Ensemble Kalman filtering with coloured observation noise

Abstract

The Kalman filter (KF) is derived under the assumption of time-independent (white) observation noise. Although this assumption can be reasonable in many ocean and atmospheric applications, the recent increase in sensor coverage, such as the launching of new constellations of satellites with global spatio-temporal coverage, will provide high density of oceanic and atmospheric observations which are expected to have time-dependent (coloured) error statistics. In this situation, the KF update has been shown to generally provide overconfident probability estimates, which may degrade the filter performance. Different KF-based schemes accounting for time-correlated observation noise were proposed for small systems by modelling the coloured noise as a first-order autoregressive model driven by white Gaussian noise. This work introduces new ensemble Kalman filters (EnKFs) which account for coloured observational noises for efficient data assimilation into large-scale oceanic and atmospheric applications.More specifically, we follow the standard and the one-step-ahead smoothing formulations of the Bayesian filtering problem with coloured observational noise, modelled as an autoregressive model, to derive two (deterministic) EnKFs. We demonstrate the relevance of the coloured observational noise-aware EnKFs and analyze their performances through extensive numerical experiments conducted with the Lorenz-96 model.

Online estimation of colored observation‐noise parameters within an ensemble Kalman filtering framework

“…Raboudi et al . (2021) reported nonuniform rank histograms when the observational error time correlations were not accounted for during assimilation, results that are clearly improved here.…”

“…A similar behavior is also observed when comparing $$$ {\mathrm{SEIK}}_{\mathrm{Col},\left(\Psi +R\right)} $$$‐OSA and $$$ {\mathrm{SEIK}}_{\mathrm{Col}-\Psi} $$$‐OSA.Comparing these results with those of Raboudi et al . (2021), obtained under the same experimental setting but when the data are assimilated using the “true” values of both $$$ \theta $$$ and $$$ \lambda $$$, suggests reasonable state estimates when $$$ \theta $$$ and $$$ \lambda $$$ are estimated. Indeed, the minimum $$$ \mathbf{x} $$$‐RMSE obtained by SEIK$$$ {}_{\mathrm{Col}} $$$ in Raboudi et al .…”

“…Raboudi et al . (2021) reported clearly biased and underdispersive forecast ensembles when neglecting the observation noise coloredness. Here, the forecast ensembles are reliable overall and their reliability improves with larger ensembles, with the RCV mean and standard deviation getting closer to 0 and 1, respectively.…”

“…The recent work by Raboudi et al . (2021) provided a comprehensive framework for these schemes, showing in particular that the Bryson and Henrikson (1968) KF is simply an OSA‐smoothing variant of the Chang (2014) KF. Using the state augmentation approach, Raboudi et al .…”

Study of a cloud-based manufacturing tracking registration scheme

“…In 1960, the Kalman filter, proposed by Kalman, overcame the shortcomings of the Wiener filter [11]. It is widely used in geological surveys, radar communications, and other fields.…”