Bayesian non-parametric methods for dynamic state-noise covariance matrix estimation: Application to target tracking

• We address the joint estimations of the state vector and the state-noise covariance matrix.
• We use Bayesian non-parametric methods implemented by particle filtering.
• Two approaches are presented.
• In both cases, the optimal proposal distribution is derived.
• Both proposed algorithms are applied to target tracking.

When using Bayesian estimation techniques, the algorithm is strongly sensitive to the system evolution model and more particularly to the setting of the state-noise covariance matrix. Recently, Bayesian non-parametric models and in particular Dirichlet processes (DPs) have been proposed as a scalable solution to this issue. They assume that the system can switch between an infinite number of state-space representations corresponding to different values of the state-noise covariance matrix. In this framework, jointly estimating the state vector and the covariance matrix is a non-linear non-Gaussian problem. The inference is thus classically carried out using particle filtering techniques. In this case, the choice of the proposal distribution for the particles is of paramount importance regarding the estimation accuracy. A first contribution of this paper is to derive an approximation of the optimal proposal distribution of the particle filter when a DP prior is placed on the distribution of the state-noise covariance matrix. Then, an alternative DP-based formulation of the inference problem is proposed to reduce its dimensionality. It takes advantage that the possible functional forms of the state-noise covariance matrices are known up to a reduced number of time-switching hyperparameters in many applications. An approximation of the optimal proposal distribution is also derived. Finally, the relevance of both proposed approaches is analyzed in the framework of target tracking and a comparative study with existing methods is carried out.