Gaussian Process Gauss-Newton: Non-Parametric State Estimation

In this paper, we present Gaussian Process Gauss-Newton (GPGN), an algorithm for non-parametric, continuous-time, nonlinear, batch state estimation. This work adapts the methods of Gaussian Process regression to the problem of batch state estimation by using the Gauss-Newton method. In particular, we formulate the estimation problem with a continuous-time state model, along with the more conventional discrete-time measurements. Our derivation utilizes a basis function approach, but through algebraic manipulations, returns to a non-parametric form by replacing the basis functions with covariance functions (i.e., the kernel trick). The algorithm is validated through hardware-based experiments utilizing the well-understood problem of 2D rover localization using a known map as an illustrative example, and is compared to the traditional discrete-time batch Gauss-Newton approach.