Piecewise-linear output-error methods for parameter estimation in direction-dependent processes

In direction-dependent processes, the dynamic responses depend on the direction of the system input. The parameter estimation of these processes under noisy conditions can be somewhat problematic in terms of predictor choice and asymptotic behaviour. For parameter estimation, a convenient way to model direction dependence is to use a piecewise-linear model formulation, whose switching depends on the input direction. This paper analyses a prediction-error minimisation method for direction-dependent processes in terms of piecewise-linear dynamics. In particular, the asymptotic convergence properties are investigated and relevant conditions for the utilisation of the estimation method are given. Further, it is demonstrated that a piecewise-linear output-error predictor is preferable in situations where the impact of disturbances is predominant. The main reason for this is that it separates the disturbances from the process model.