Progressive Gaussian filtering using explicit likelihoods

In this paper, we introduce a new sample-based Gaussian filter. In contrast to the popular Nonlinear Kalman Filters, e.g., the UKF, we do not rely on linearizing the measurement model. Instead, we take up the Gaussian progressive filtering approach introduced by the PGF 42 but explicitly rely on likelihood functions. Progression means, we incorporate the information of a new measurement gradually into the state estimate. The advantages of this filtering method are on the one hand the avoidance of sample degeneration and on the other hand an adaptive determination of the number of likelihood evaluations required for each measurement update. By this means, less informative measurements can be processed quickly, whereas measurements containing much information automatically receive more emphasis by the filter. These properties allow the new filter to cope with the demanding problem of very narrow likelihood functions in an efficient way.