Frisch scheme identification for dynamic diagonal bilinear models

Abstract

The article addresses the problem of dynamic system identification in the errors-in-variables framework for a class of discrete-time time-invariant input-output bilinear models when subjected to a white input signal. The proposed algorithm is based on an extension of the bias-compensated least squares method and utilises the Frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences. The appropriateness of the approach is analysed and its performance evaluated when compared to other errors-in-variables identification techniques by means of a Monte Carlo simulation. The results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed.

Algorithms for recursive/semi-recursive bias-compensating least squares system identification within the errors-in-variables framework

“…In practice, however, a model selection criterion is required to be utilised, in order to choose an 'optimal' solution from a set of all admissible Frisch scheme models. Three different options are discussed in Hong, So¨derstro¨m, Soverini, and Diversi (2008), whilst an extension towards bilinear model structures has been considered in Larkowski, Linden, Vinsonneau, and Burnham (2009) and Larkowski (2009).…”

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

“…Lopes dos Santos et al presented a subspace identification method for bilinear systems by regarding the bilinear term as a second‐order white noise process based on the Picard decomposition . Larkowski et al used the Frisch equations to determine the model parameters and the noise variances based on the bias‐compensated least squares method . A class of fractional adaptive signal processing algorithms for nonlinear system identification have been proposed using the multidirectional step‐size strategy, the step‐size was adjusted according to the status of the active noise control system for faster convergence .…”

“…7 Larkowski et al used the Frisch equations to determine the model parameters and the noise variances based on the bias-compensated least squares method. 8 A class of fractional adaptive signal processing algorithms for nonlinear system identification have been proposed using the multidirectional step-size strategy, the step-size was adjusted according to the status of the active noise control system for faster convergence. 9 In addition, the fractional calculus-based adaptive algorithms can be applied in various physics and engineering problems.…”

A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise

“…In the literature of bilinear system identification, Verdult and Verhaegen applied the subspace identification techniques for multi-input multi-output bilinear systems by using the separable least squares principle [32]. Larkowski et al handled the parameter estimation problem of the diagonal bilinear errors-in-variables system and employed the bias-compensated least squares method to estimate the parameters [33]. Hizir et al transformed a bilinear system into its equivalent linear model and used the observer Kalman filter identification algorithm to identify the bilinear system [34].…”