AbstractIn this paper a decomposition method is introduced for the solution of the optimal Kalman filter gains in singularly perturbed systems by solving two reduced‐order linear equations. The decomposition is achieved via the use of the Chang transformation, which is applied to the Hamiltonian matrix of the singularity perturbed Kalman filter. 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 obtaining the Kalman filter gains. A numerical example is given to demonstrate the efficiency of the metho
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