Stochastic Approximation for High-frequency Observations in Data Assimilation

TL;DR

This paper introduces a stochastic approximation approach tailored for high-frequency data assimilation, enabling high-quality estimates without computational burdens or loss of statistical accuracy.

Contribution

It adapts stochastic approximation methods to handle high-frequency observations, avoiding data modification and preserving estimate quality.

Findings

Achieves high statistical accuracy with high-frequency data

Reduces computational complexity in data assimilation

Maintains estimate quality without data averaging or sampling

Abstract

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but their frequency results in a plethora of computational problems in data assimilation tasks. The high-frequency of these observations has been traditionally dealt with by using data modification strategies such as accumulation, averaging, and sampling. However, these data modification strategies will reduce the quality of the estimates, which may be untenable for many systems. Therefore, to ensure high-quality estimates, we adapt stochastic approximation methods to address the unique challenges of high-frequency observations in data assimilation. As a result, we are able to produce estimates that leverage all of the observations in a manner that avoids the aforementioned computational problems and preserves the statistical accuracy of the estimates.