# An asymptotically optimal indirect approach to continuous-time system identification

## TL;DR

This paper introduces an asymptotically optimal indirect method for continuous-time system identification that enforces a fixed relative degree, improving estimation accuracy and efficiency over existing approaches.

## Contribution

It develops a refined indirect PEM-based method that ensures the estimated transfer function has a fixed relative degree, achieving consistency and asymptotic efficiency.

## Key findings

- The proposed estimator outperforms existing methods in numerical simulations.
- Enforcing fixed relative degree improves the accuracy of continuous-time models.
- The method is asymptotically efficient and consistent.

## Abstract

The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by indirect PEM, we propose a method that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the resulting estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification.