Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their robustness depends on a close approximation of the real error distribution, their parametrization is crucial.We propose a novel approach that allows to adapt a multimodal Gaussian mixture model to the error distribution of a sensor fusion problem. By combining expectation-maximization and non-linear least squares optimization, we are able to provide a computationally efficient solution with well-behaved convergence properties.We demonstrate the performance of these algorithms on several real-world GNSS and indoor localization datasets. The proposed adaptive mixture algorithm outperforms state-of-theart approaches with static parametrization. Source code and datasets are available under https://mytuc.org/libRSF.

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Factor graph optimization (FGO) recently has attracted attention as an alternative to the extended Kalman filter (EKF) for GNSS‐INS integration. This study evaluates both loosely and tightly coupled integrations of GNSS code pseudorange and INS measurements for real‐time positioning, using both conventional EKF and FGO with a dataset collected in an urban canyon in Hong Kong. The FGO strength is analyzed by degenerating the FGO‐based estimator into an “EKF‐like estimator.” In addition, the effects of window size on FGO performance are evaluated by considering both the GNSS pseudorange error models and environmental conditions. We conclude that the conventional FGO outperforms the EKF because of the following two factors: (1) FGO uses multiple iterations during the estimation to achieve a robust estimation; and (2) FGO better explores the time correlation between the measurements and states, based on a batch of historical data, when the measurements do not follow the Gaussian noise assumption.

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Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set registration or tracking. However, using them with common least squares solvers is still difficult. Existing approaches are either approximations of the true mixture or prone to convergence issues due to their strong nonlinearity. We propose a novel least squares representation of a Gaussian mixture, which is an exact and almost linear model of the corresponding log-likelihood. Our approach provides an efficient, accurate and flexible model for many probabilistic estimation problems and can be used as cost function for least squares solvers. We demonstrate its superior performance in various Monte Carlo experiments, including different kinds of point set registration. Our implementation is available as open source code for the state-of-the-art solvers Ceres and GTSAM.