Iterative smoothing approach using Gaussian mixture models for nonlinear estimation

An iterative smoothing algorithm is developed using Gaussian mixture models in order to tackle challenging nonlinear estimation problems. Gaussian mixture models naturally capture nonlinear and non-Gaussian systems, while smoothing algorithms provide ability to update using measurements obtained in the past. A tree structure and Gaussian distribution splitting method are proposed to mitigate nonlinearity effects and complexities. Two methods, Children Collapsing and Parent Splitting, are developed to utilize sigma-points smoother for Gaussian mixture model. An indoor localization problem is used to explore and validate the approach. Performance of these new methods is compared to a baseline sigma-points smoother, in both simulation and experiment, and shows much improvement in overall error compared to the truth.