Posterior Cramer Rao Lower Bounds for the respiratory model parameter estimation

In this paper, we introduce a new approach for the evaluation of dual Posterior Cramer-Rao Lower Bounds (PCRLBs) where the estimation procedure involves time-invariant, stationary system parameters and system states. Dual estimation may be required in respiratory system modeling where the parameters are usually physiological model settings. Bayesian solution of the parameter estimation lets us derive the dual PCRLBs with the help of the block matrix algebra. For the state estimation bound, our results give the same expressions as in the previous studies. In addition, we have obtained the iterative PCRLB expressions for the parameter estimation in the Mead respiratory model. Dual UKF and EKF error variances that were obtained in our previous work are demonstrated with respect to these bounds. Results show that UKF performs better than the EKF for the dual estimation in the Mead model.