Constrained state estimation for nonlinear systems with non-Gaussian noise

This paper addresses a state-estimation problem for nonlinear systems with non-Gaussian noise and interval constraints on the state vector. We propose new efficient algorithms, which are based on Unscented Kalman filter(UKF) and Ensemble Kalman filter(EnKF). We use Truncated UKF(TUKF) in Gaussian sum filter(GSF) framework, which is named Constrained Unscented GSF(CUGSF). And we proposed an Efficient constrained EnKF(E-CEnKF), which does not require to solve complicate optimization problem like the conventional method. Validity of the proposed methods are illustrated in numerical examples.

[1]  Dennis S. Bernstein,et al.  Unscented filtering for interval-constrained nonlinear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[2]  H. Sorenson,et al.  Nonlinear Bayesian estimation using Gaussian sum approximations , 1972 .

[3]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[4]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[5]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[6]  C. W. Chan,et al.  Performance evaluation of UKF-based nonlinear filtering , 2006, Autom..

[7]  Masaki Yamakita,et al.  Efficient unscented filtering for nonlinear systems with state constraints , 2009, 2009 European Control Conference (ECC).

[8]  Jindrich Dunik,et al.  SIGMA POINT GAUSSIAN SUM FILTER DESIGN USING SQUARE ROOT UNSCENTED FILTERS , 2005 .

[9]  P. Vachhani,et al.  Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation , 2006 .

[10]  James B. Rawlings,et al.  Particle filtering and moving horizon estimation , 2006, Comput. Chem. Eng..

[11]  L. Imsland,et al.  Constrained state estimation using the Unscented Kalman Filter , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[12]  Raphael Andreas Hauser,et al.  Kalman Filtering with Equality and Inequality State Constraints , 2007, 0709.2791.

[13]  Nikos A. Vlassis,et al.  Accelerated EM-based clustering of large data sets , 2006, Data Mining and Knowledge Discovery.

[14]  Prem K. Goel,et al.  Bayesian estimation via sequential Monte Carlo sampling - Constrained dynamic systems , 2007, Autom..

[15]  D. Bernstein,et al.  What is the ensemble Kalman filter and how well does it work? , 2006, 2006 American Control Conference.

[16]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[17]  Robert J. Elliott,et al.  Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature , 2007, Proceedings of the IEEE.

[18]  S.L. Shah,et al.  Constrained state estimation using the ensemble Kalman filter , 2008, 2008 American Control Conference.

[19]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[20]  Nando de Freitas,et al.  The Unscented Particle Filter , 2000, NIPS.