We present the Posterior Cramer-Rao Lower Bounds (PCRLB) for the dual Kalman filter estimation where the parameters are assumed to be time-invariant and stationary random variables. Relations between the PCRLB, the states, and the parameters are established and recursions are obtained for finite observation time. As a case study, the closed-form expressions of the PCRLB for a linear lung model, called the Mead respiratory model, are derived. Distribution of the parameters is assumed to be Generalized Gaussian Distribution (GGD) which enabled an investigation of different shape factors. Simulations performed on the signals collected from the human respiratory system yielded encouraging results. It is concluded that the parameter distribution should be chosen as Gaussian to super-Gaussian in order for the PCRLB algorithm to converge.