Data-driven Kalman Filter with Kernel-based Koopman Operators for Nonlinear Robot Systems

Abstract

Designing the Kalman filter for nonlinear robot systems with theoretical guarantees is challenging, especially when the dynamics model is unavailable. This paper proposes a data-driven Kalman filter algorithm using kernel-based Koop-man operators for unknown nonlinear robot systems. First, the Koopman operator using sparse kernel-based extended dynamic decomposition (EDMD) is presented to learn the unknown dynamics with input-output datasets. Unlike classic EDMD, which requires manual selection of kernel functions, our approach automatically constructs kernel functions using an approximate linear dependency analysis method. The resulting Koopman model is a linear dynamic evolution in the kernel space, enabling us to address the nonlinear filtering problem using the standard linear Kalman filter design process. Despite this, our approach generates a nonlinear filtering law thanks to the adopted nonlinear kernel functions. Finally, the effectiveness of the proposed approach is validated by simulated experiments.