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.
翻译:我们提出Koopman State Estimator(Koopman State Estimator (KoopSE),这是对控制-动物系统进行无模型状态分批估算的框架,没有线性假设,不需要进行线性假设,不需要针对特定问题的特征选择,并且有一个独立于培训点数目的推论计算成本。我们将原非线性系统提升到一个高维的再生Kernel Hilbert空间(RKHS),这个系统成为双线性。时间变化模型矩阵可以通过解决培训轨迹的最小方位问题来学习。在测试时,这个系统被代数操纵成一个线性时间变换系统,在这个系统中,标准的分流性估算技术可以用于高效率地计算国家手段和共变。随机的四重线性特征(RKRFF)被用来将Koopman法方法的计算效率和内嵌合方法的一般性结合起来。 KOopSESE通过实验性验证一个本地化任务,涉及配备超宽带接收器和轮式观察模型模型模型的移动机器人。 KOopSEVERS,尽管有更精确、更一致的先定的系统,但比SE-SE-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-