A New Approach of State estimation of Linear Discrete Systems

Abstract

In this paper a new technique is developed to estimate the states of both deterministic and uncertain discrete-time stochastic linear systems. The proposed approach is based on pole placement technique in which a set of constraints is imposed on the estimated output. The stability of the estimation error is rigorously analyzed for both deterministic and   stochastic cases. The developed approach is then applied to estimation problems of discrete-time deterministic linear system as well as uncertain stochastic systems for which the system model and the output measurements are assumed to be corrupted with Gaussian or non- Gaussian zero mean white noise sequences. Simulations results are presented to illustrate the effectiveness of the developed procedure. For the deterministic case, the application of the proposed approach gives much better results when compared with those using Luenberger observer. For the stochastic case, the developed state estimator gives better results when compared with Kalman filter if the statistics of the random signals and/or the system parameters are unknown and/or the noise signals are non-Gaussian.