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A Gamma Filter for Positive Parameter Estimation

: Govaers, F.; Alqaderi, H.


Institute of Electrical and Electronics Engineers -IEEE-; IEEE Robotics and Automation Society; Informationstechnische Gesellschaft -ITG-; Verband der Elektrotechnik, Elektronik, Informationstechnik -VDE-:
IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, MFI 2020 : 14-16 September 2020, virtuell, Karlsruhe, Germany
Piscataway, NJ: IEEE, 2020
ISBN: 978-1-7281-6422-9
ISBN: 978-1-7281-6421-2
ISBN: 978-1-7281-6423-6
International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI) <2020, Online>
Fraunhofer FKIE ()

In many data fusion applications, the parameter of interest only takes positive values. For example, it might be the goal to estimate a distance or to count instances of certain items. Optimal data fusion then should model the system state as a positive random variable, which has a probability density function that is restricted to the positive real axis. However, classical approaches based on normal densities fail here, in particular whenever the variance of the likelihood is rather large compared to the mean. In this paper, it is considered to model such random parameters with a Gamma distribution, since its support is positive and it is the maximum entropy distribution for such variables. For a Bayesian recursion, an approximative moment matching approach is proposed. An example within the framework of an autonomous simulation and further numerical considerations demonstrate the feasibility of the approach.