Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems
This addresses state estimation for robotics and control systems, offering a model-free alternative that avoids linearization assumptions and reduces computational costs, though it builds incrementally on existing Koopman and kernel methods.
The paper tackles batch state estimation for control-affine systems by introducing KoopSE, a model-free framework that uses Koopman linearization and kernel embeddings to achieve more accurate and consistent estimates than a model-based smoother, as validated on a mobile robot localization task.
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.