Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Posterior Cramér-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process-based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process-based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posterior filtering CRBs for this specific application. Finally, the theory is illustrated with a positioning problem, with experimental data from an office environment where the obtained estimation performance is compared to the derived CRBs.Funding agencies: ELLIT - Swedish Government; European Union FP7 Marie Curie training program on Tracking in Complex Sensor Systems (TRAX) [607400]; Senion; Shenzhen Science and Technology Innovation Council [JCYJ20170307155957688, JCYJ20170411102101881]; National Natural