Subspace Identification Method for Combined Deterministic-stochastic Bilinear Systems

In this paper, a ‘four-block’ subspace system identification method for combined deterministic-stochastic bilinear systems is developed. Estimation of state sequences, followed by estimation of system matrices, is the central component of subspace identification methods. The prominent difference of our new approach is a ‘four-block’ arrangement of data matrices which leads to a linearization of the system state equation, when written in block form. A major advantage of this approach, over a previous bilinear subspace algorithm, is that the measured input is not restricted to be white. We show that, providing a certain data-dependent eigenvalue condition is met, our algorithm provides asymptotically unbiased estimates, and we indicate the rate at which the bias decreases. Simulation results show that this algorithm requires a smaller sample size than earlier algorithms (for comparable performance) and that the computational complexity is significantly lower. Copyright c ©2000 IFAC