Iterated stochastic filters with additive updates for dynamic system identification: Annealing-type iterations and the filter bank

• A Gaussian sum Monte Carlo filter incorporating an iterative form of additive updates is proposed.
• The enhanced particle scatter through an annealing-type iterative update improves convergence and estimation accuracy.
• The additive nature of the update also bypasses the curse of weight collapse and particle impoverishment.
• The Gaussian sum approach provides a means to capturing non-Gaussianity owing to process and measurement nonlinearity.
• Numerical experiments confirm the applicability of the filter to higher dimensional dynamic system identification problems.

A nonlinear stochastic filtering scheme based on a Gaussian sum representation of the filtering density and an annealing-type iterative update, which is additive and uses an artificial diffusion parameter, is proposed. The additive nature of the update relieves the problem of weight collapse often encountered with filters employing weighted particle based empirical approximation to the filtering density. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner–Stratonovich) equation and possesses excellent mixing properties enabling adequate exploration of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its remarkable performance in terms of filter convergence and estimation accuracy vis-à-vis most other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states.