Risk-sensitive identification of ARMA processes

A new definition of risk-sensitive recursive identification is given, which is applicable to ARMA-system and even to general linear stochastic systems. The new identification criterion is defined in terms of a suitably transformed estimation-error process, and an exponential cost function. Applying stochastic realization theory and the bounded real lemma we derive an alternative expression for the LEQG cost function. A key design parameter is the weight matrix that is used in the recursive estimation. Its optimal value is found in explicit form. These results generalize the results of Stoorvogel and van Schuppen (1995) for risk-sensitive identification of AR-processes.