Tensor regression for LTI subspace identification

The biggest bottleneck of Linear Parameter Varying (LPV) subspace identification methods is the unavoidable over-parametrization in its first, rank-revealing estimation step. This motivated us to look at less superfluous parametrizations for Linear Time Invariant (LTI) subspace methods which have the potential to be extended to the LPV case. In this paper, we propose a method based on tensor regression and Multiple Inputs Multiple Outputs (MIMO) canonical forms which has a less superfluous parametrization. The proposed method can be used to obtain consistent estimates with comparable variance to the over-parametrized linear regression estimates, but uses much less parameters. Additionally, the linearised variant of our proposed method is presented, which reduces the parameter count even more. The effectiveness of the proposed method is illustrated with a simulation example.