Risk-sensitive identification of ARMA processes

Abstract

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 [5] given for risk-sensitive identification of AR-processes.