On the uniqueness of maximum likelihood identification

The maximum likelihood method of identification is a powerful tool for obtaining mathematical models of dynamic processes. To apply this method a loss function has to be minimized. The aim of the paper is an investigation of the local minimum points of this loss function for a common structure of a general form. If the loss function has more than one local minimum point, numerical problems can occur during the minimization. Sufficient conditions are given for the existence of a unique stationary point, which then also gives the desired global minimum. It is also shown by counter-examples that there are systems without peculiarities, which have more than one local minimum point of the loss function.