Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems

TL;DR

The paper introduces KoopSE, a model-free, kernel-based batch state estimator for control-affine systems that outperforms traditional methods without requiring system linearization or feature selection.

Contribution

KoopSE is a novel framework that lifts nonlinear systems into RKHS, enabling efficient, model-free batch state estimation with no linearization assumptions or problem-specific features.

Findings

KoopSE achieves higher accuracy than RTS smoother in localization tasks.

KoopSE's computational cost is independent of training data size.

KoopSE effectively estimates states without prior system knowledge.

Abstract

We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points. We lift the original nonlinear system into a higher-dimensional Reproducing Kernel Hilbert Space (RKHS), where the system becomes bilinear. The time-invariant model matrices can be learned by solving a least-squares problem on training trajectories. At test time, the system is algebraically manipulated into a linear time-varying system, where standard batch linear state estimation techniques can be used to efficiently compute state means and covariances. Random Fourier Features (RFF) are used to combine the computational efficiency of Koopman-based methods and the generality of kernel-embedding methods. KoopSE is validated experimentally on a localization task involving a mobile robot equipped with ultra-wideband receivers and wheel odometry. KoopSE estimates are more accurate and consistent than the standard model-based extended Rauch-Tung-Striebel (RTS) smoother, despite KoopSE having no prior knowledge of the system's motion or measurement models.