Parametric lower bound for nonlinear filtering based on Gaussian process regression model

Assessing the fundamental performance limitations in Bayesian filtering can be carried out using the parametric Cramér-Rao bound (CRB). The parametric CRB puts a lower bound on mean square error (MSE) matrix conditioned on a specific state trajectory realization. In this work, we derive the parametric CRB for state-space models, where the measurement equation is modeled by a Gaussian process regression. These models appear, for instance in proximity report-based positioning, where proximity reports are obtained by hard thresholding of received signal strength (RSS) measurements, that are modeled through Gaussian process regression. The proposed parametric CRB is evaluated on selected state trajectories and further compared with the positioning performance obtained by the particle filter. The results corroborate that the positioning accuracy achieved in this framework is close to the parametric CRB.