State estimation on correlated noise and unit timedelay systems

This paper concentrates on the problem of states estimation for discrete unit - time delay system based on some available correlation between process and measurement noise. Kalman filter is used as the model based estimation algorithms which assumed that disturbances are noisy with zero mean. By appending a unit time delay state vector to the original discrete time system we obtained an increased dimensional system. The states of this system will be the states in which the noise is assumed to act on which in turn act on the original model states. Without altering the Kalman filtering framework, prediction and filtering cycles of Kalman filter with unit time delay state vector and correlated noise will be derived. The filtering performance for the propose system with estimation error covariance as the performance index will be analyzed. As a result, when the correlation coefficient between process and measurement noise is larger in the positive direction, the estimation error covariance will be minimized. A simple numerical example illustrates the results.