Linear regression techniques for state-space models with application to biomedical/biochemical example

In this paper a novel approach to estimate parameters in an LTI continuous-time statespace model is proposed. Essentially, the approach is based on a so-called pqR-decomposition of the numerator and denominator polynomials of the system’s transfer function. This approach allows the physical knowledge of the system to be preserved. As an illustrative example, a biomedical/biochemical process with two compartments in parallel and with first-order reaction is used.First, the process is approximated by a discrete-time state-space model. Next, after deriving the corresponding discrete-time transfer function, the rational transfer function is decomposed into pqR form and then reparametrized to obtain a set of linear regressive equations. Subsequently, the unknown linear regression parameters, which are a polynomial function of the original physical parameters, are uniquely estimated from real data of the biomedical/biochemical process using the ordinary least-squares method. This approach is favourable when there is a need to preserve physical interpretations in the parameters. Furthermore, by taking into account the original model structure, a smaller number of parameters than in the case of direct transfer function estimation may result and the identifiability property naturally appears.