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This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics (e.g., mean and covariance) conditioned on the system's measurement data. This article offers a systematic introduction of the Bayesian state estimation framework and reviews various Kalman filtering (KF) techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including the Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation forward to more complicated problems such as simultaneous state and parameter/input estimation.

SUMMARYThis paper investigates the problem of adaptive control for networked control systems with unknown model parameters and randomly missing outputs. In particular, for a system with the autoregressive model with exogenous input placed in a network environment, the randomly missing output feature is modeled as a Bernoulli process. Then, an output estimator is designed to online estimate the missing output measurements, and further a Kalman filter-based method is proposed for parameter estimation. Based on the estimated output and the available output, and the estimated model parameters, an adaptive control is designed to make the output track the desired signal. Convergence properties of the proposed algorithms are analyzed in detail. Simulation examples illustrate the effectiveness of the proposed method.

Fang, H.; Sahinoglu, Z.; Wada, T.; Hara, S. TR2014-094 September 2014Abstract This paper considers the state of charge (SoC) and parameter estimation of lithium-ion batteries. Different from various prior arts, where estimation is based on local linearization of a nonlinear battery model, nonlinear geometric observer approach is followed to design adaptive observers for the SoC and parameter estimation based on nonlinear battery models. A major advantage of the proposed approach is the possibility to establish the exponential stability of the resultant error dynamics of state and parameter estimation. The proposed adaptive observers are shown to be robust with respect to unmodeled process uncertainties. Analysis also shows the design tradeoff between the convergence rate and the robustness of the estimation error dynamics with respect to the measurement noise. Simulation and experimental results validate the effectiveness and main advantages of the proposed approach. Error analysis is presented and explains the experimental results. IEEE Transactions on Control Systems TechnologyThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-This paper considers the State of Charge (SoC) and parameter estimation of Lithium-ion batteries. Different from various prior art, where estimation is based on local linearization of a nonlinear battery model, nonlinear geometric observer approach is followed to design adaptive observers for the SoC and parameter estimation based on nonlinear battery models. A major advantage of the proposed approach is the possibility to establish the exponential stability of the resultant error dynamics of state and parameter estimation. The proposed adaptive observers are shown to be robust with respect to unmodeled process uncertainties. Analysis also shows the design tradeoff between the convergence rate and the robustness of the estimation error dynamics with respect to the measurement noise. Simulation and experimental results validate the effectiveness and main advantages of the proposed approach. Error analysis is presented and explains the experimental results.