampled data. These results are obtained using the optimal Refined Instrumental Variable method of identification for Continuous-time systems (RIVC) (Young et al, 2006) and they are compared with alternative 'indirect' approaches to the problem, where the CT model parameters are inferred from the parameters of discrete-time (DT) models. Such DT models are normally identified using conventional stochastic DT estimation methods available for use in Matlab, such as the Refined Instrumental Variable (RIV) approach in the CAPTAIN Toolbox (Young, 2006a) and the Prediction Error Method (PEM) in the Matlab System IDentification (SID) Toolbox.…”

Nonlinear Dynamic Transformer Time-Domain Identification for Power Converter Applications

“…Various methods can be applied to the transformer model estimation problem [16]. However, only the most reliable method, denoted the simplified refined instrumental variable method for continuous-time system identification (SRIVC) [17], is chosen here. Let the continuous-time model of the actual system be…”