Robust linear estimation by a first order polynomial chaos expansion

In this work, a mathematical model for stochastic uncertain systems where the system uncertainty is handled by polynomial chaos method is developed. For uncertain systems where the system uncertainty is modeled by a first order polynomial chaos expansion, the estimation of the system states are done by an augmented Kalman filter equations developed by averaged least square method. The performance of the proposed robust estimation algorithm is shown by an uncertain system used as a framework example in previous works.