Ab-initio Functional Decomposition of Kalman Filter: A Feasibility Analysis on Constrained Least Squares Problems

Abstract

The standard formulation of Kalman Filter (KF) becomes computationally intractable for solving large scale state space estimation problems as in ocean/weather forecasting due to matrix storage and inversion requirements. We introduce an innovative mathematical/numerical formulation of KF using Domain Decomposition (DD) approach. The proposed DD approach partitions ab-initio the whole KF computational method giving rise to local KF methods that can be solved independently. We present its feasibility analysis using the constrained least square model underlying variational Data Dssimilation problems. Results confirm that the accuracy of solutions of local KF methods are not impaired by DD approach.