Optimal state estimation of a dynamical system corrupted with colored noises using Mixed Kalman/H-infinity filter

Control engineers are interested in state estimation problems as one of the most interesting subject. In this way, Kalman filter, H-infinity, and Mixed Kalman/H-infinity filter are the most widely used filters for state estimation of the discrete linear dynamical system corrupted with Gaussian and white noises. These filters will be, however, suboptimal for state estimation when the process noise and/or measurement noise are color noises. In this paper, a multi-objective Pareto optimization (multi-objective genetic algorithm) approach is presented for the design of combined Kalman/H-infinity filters to estimate states corrupted with color noises. In this way, a state augmentation procedure is used to analyze the effect of the colored noises on states estimation of an inverted pendulum. Some Pareto curves are then obtained to compromise between the Kalman and H-infinity filters. It is shown that the use of such approach can evidently improve the effectiveness of the filters when the color noises are significant. Therefore, by using the proposed approach, we can employ the advantages of both Kalman and H-infinity filters simultaneously to minimize both the mean of squared errors and the upper bounds limit of estimation errors.