Binary search for time-constant estimation in first order systems, FiO2 - SpO2 case study

A binary search method for fast identification of the time-constant in first order systems is proposed. The unimodality of the Root Mean Square Error (RMSE) is exploited to achieve fast convergence. As an application example, the method is applied to the oxygen transport system of a preterm infant. Performance of the proposed binary algorithm is compared with a direct search method for two different selections of primary range and estimation precision. The results verify convergence, accuracy, and speed of the proposed algorithm in a practical identification application with noisy recorded signals. The algorithm is also shown to be successful in following the correct trajectory even when the best value of the time constant is out of the primary search space. This method can be applied to any one-dimensional optimization problem where the parameter of interest is a unimodal function of the unknown variable.