Kalman filter design for large-scale systems by using unified approach
In this thesis, a method of designing a Kalman filter for a linear, discrete-time, singularly perturbed stochastic system using the delta operator was introduced. This unified approach, which is based on the delta operator, was the main method used to unify the continuous-time system and the discrete-time system. This method has many advantages over the q-operator: it makes the system simpler, it has better finite word-length characteristics, and the truncation and round-off error is less. One of the singular perturbation techniques, quasi-steady state approximation, was used to separate the system into a slow subsystem and a fast subsystem. Then, the exact solution of the Kalman filter and the minimized mean square error for the full-order system, and the composite solution of the Kalman filter and minimized mean square error for the two subsystems were solved. This method was applied using a numerical example in which the steady-state Kalman filter solution was found.