Robust Estimation and Filtering for Poorly Known Models

This letter addresses the estimation and filtering problems of systems when only a rough model is available. Based on a modified version of the classic regularized least square problem, a new design criterion for estimation is proposed that considers measurements and innovations as a possible source of uncertainty. Under Gaussian assumption, it performs as an upper bound for the maximum a posteriori Bayesian estimator. The optimal solution is obtained by exploiting non-smooth analysis tools and the optimal solution reveals a region in the residue space for which the non-variation of the estimate is optimal. The approach provides robust estimators from a stochastic point of view in recursive form. To illustrate, a Kalman-like filter is derived and comparison with classic worst-case robust design filters are made.

[1]  Mehdi Rahmani,et al.  Robust deterministic least-squares filtering for uncertain time-varying nonlinear systems with unknown inputs , 2018, Syst. Control. Lett..

[2]  C. Hutchinson,et al.  Low sensitivity filters for state estimation in the presence of large parameter uncertainties , 1969 .

[3]  João Yoshiyuki Ishihara,et al.  Optimal robust filtering for systems subject to uncertainties , 2015, Autom..

[4]  Ian R. Petersen,et al.  Robust Kalman Filtering for Signals and Systems with Large Uncertainties , 1999 .

[5]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[6]  Ali H. Sayed,et al.  A framework for state-space estimation with uncertain models , 2001, IEEE Trans. Autom. Control..

[7]  João Bosco Ribeiro do Val,et al.  Modeling and Control of Stochastic Systems With Poorly Known Dynamics , 2017, IEEE Transactions on Automatic Control.

[8]  D. McFarlane,et al.  Optimal guaranteed cost filtering for uncertain discrete-time linear systems , 1996 .

[9]  Hossein Hassani,et al.  On the Folded Normal Distribution , 2014, 1402.3559.

[10]  Charles R. Johnson,et al.  Matrix Analysis, 2nd Ed , 2012 .

[11]  Ali H. Sayed,et al.  A Regularized Robust Design Criterion for Uncertain Data , 2001, SIAM J. Matrix Anal. Appl..

[12]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[13]  S. Chandrasekaran,et al.  Parameter estimation in the presence of bounded modeling errors , 1997, IEEE Signal Processing Letters.

[14]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .