Parsimonious System Identification from Fragmented Quantized Measurements.

Area of Science:

• Signal Processing
• Control Systems Engineering
• System Identification

Background:

• Quantization is a non-linear, irreversible process complicating traditional system identification.
• Existing methods struggle with noisy, fragmented, and quantized observational data.

Purpose of the Study:

• To develop a method for parsimonious linear time-invariant (LTI) system identification from quantized observations.
• To address challenges posed by noisy data and potential data fragmentation.
• To identify the lowest-order system consistent with available information and prior knowledge.

Main Methods:

• Utilizes a priori information about system poles within a compact set.
• Employs an Alternating Direction Method of Multipliers (ADMM) algorithm.
• Solves a mixed $\ell$₁, $\ell$₂ quasi-norm objective problem.

Main Results:

• The proposed ADMM-based method successfully identifies LTI systems from quantized, noisy, and fragmented data.
• Achieves parsimonious system identification, favoring lower-order models.
• Demonstrates superior performance compared to $\ell$₁ minimization in terms of solution sparsity.

Conclusions:

• The developed ADMM approach offers an effective solution for system identification under quantization constraints.
• The method provides a robust way to handle imperfect observational data in system modeling.
• This work advances the field of system identification by enabling accurate modeling with limited, quantized information.