Statistical estimation of multiple parameters via symbolic dynamic filtering

Authors:
Chinmay Rao;Kushal Mukherjee;Soumik Sarkar;Asok Ray
Affiliations:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA;Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA;Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA;Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Venue:
Signal Processing
Year:
2009

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Abstract

This paper addresses statistical estimation of multiple parameters that may vary simultaneously but slowly relative to the process response in nonlinear dynamical systems. The estimation algorithm is sensor-data-driven and is built upon the concept of symbolic dynamic filtering for real-time execution on limited-memory platforms, such as local nodes in a sensor network. In this approach, the behavior patterns of the dynamical system are compactly generated as quasi-stationary probability vectors associated with the finite-state automata for symbolic dynamic representation. The estimation algorithm is validated on nonlinear electronic circuits that represent externally excited Duffing and unforced van der Pol systems. Confidence intervals are obtained for statistical estimation of two parameters in each of the systems.