An Improved Probability Density Function for Representing Landmark Positions in Bearing-only SLAM Systems

Abstract

To navigate successfully, a mobile robot must be able to estimate the spatial relationships of the objects of interest in its environment accurately. The
main advantage of a bearing-only SLAM (Simultaneous Localization and Mapping)
system is that it requires only a cheap vision sensor to enable a mobile robot to
gain knowledge of its environment and navigate. In this paper, we focus on the
representation of the spatial uncertainty of landmarks caused by sensor noise. This
representation is critical for the initialization of landmark positions in bearing-only
SLAM systems. We follow a principled approach for computing the Probability Density Functions (PDFs) of landmark positions when an initial observation is made.
We characterize the PDF p(r,alpha) of a landmark position expressed in polar coordinates when r and alpha are independent, and the marginal probability p(r) of the
PDF is constrained to be uniform. Existing methods that approximate the PDF
of a landmark position with a mixture of Gaussians do not satisfy this uniformity
requirement. We also show how to use the proposed PDFs for a 2D bearing-only
SLAM system that relies only on the landmark bearings measured by a panoramic
camera.