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

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 Koopman 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.