An Improved Approach to Kalman Bucy Filter using the Identification Algorithm

Abstract

The Kalman Bucy filter is a well-known observer to estimate the state vector from the incomplete state measurements. However, when the time delay is taken into account, the filter can become ineffective. In this paper, the identification algorithm presented in a previous paper (Anh 2000) is used to improve the Kalman Bucy filter in the presence of time delay. The differential equation of the observer error vector is expanded by modal eigenfunction technique. Using the identification algorithm, the external excitation acting on some first modes is identified with a time delay and with a small error depending on the sensor locations. Then the identified excitation is eliminated from the observer equation. A numerical calculation is applied to an eight story building subjected to base acceleration and controlled by active mass damper system. In the presence of time delay, the comparison between performance indexes shows the effectiveness of improved Kalman Bucy filter to the classical Kalman Bucy filter