Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models Articles uri icon

publication date

  • December 2021

start page

  • 1

end page

  • 13


  • 189

International Standard Serial Number (ISSN)

  • 0165-1684

Electronic International Standard Serial Number (EISSN)

  • 1872-7557


  • 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 and for a stochastic volatility model with real data.


  • Telecommunications


  • bayesian inference; filtering; kalman; monte carlo; parameter estimation