Advancing Mixture Models for Least Squares Optimization

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 l...

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Bibliographic Details
Published in:IEEE robotics and automation letters 2021-04, Vol.6 (2), p.3941-3948
Main Authors: Pfeifer, Tim, Lange, Sven, Protzel, Peter
Format: Article
Language:English
Subjects:
Convergence
Cost function
Least squares
Localization
Mixture models
Optimization
probabilistic inference
Probabilistic logic
Probabilistic models
probability and statistical methods
sensor fusion
Simultaneous localization and mapping
SLAM
Solvers
Source code
State estimation
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Summary: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.
ISSN:2377-3766
2377-3766
DOI:10.1109/LRA.2021.3067307