  In this paper, we establish a unified framework for subspace identification
(SID) of linear parameter-varying (LPV) systems to estimate LPV state-space
(SS) models in innovation form. This framework enables us to derive novel LPV
SID schemes that are extensions of existing linear time-invariant (LTI)
methods. More specifically, we derive the open-loop, closed-loop, and
predictor-based data-equations, an input-output surrogate form of the SS
representation, by systematically establishing an LPV subspace identification
theory. We show the additional challenges of the LPV setting compared to the
LTI case. Based on the data-equations, several methods are proposed to estimate
LPV-SS models based on a maximum-likelihood or a realization based argument.
Furthermore, the established theoretical framework for the LPV subspace
identification problem allows us to lower the number of to-be-estimated
parameters and to overcome dimensionality problems of the involved matrices,
leading to a decrease in the computational complexity of LPV SIDs in general.
To the authors' knowledge, this paper is the first in-depth examination of the
LPV subspace identification problem. The effectiveness of the proposed subspace
identification methods are demonstrated and compared with existing methods in a
Monte Carlo study of identifying a benchmark MIMO LPV system.
