Adaptive Unscented Kalman Filter and Its Applications in Nonlinear Control

Abstract

Active estimation is becoming a more important issue in control theory and its application, especially in the nonlinear control of uncertain systems, such as robots and unmanned vehicles where time-varying parameters and uncertainties exist extensively in the dynamics and working environment. Among the available techniques for active modeling, Neural Networks (NN) and NN-based self learning have been proposed as one of the most effective approaches in 1990s (Pesonen et al., 2004). However the problems involved in NN, such as training data selection, online guaranteed convergence, robustness, reliability and real-time implementation, still remain open and limit its application in real systems, especially those requiring high reliable control. Most recently, the encouraging achievements in sequential estimation makes it becoming an important direction for online modeling and model-reference control (Napolitano, et al., 2000). Among stochastic estimations, the most popular one for nonlinear system is the Extended Kalman Filter (EKF). Although widely used, EKF suffers from the deficiencies including the requirement of sufficient differentiability of the state dynamics, the susceptibility to bias and divergence during the estimation. Unscented Kalman Filter (UKF) (Julier et al., 1995; Wan & Van der Merwe, 2000) provides a derivative-free way to the state parameter estimation of nonlinear systems by introducing the so called ‘unscented transformation’, while achieving the second-order accuracy (the accuracy of EKF is first order) with the same computational complexity as that of EKF. Although the nonlinear state dynamics are used without linearization and the calculations on Jacobians or Hessians are not involved, UKF still falls into the framework of Kalman-type filters, which can only achieve good performance under a priori assumptions (Jazwinski, 1970), which includes: 1) accurate reference models, 2) complete information of the noise distribution, and 3) proper initial conditions. However, such a priori knowledge is often not accurate, or even not available in practice. The normal UKF will suffer from performance degradation or even instability due to the mismatch between the a priori assumptions and the real ones within the system to be controlled. One of the approaches solving this problem is to introduce adaptive mechanism into a normal filter, i.e., the adaptive law automatically tunes the filter parameters to match the O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg