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The results are obtained using Monte Carlo simulations and the comparison is done with the non-iterative EKF and multiplicative EKF (MEKF) as baseline.The result clearly shows that the IMEKF and the NLS-based method are superior to q-IEKF and all three outperform the non-iterative methods.Third, we show that the posterior distribution in these models is a m Gv M distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning. Consequently, a wealth of GP approximation schemes have been developed over the last 15 years to address these key limitations.Many of these schemes employ a small set of pseudo data points to summarise the actual data.
Crucially, we demonstrate that the new framework includes new pseudo-point approximation methods that outperform current approaches on regression and classification tasks. These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales.Previously proposed multivariate circular distributions are shown to be special cases of this construction.Second, we introduce a new probabilistic model for circular regression, that is inspired by Gaussian Processes, and a method for probabilistic principal component analysis with circular hidden variables.We test our method on the cartpole swing-up task, which involves nonlinear dynamics and requires nonlinear control. The first is using the well-known unit quaternion as state (q-IEKF) while the other is using orientation deviation which we call IMEKF.The third method is based on nonlinear least squares (NLS) estimation of the angular velocity which is used to parametrise the orientation.