The observer follower filter: A new approach to nonlinear suboptimal filtering

This paper investigates the state estimation problem for a class of stochastic nonlinear differential systems. A novel algorithm is proposed, denoted as Observer Follower Filter (OFF), based on a two-steps, mixed approach: the first step makes use of a high-gain observer-based estimator for nonlinear systems, applied to the system equations in order to provide the trajectory around which a @n-degree Carleman approximation of the stochastic differential system is achieved, second step. In principle, any other high-gain estimator can be used, but in this note we prove that the one here proposed provides a bounded mean square error. Numerical simulations show the effectiveness of the proposed methodology, and the improvements of the OFF with respect to the standard Extended Kalman-Bucy Filter (EKBF) obtained by increasing the order of the Carleman approximation.

[1]  Nicolas Boizot,et al.  An adaptive high-gain observer for nonlinear systems , 2010, Autom..

[2]  Alfredo Germani,et al.  A state observer for nonlinear dynamical systems , 1997 .

[3]  W. Wong,et al.  The estimation algebra of nonlinear filtering systems , 1998 .

[4]  Hassan K. Khalil,et al.  High-gain observers in the presence of measurement noise: A switched-gain approach , 2009, Autom..

[5]  Alfredo Germani,et al.  Filtering of Stochastic Nonlinear Differential Systems via a Carleman Approximation Approach , 2007, IEEE Transactions on Automatic Control.

[6]  Alessandro Astolfi,et al.  High gain observers with updated gain and homogeneous correction terms , 2009, Autom..

[7]  B. Hanzon,et al.  Singular filtering problems , 1989 .

[8]  Alfredo Germani,et al.  A new approach to nonlinear filtering via a mixed state observer and polynomial scheme , 2011 .

[9]  R. Elliott,et al.  Approximations to solutions of the zakai filtering equation , 1989 .

[10]  Alfredo Germani,et al.  A state observer approach to filter stochastic nonlinear differential systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  K. Ito.  Approximation of the Zakai Equation for Nonlinear Filtering , 1996 .

[12]  Alfredo Germani,et al.  A New Suboptimal Approach to the Filtering Problem for Bilinear Stochastic Differential Systems , 2000, SIAM J. Control. Optim..

[13]  Alfredo Germani,et al.  The Observer Follower Filter , 2012 .

[14]  Alfredo Germani,et al.  Design of state observers from a drift-observability property , 2000, IEEE Trans. Autom. Control..

[15]  A. Germani,et al.  A Luenberger-like observer for nonlinear systems , 1993 .

[16]  Wolfgang J. Runggaldier,et al.  An approximation for the nonlinear filtering problem, with error bound † , 1985 .

[17]  Andrew N. Phillips,et al.  Reduction of HIV Concentration During Acute Infection: Independence from a Specific Immune Response , 1996, Science.

[18]  Michael V. Basin,et al.  Optimal Filtering for Incompletely Measured Polynomial Systems with Multiplicative Noise , 2009, 2008 American Control Conference.

[19]  Alfredo Germani,et al.  Polynomial extended Kalman filter , 2005, IEEE Transactions on Automatic Control.