Reduced order Kalman filter design for interconnected singularly perturbed systems

The paper aims to design a reduced order Kalman filter for a class of large scale interconnected singularly perturbed linear systems to achieve the minimum estimation error for the estimation problem. Our assumption is that the large scale system consists of several local subsystems interconnected to a main subsystem. Two different approaches are applied. First, the optimal projection equations approach has been used to achieve the optimal solution. The optimal reduced order Kalman filter is completely characterized by necessary conditions, resulting from optimal projection equations. The first order necessary conditions consist of one modified Riccati equation, and two modified Lyapunov equations. They are coupled by a projection matrix whose rank is precisely equal to the order of the filter and which determines the optimal filter gains. Second, the singular perturbation theory has been used to achieve the near optimal Kalman filter. This is approximately decomposed into two filters in different time scales yielding the estimates of the slow mode and the fast mode states