Dynamic Likelihood Filter: A Data Assimilation Scheme that Exploits Hyperbolicity in Wave Problems to Propagate Observations

Abstract: ‘We extend the capabilities of the Dynamic Likelihood Filter (DLF). The DLF creates richer and more informative likelihoods from observations by evolving their information along characteristics via stochastic differential equations. Through this approach the DLF approach can generate approximate likelihoods in the near future, enabling Bayesian, conditional prediction. The DLF is particularly effective when observations have small inherent measurement errors and are sparse in space and time, a common situation in geophysical and optics wave problems.’