A Novel Polynomial-Chaos-Based Kalman Filter

This letter proposes a new polynomial-chaos-based Kalman filter (PCKF) that is able to track the dynamics of nonlinear dynamical systems subject to strong nonlinearities. Specifically, by resorting to the polynomial chaos theory, the uncertainties of the model and the measurements can be effectively propagated through a set of collocation points. However, this polynomial-chaos-based algorithm suffers from the curse of dimensionality. To overcome this weakness, a dimension reduction strategy is proposed based on variance analysis. This allows us to construct more effective collocations points and to significantly improve the computational efficiency of the PCKF without any loss of estimation accuracy. Simulations carried out on various IEEE systems validate the effectiveness of the proposed method.