Bearing-only SLAM using a SPRT based Gaussian sum filter

Use of a Gaussian Sum filter (GSF) to efficiently solve the initialisation problem in bearing-only simultaneous localisation and mapping (SLAM) is the main contribution of this paper. When information about the range is not available, the initial probability density function (pdf) of a landmark in the environment can not be represented using a Gaussian. The GSF is an attractive candidate for estimation in this scenario as it can deal with arbitrary pdfs represented as sets of Gaussians. However, the implementation of the GSF requires maintaining a bank of extended Kalman filters. The resulting computational complexity needs to be reduced by employing a minimum number of filters. In this work, the performance of each extended Kalman filter (EKF) in the GSF is evaluated using the sequential probability ratio test (SPRT). As such the number of members in the Gaussian sum can be reduced rapidly and the efficiency of the GSF can be significantly increased, providing a solution to the important problem of bearing-only SLAM. The effectiveness of the proposed approach is demonstrated by simulation and experiment conducted using a Pioneer mobile robot.