An Assessment of Ensemble Kalman Filter and Azouani-Olson-Titi Algorithms for Data Assimilation: A Comparative Study

TL;DR

This paper compares the performance of the Azouani-Olson-Titi (AOT) algorithm and the ensemble Kalman filter (EnKF) in continuous data assimilation, highlighting the computational efficiency of AOT through numerical experiments on key dynamical systems.

Contribution

It provides the first extensive numerical comparison between AOT and EnKF for CDA, demonstrating AOT's significant computational advantages.

Findings

AOT outperforms EnKF in computational efficiency.

Both algorithms effectively assimilate data in complex systems.

AOT shows promise for real-time data assimilation applications.

Abstract

Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its efficiency in incorporating observational data to enhance model accuracy. However, no research to date has evaluated the performance of the AOT algorithm compared to the most widely used DA method, the ensemble Kalman filter (EnKF). Hence, in this paper, we conduct an extensive numerical examination to evaluate and compare these two algorithms for CDA problems with measurement error, addressing this gap. By analyzing the one-dimensional Kuramoto-Sivashinsky equation and the two-dimensional Navier-Stokes equation, which are central to many applications and representative in CDA problems, we found a significant computational advantage of the AOT algorithm.