Efficient Identification of Error-in-Variables Switched Systems Using a Riemannian Embedding

This article considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP-hard, several relaxations have been proposed in the literature. However, while these approaches work well for low-dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this difficulty, we propose a computationally efficient alternative, based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric there to perform the identification. Our main result shows that, under dwell-time assumptions, the proposed algorithm is convergent, in the sense that it is guaranteed to identify the system for suitably low noise. In scenarios with larger noise levels, we provide experimental results showing that the proposed method outperforms existing ones. This article concludes by illustrating these results with academic examples and a nontrivial application: action video segmentation.