  We introduce a new sequential methodology to calibrate the fixed parameters
and track the stochastic dynamical variables of a state-space system. The
proposed method is based on the nested hybrid filtering (NHF) framework of [1],
that combines 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 for Gaussian approximation in the first layer of the algorithm,
instead of the Monte Carlo methods employed in the original procedure. The
resulting scheme reduces the computational cost and so makes the algorithms
potentially better-suited for high-dimensional state and parameter spaces. We
describe a specific instance of the new method and then study its performance
and efficiency of the resulting algorithms for a stochastic Lorenz 63 model
with uncertain parameters.
