Weighted Null Space Fitting (WNSF): A Link between The Prediction Error Method and Subspace Identification
Year: 2024
Type: preprint
Abstract: Subspace identification methods (SIMs) have proven to be very useful and numerically robust for building state-space models. While most SIMs are consistent, few if any can achieve the efficiency of the maximum likelihood estimate (MLE). Conversely, the prediction error method (PEM) with a quadratic criteria is equivalent to MLE, but it comes with non-convex optimization problems and requires good initialization points. This contribution proposes a weighted null space fitting (WNSF) approach for estimating state-space models, combining some key advantages of the two aforementioned mainstream approaches. It starts with a least-squares estimate of a high-order ARX model, and then a multi-step least-squares procedure reduces the model to a state-space model on canoncial form. It is demonstrated through statistical analysis that when a canonical parameterization is admissible, the proposed method is consistent and asymptotically efficient, thereby making progress on the long-standing open problem about the existence of an asymptotically efficient SIM. Numerical and practical examples are provided to illustrate that the proposed method performs favorable in comparison with SIMs.
Source: arXiv (Cornell University)
Authors: He, Jiabao, Qin, S. Joe, Hjalmarsson, Håkan
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404345174