Inverse Gaussian Process Interpolation for High-Quality Assumed Gaussian Filtering

In this paper, we propose a novel Gaussian Assumed Density Filter (GADF) for high-quality state estimation of nonlinear dynamic systems. Our approach focuses on the measurement update, utilizing a non-Gaussian local approximation of the true joint measurement/prior state density. This is achieved through the sequential use of two Inverse Gaussian Processes (IGPs): the first IGP interpolates the means, and based on these results, the second IGP is trained to interpolate the covariances. Together, they fully characterize the conditional Gaussian densities of the hidden state on concrete measurements. Consequently, our method does not require the second Gaussian assumption for the joint density anymore, thereby enhancing filter performance. Moreover, our approach eliminates the need for an explicit likelihood function within the filter step, making it a higher-quality plug-in replacement for the commonly used Linear Regression Kalman Filter (LRKF).