Explicit linear regressive model structures for estimation, prediction and experimental design in compartmental diffusive systems

A linear regressive model structure and output predictor, both in algebraic form, are deduced from an LTI state space system with certain properties without the need of direct matrix inversion. On the basis of this, explicit expressions of parametric sensitivities are given. As an example, a diffusion process is approximated by a state space discrete time model with n compartments in the spatial plane and is then reparametrized. The system output can then be explicitly predicted by ŷk = θT φk-n - ेk-n as a function of n, the sensor position, the parameter vector θ, and input-output data. This method is attractive for estimation, prediction and insight in experimental design issues, when physical knowledge is to be preserved.