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.

我们为通过低维随机输入耦合的多个动力学系统制定了递归估计问题，并提出了一种有效的次优解决方案。所建议的方法是卡尔曼滤波器的近似，该卡尔曼滤波器在“更新”步骤中丢弃相关矩阵的非对角线条目。与整个卡尔曼滤波器的三次复杂度相比，与传播此近似块对角协方差相关的时间复杂度在系统数量上是线性的。在某些简单情况下，分析了所提出的块对角线滤波器的稳定性及其在大量系统中的行为。然后在为其设计的高对比度空间日冕仪中的电场估计中对其进行检查。