Parsimonious system identification from fragmented quantised measurements

Abstract

Quantisation is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantised observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantised realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a ${\ell }_p,(0<p<1),$ quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the ${\ell }_1$ minimisation in terms of the sparsity of the induced solution.

Keywords:

• System identification
• sparsity
• quantisation
• ADMM

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by National Institutes of Health (NIH) [grant number R01 HL142732], and National Science Foundation (NSF) [grant number 1808266].