Robust and optimal control
Nonlinear Control Systems II
Nonlinear Control Systems: An Introduction
Nonlinear Control Systems: An Introduction
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Robust mixed generalized H2/H∞ filtering of 2-D nonlinear fractional transformation systems
IEEE Transactions on Signal Processing
Robust filtering for uncertain nonlinearly parameterized plants
IEEE Transactions on Signal Processing
Gain-scheduled filtering for time-varying discrete systems
IEEE Transactions on Signal Processing
New fuzzy control model and dynamic output feedback parallel distributed compensation
IEEE Transactions on Fuzzy Systems
Brief Robust maximum likelihood estimation in the linear model
Automatica (Journal of IFAC)
| Hi-index | 35.68 |
For nonlinear state space model involving random variables with arbitrary probability distributions, the state estimation given a sequence of observations is based on an appropriate criterion such as the minimum mean square error (MMSE). This leads to linear approximation in the state space of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), which work reasonably well only for mildly nonlinear systems. We propose a Bayesian filtering technique based on the MMSE criterion in the framework of the virtual linear fractional transformation (LFT) model, which is characterized by a linear part and a simple nonlinear structure in the feedback loop. LFT is an exact representation for any differentiable nonlinear mapping, so the virtual LFT model is amenable to a wide range of nonlinear systems. Simulation results demonstrate that the proposed filtering technique gives better approximation and tracking performance than standard methods like the UKF. Furthermore, for highly nonlinear systems where UKF diverges, the LFT model estimates the conditional mean with reasonable accuracy.