Kalman-based nested hybrid filters for recursive inference in state-space models

We introduce a new sequential methodology to calibrate the fixed parameters and trace the stochastic dynamical variables of a state-space system. The proposed framework is based on the nested hybrid filters (NHF) of [1], that combine two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques in the first layer of the algorithm, instead of Monte Carlo methods, which reduces computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We present numerical results for a stochastic Lorenz 63 model.