Decomposition Method for Solving the Gains of Kalman Filter in Singularly Perturbed Systems

In this paper, a decomposition method is introduced to get the solution of the optimal gains of Kalman filters in singularly perturbed systems by solving two reduced order linear equations. The decomposition is achieved via the use of the Chang´s transformation applied to the Hamiltonian matrix of the singularly perturbed kalman filters. Since the decoupling transformation can be obtained, up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving the gains of Kalman filters. A numerical example is given to demonstrate the efficiency of the method.