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              <p>Although Kalman filter (KF) was originally proposed for system control i.e. steering a system as desiredby monitoring the system states, its application for parameter estimation problems is widespread because of theexcellent similarity between these two apparently different problem types in state space description.In standard Kalman filter, system dynamics is described through the dynamics of certain internal variable,termed as states, evolving over time as defined by an assumed process model, while a measurement model mapsthese states to measurements. In some parameter estimation problems, the system is replaced by a state spaceformulation of the dynamic model with parameters appended in the unobserved states and collectively observedthrough the response measurements. Filtering based parameter estimation problems are thus inherently nonlineardue to the required nonlinear mapping of parameters to the corresponding observations.Being a linear estimator, Kalman Filter (KF) cannot be employed for such nonlinear system estimation andalternative filtering algorithms (eg. Particle filter) are therefore generally used. However, being model based,these filters optimally estimate the parameters of a quasi-static model of the real dynamic system. Consequently,any time variation in the system dynamics may completely diverge the estimation yielding a false or infeasiblesolution. By decoupling the estimation of system states and parameters, and applying concurrent filtering strategythat attempts conditional estimation of states based on parameters and vice versa, time varying systems can beestimated.This article attempts to combine KF with Particle filter (PF) and apply them for estimation of states and systemparameters respectively on a system with correlated noise in process and measurement. The idea is to nest abank of linear KFs for state estimation within a PF environment that estimates the parameters. This facilitatesemploying relatively less expensive linear KF for linear state estimation problem while costly PF is employedonly for parameter estimation. Additionally, the proposed algorithm also takes care of those systems for whichsystem and measurement noises are not uncorrelated as it is commonly idealized in standard filtering algorithms.As an example, for mechanical systems under ambient vibration it happens when acceleration response isconsidered as measurement. Thus the process and measurement noise in these system descriptions are obviouslycorrelated. For this, an improved description for the Kalman gain is developed. Further, to enhance the consistencyof particle filtering based parameter estimation involving high dimensional parameter space, a new temporalevolution strategy for the particles is defined. This strategy aims at restricting the solution from diverging (up tothe point of no return) because of an isolated event of infeasible estimation which is very much likely especiallywhen dealing with high dimensional parameter space.</p>
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