Linear filtering for bilinear stochastic differential systems with unknown inputs

This note investigates the problem of state estimation for bilinear stochastic multivariable differential systems in presence of an additional disturbance, whose statistics are completely unknown. A linear filter is proposed, based on a suitable decomposition of the state of the bilinear system into two components. The first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm. No a priori information on the disturbance is required for the filter implementation. The proposed filter is robust with respect to the unknown input, in that the covariance of the estimation error is not affected by such input. Numerical simulations show the effectiveness of the proposed filter.