A set-membership smoother for state estimation in disturbances of unknown distribution

A novel set-membership-based smoothing method for state estimation using the optimal bounding ellipsoid (OBE) algorithms is presented. OBE filters have been proven to be effective in state estimation problems with unknown but bounded errors. Compared with filtering methods, smoothing methods provide a much more accurate and reliable state estimate because observations beyond the current estimation time are used. The new method is a Rauch-Tung-Striebel (RTS)-type smoother which employs both forward and backward passes to estimate the system state. The forward pass is performed using the OBE filter, while the backward pass maintains the fundamental spirit of OBE algorithm in the backward direction. The minimum-volume and minimum-trace bounding ellipsoids containing the feasible state set are derived from this algorithm. Simulation results show the performance of the proposed smoother is superior to both the traditional OBE filter and Kalman filter for state estimation.

[1]  J. Norton,et al.  State bounding with ellipsoidal set description of the uncertainty , 1996 .

[2]  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..

[3]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[4]  Simo Särkkä,et al.  Continuous-time and continuous-discrete-time unscented Rauch-Tung-Striebel smoothers , 2010, Signal Process..

[5]  John R. Deller,et al.  Set-membership identification and filtering for signal processing applications , 2002 .

[6]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[7]  韩建达,et al.  Adaptive UKF Based Tracking Control for Unmanned Trimaran Vehicles , 2008 .

[8]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[9]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[10]  Patrick Nima Raanes,et al.  On the ensemble Rauch‐Tung‐Striebel smoother and its equivalence to the ensemble Kalman smoother , 2016 .

[11]  Eric Walter,et al.  Ellipsoidal parameter or state estimation under model uncertainty , 2004, Autom..

[12]  Reza Arablouei,et al.  Low-complexity implementation of quasi-OBE algorithm , 2012 .

[13]  J. R. Deller,et al.  Unifying the landmark developments in optimal bounding ellipsoid identification , 1994 .

[14]  Boris Polyak,et al.  Multi-Input Multi-Output Ellipsoidal State Bounding , 2001 .

[15]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[16]  Alessio Benavoli,et al.  A probabilistic interpretation of set-membership filtering: Application to polynomial systems through polytopic bounding , 2015, Autom..

[17]  Fuwen Yang,et al.  Robust set-membership filtering for systems with missing measurement: a linear matrix inequality approach , 2012, IET Signal Process..

[18]  T. Alamo,et al.  A set-membership state estimation algorithm based on DC programming , 2008, Autom..

[19]  Thia Kirubarajan,et al.  IMM Forward Filtering and Backward Smoothing for Maneuvering Target Tracking , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[20]  François Desbouvries,et al.  On Bayesian Fixed-Interval Smoothing Algorithms , 2008, IEEE Transactions on Automatic Control.