Advancing Mixture Models for Least Squares Optimization

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They able describe measurement errors that follow arbitrary distributions 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 either approximations of the true mixture prone convergence issues due their strong nonlinearity. We propose novel representation mixture, which an exact almost linear corresponding log-likelihood. Our approach provides efficient, accurate flexible for many probabilistic problems be as cost function solvers. demonstrate its superior performance various Monte Carlo experiments, including different kinds registration. implementation available open source code state-of-the-art Ceres GTSAM.