Available online at www.sciencedirect.com Journal of the Franklin Institute 351 (2014) 1093–1111 Iterated gain-based stochastic filters for dynamic system identification Tara Raveendran a , Debasish Roy b,n , Ram Mohan Vasu a a Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, India b Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore, India Received 30 November 2012; received in revised form 1 August 2013; accepted 2 October 2013 Available online 11 October 2013 Abstract We propose a novel form of nonlinear stochastic filtering based on an iterative evaluation of a Kalman- like gain matrix computed within a Monte Carlo scheme as suggested by the form of the parent equation of nonlinear filtering (Kushner–Stratonovich equation) and retains the simplicity of implementation of an ensemble Kalman filter (EnKF). The numerical results, presently obtained via EnKF-like simulations with or without a reduced-rank unscented transformation, clearly indicate remarkably superior filter convergence and accuracy vis-à-vis most available filtering schemes and eminent applicability of the methods to higher dimensional dynamic system identification problems of engineering interest. & 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. 1. Introduction System identification of dynamical systems typically belongs to a set of (nonlinear) stochastic filtering problems where the properties of a hidden Markov stochastic process, the system dynamics, are estimated conditioned on the available noisy partial observations. The hidden states are characterized, subject to modeling errors, by the weak solutions (e.g. the Markov transition kernel) of the so-called process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown or inaccurately known system parameters may be included within the process model wherein they evolve as pseudo-states described by Wiener processes or their temporal discretizations, i.e. random walks. The observations, often collected at discrete time instants, are also modeled by a set of measurement SDEs or, equivalently, www.elsevier.com/locate/jfranklin 0016-0032/$32.00 & 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfranklin.2013.10.003 n Corresponding author. Tel.: þ91 8022933129; fax: þ91 8023600404. E-mail address: royd@civil.iisc.ernet.in (D. Roy).