The frisch scheme in dynamic system identification (original) (raw)

Gradient-based approaches for recursive Frisch scheme identification

IFAC Proceedings Volumes, 2008

An algorithm for recursive Frisch scheme system identification of linear single-input single-output errors-in-variables systems is developed. For the update of the estimated model parameters, a recursive bias-compensating least squares algorithm, which is based on the wellknown recursive least squares technique, is considered. The estimate of the output measurement noise variance is determined using a conjugate gradient method, which tracks the smallest eigenvalue of a slowly varying matrix. For the update of the input measurement noise estimate, a steepest gradient search is applied. It tracks the minimum of a model selection cost function, which is based on a set of high order Yule-Walker equations.

Nonlinear system identification for autonomous systems via functional equations methods

2016 American Control Conference (ACC), 2016

The problem of identifying an autonomous nonlinear systems, that is, the problem of finding a state-space description of a given sequence generated by sampling the output of an unknown nonlinear system without input, is studied. A theoretical framework which combines the use of functional equations with realization-theoretic techniques is developed and used to solve the problem.

Frequency domain identification of FIR models from noisy input – output data

2019

This paper describes a new approach for identifying FIR mode ls from a finite number of measurements, in the presence of additive and uncorrelated white noise. In particular, two different frequency domain algorithms are proposed. The first algorit hm is based on some theoretical results concerning the dynamic Frisch scheme. The second algorithm maps the FIR identification problem into a quadratic eigenvalue problem. Both methods resemble in many aspects some other identification algorithms, originally developed in the time domain. The fe atures of the proposed methods are compared with each other and with those of some time domain algorithms by means of Monte Carlo simulations.

The Frisch scheme for EIV system identification: time and frequency domain formulations

IFAC-PapersOnLine

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

A priori nonlinear model structure selection for system identification

Control Engineering Practice, 1997

When performing nonlinear system identification few tools exist for the a priori nonlinear model structure selection of the nonlinear system. This paper presents a possible approach as a first step towards selecting a nonlineAtr system model structure, based on using the results of Lyapunov exponents, Poincar~ maps and dimension techniques. The approach is illusUated by applying it to the Chua circuit, a nonlinear dynamic system exhibiting chaotic dynamic behaviour.

Recent Advancements & Methodologies in System Identification: A Review

System Identification (SI) is a discipline in control engineering concerned with inferring mathematical models from dynamic systems based on its input/output observations. Rich literature is available regarding SI due to its applications in understanding complex systems as well as to design control systems for complex processes. A summary of those literatures is presented in this paper, which covers general classifications of SI, methodologies for design and implementation of the models, as well as recent advancements in application of optimization techniques for SI. It is hoped that this paper would serve as a guide for budding practitioners regarding the fundamentals of the discipline, while serving as a summary of new research trends for experienced researchers in the area.

Maximum likelihood identification of noisy input–output models

Automatica, 2007

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cràmer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations. ᭧