# Useful redundancy in parameter and time delay estimation for continuous-time models

## TL;DR

This paper introduces an algorithm for estimating parameters and time delay in continuous-time systems using instrumental variable methods, enhanced by useful redundancy to ensure convergence to the global minimum.

## Contribution

It presents a novel approach combining useful redundancy with filtering to improve the convexity of the cost function in time delay estimation.

## Key findings

- Effective convergence to the global minimum demonstrated
- Algorithm outperforms traditional methods in numerical tests
- Improved robustness in parameter and delay estimation

## Abstract

This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.