A new subspace identification method for bilinear systems

Abstract

In this paper, a subspace method for the identification of bilinear systems is developed. A two-block subspace method is developed in the deterministic system case and a three-block one is set up for the combined deterministic-stochastic system. An extended non-steady state bilinear Kalman filter is also derived. The input signal to the system does not have to be white, which is a major advantage over an existing subspace method for bilinear systems. Simulation results also show that the new algorithm converges much more rapidly (with sample size) than the existing method, and hence is more effective with small sample sizes. The faster convergence is presumably due to the insensitivity of the algorithm to the sample-spectrum of the input signal. These advantages are achieved by a different arrangement of the input-output equations into ‘blocks’, and projections onto different spaces than the ones used in the existing method. A further advantage of our algorithm is that the dimensions of the matrices involved are significantly smaller, so that the computational complexity is lower. Corresponding author