Data Assimilation using Time-Delay Nudging in the Presence of Gaussian Noise

TL;DR

This paper investigates a time-delay nudging data assimilation method for Navier-Stokes equations with noisy observations, demonstrating that the expected error scales with noise variance and confirming findings through numerical simulations.

Contribution

It introduces a discrete-time data assimilation algorithm using time-delay nudging that accounts for Gaussian noise in observations, with theoretical error bounds and numerical validation.

Findings

Expected error proportional to noise variance with logarithmic correction.

Numerical simulations confirm theoretical error estimates.

Method effectively handles noisy observational data in fluid dynamics.

Abstract

We study a discrete-in-time data-assimilation algorithm based on nudging through a time-delayed feedback control in which the observational measurements have been contaminated by a Gaussian noise process. In the context of the two-dimensional incompressible Navier-Stokes equations we prove the expected value of the square-error between the approximating solution and the reference solution over time is proportional to the variance of the noise up to a logarithmic correction. The qualitative behavior and physical relevance of our analysis is further illustrated by numerical simulation.