Abstract
Linear time invariant state-space models have several applications related to prediction and control. When models cannot be derived based on physical principles, these must be identified based on measurements of the input- and corresponding output vector. In this article we show that for the purpose of system identification it is useful to transform the state-space model into an autoregressive moving-average model with exogenous (ARMAX) inputs as this removes model redundancy related to the state vector. Our main result is a Kalman-like filter with forgetting factor that recursively estimates parameters of the ARMAX model based on new input and output measurements. We prove that the estimated parameters produce the smallest, weighted model errors. The recursive nature of the algorithm is advantageous computationally compared to batch processing if the data set is large, and moreover it can adapt to changes in model parameters online. The benefit of the algorithm is illustrated in a simulation of two stirred tanks in series.