  Despite the cheap availability of computing resources enabling faster Monte
Carlo simulations, the potential benefits of particle filtering in revealing
accurate statistical information on the imprecisely known model parameters or
modeling errors of dynamical systems, based on limited time series data, have
not been quite realized. A major numerical bottleneck precipitating this
under-performance, especially for higher dimensional systems, is the
progressive particle impoverishment owing to weight collapse and the aim of the
current work is to address this problem by replacing weight-based updates
through additive ones. Thus, in the context of nonlinear filtering problems, a
novel additive particle update scheme, in its non-iterative and iterative
forms, is proposed based on manipulations of the innovation integral in the
governing Kushner-Stratonovich equation. Numerical evidence for the
identification of nonlinear and large dimensional dynamical systems indicates a
substantively superior performance of the non- iterative version of the EnKS
vis-\`a-vis most existing filters. The costlier iterative version, though
conceptually elegant, mostly appears to effect a marginal improvement in the
reconstruction accuracy over its non-iterative counterpart. Prominent in the
reported numerical comparisons are variants of the Ensemble Kalman Filter
(EnKF) that also use additive updates, albeit with many inherent limitations of
a Kalman filter.
