Bearing-only tracking with a mixture of von Mises distributions

This paper presents a novel method for Bayesian bearing-only tracking. Unlike the classical approaches, which involve using Gaussian distribution, the tracking procedure is completely covered with the von Mises distribution, including state representation, transitional probability, and measurement model, since it captures and models well the peculiarities of directional data. The state is represented with a mixture of von Mises distributions, thus offering advantages of being able to model multimodal distributions, handle nonlinear state transition and measurement models, and to completely cover the whole state space, all with a modest number of parameters. The tracking procedure is solved by convolution with a von Mises distribution (prediction step) and multiplication with a mixture representing the measurement model (update step). Since in the update step the number of mixture components grows exponentially, a method is presented for component reduction of a von Mises mixture. Furthermore, a closed-form solution is derived for quadratic Rényi entropy of the von Mises mixture. The algorithm is tested and compared to a particle filter representation in a speaker tracking scenario on a synthetic data set and real-world recordings. The results supported the proposed approach and showed similar performance to the particle filter.