Linear filtering for bilinear stochastic differential systems with unknown inputs

This work 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.