Exact nonlinear state estimation

While such approximations facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Nonparametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges.

Drawing inspiration from recent advances in the fields of measure transport and generative artificial intelligence, this paper develops a new estimation-theoretic framework which can incorporate general invertible transformations in a principled way. Specifically, a conjugate transform filter (CTF) is derived and shown to extend the celebrated Kalman filter to a much broader class of non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and converge to highly accurate observations.