A Low Cost Filter Design for State and Parameter Estimation in Very High Dimensional Systems

In this paper we consider the filter design problem for very high dimensional systems. Assuming the hypothesis on separability of the vertical and horizontal structure for the error covariance, the number of unknown elements in the error covariance is reduced drastically and are estimated from generated error samples. A low-cost filtering algorithm is thus determined and parameterized up to some pertinent gain coefficients to be tuned to optimize the filter performance. Results from the experiment on assimilation of the sea surface height (SSH) into an oceanic numerical model demonstrate the high effectiveness of the proposed filtering approach.