Sequential particle filtering in the presence of additive Gaussian noise with unknown parameters

In sequential signal processing, the main objective is to estimate evolving states. Often, however, the models under consideration contain additional unknowns, which are time invariant. When the state estimation is carried out by sequential importance sampling methods, the presence of fixed unknowns can present a nontrivial problem. In this paper, we provide a solution to this problem when the fixed unknowns are the covariance matrices of the additive Gaussian noise vectors in the state and observation equations. These matrices are first marginalized, and then the sequential processing carried out as usual. In the implementation of this approach, besides the assignment of a weight to every particle, two additional evolving quantities are required. Simulation results are provided that show the performance of the method.