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We formulate a recursive estimation problem for multiple dynamical systemscoupled through a low dimensional stochastic input, and we propose an efficientsub-optimal solution. The suggested approach is an approximation of the Kalmanfilter that discards the off diagonal entries of the correlation matrix in its"update" step. The time complexity associated with propagating this approximateblock-diagonal covariance is linear in the number of systems, compared to thecubic complexity of the full Kalman filter. The stability of the proposedblock-diagonal filter and its behavior for a large number of systems areanalyzed in some simple cases. It is then examined in the context of electricfield estimation in a high-contrast space coronagraph, for which it wasdesigned. The numerical simulations provide encouraging results for thecost-efficiency of the newly suggested filter.

An Efficient Approximation of the Kalman Filter for Multiple Systems Coupled via Low-Dimensional Stochastic Input