Fixed-order FIR approximation of linear systems from quantized input and output data

Abstract

The problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order FIR model providing the best approximation of the input-output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example.

Learning Dynamical Systems From Quantized Observations: A Bayesian Perspective

“…Several contributions have been also proposed in the more general case of multi-level quantized data. Results on identification of FIR and IIR models are given in [5]- [7], [21] in the set-membership setting, where a bounded description of the quantization error is adopted. Contributions are also available in the stochastic framework.…”

FIR system identification under either–or communication with quantised inputs and quantised output observations

“…and the likelihood function of the measured signal. Cerone et al [11] dealt with the problem of identifying a fixed‐order FIR (finite impulse response) approximation of linear systems with unknown structure, whose input and output measurements were subjected to quantisation. Zhao et al [12] considered linear system identification with batched binary‐valued observations and constructed an iterative parameter estimate algorithm to achieve the maximum likelihood estimate.…”

Parameter estimation for systems with structural uncertainties based on quantised inputs and binary‐valued output observations

“…For the systems with stochastic measurement noises and structural uncertainties, Kan et al [2] studied the identification of linear systems with periodic inputs and binary‐valued observations. In [15–17], the fixed‐order FIR (finite impulse response) approximation of linear systems and identification of FIR systems and Wiener systems were investigated under both quantised inputs and quantised output observations, estimation algorithms were designed and their convergence were also established.…”