This paper proposes a novel Gaussian Mixture Filter (GMF) that allows components with negative weights. In the case of a ring-shaped likelihood function, the new filter keeps the number of components low by approximating the likelihood as a Gaussian mixture (GM) of two components, one with positive and the other with negative weight. In this article, the filter is applied to positioning with received signal strength (RSS) based range measurements. The filter is tested using simulated measurements, and the tests indicate that the new GMF outperforms the Extended Kalman Filter (EKF) in both accuracy and consistency.
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