Smoothing Algorithm for Nonlinear Systems Using Gaussian Mixture Models

A smoothing method for nonlinear systems using Gaussian mixture models is presented. Problems of interest include applications with highly nonlinear dynamics and/or measurement models, and sparse measurements. Two new smoothing methods are presented that incorporate adaptive Gaussian splitting in the forward path, and condensation in the backward path. A nonlinear forward–backward smoothing algorithm with Gaussian mixture models is also enabled by a novel technique to estimate the “backward corrector.” An experiment of a robot performing indoor navigation in a sparse featured environment demonstrates the performance of the smoothing algorithms in typical applications. Experimental results demonstrate that the new smoothing algorithms give more accurate and consistent estimates than a traditional Kalman smoother, even in the presence of a sparse featured environment and sparse measurements.

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