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

TL;DR

This paper introduces a computationally efficient approximation of the Kalman filter for multiple coupled systems, reducing complexity while maintaining stability, demonstrated in space coronagraph electric field estimation.

Contribution

It proposes a low-complexity, block-diagonal approximation of the Kalman filter for coupled systems, enabling scalable real-time estimation.

Findings

Linear time complexity in the number of systems

Stable behavior of the approximate filter in simple cases

Encouraging simulation results in space coronagraph applications

Abstract

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter that discards the off diagonal entries of the correlation matrix in its "update" step. The time complexity associated with propagating this approximate block-diagonal covariance is linear in the number of systems, compared to the cubic complexity of the full Kalman filter. The stability of the proposed block-diagonal filter and its behavior for a large number of systems are analyzed in some simple cases. It is then examined in the context of electric field estimation in a high-contrast space coronagraph, for which it was designed. The numerical simulations provide encouraging results for the cost-efficiency of the newly suggested filter.