Identification of multiplicative parameters in stochastic bilinear systems

A new method for identifying multiplicative parameters (i.e. the matrix-valued coefficients of the multiplicative state feedback) appearing in discrete-time bilinear models is proposed. The system is supposed to operate in a stochastic environment where the noisy output is the only sequence available for measurements. Ergodicity is not assumed, and the probability distributions involved may be arbitrary and unknown. A correlative identification technique is presented which uses stochastic approximation algorithms for estimating (with probability one) the unknown parameters. Simulated results are included.