A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

• Based on unscented Gaussian sum representations, a Monte Carlo filter is proposed for large dimensional structural system identification.
• In order to reduce the risk of particle degeneracy, an additional scaled gain-weighted innovation term is introduced in the process model.
• Numerical evidence confirms the filter's efficacy in arresting weight collapse whilst treating higher dimensional states pace models.

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-à-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems.