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

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 Simultaneous Localization and Mapping (SLAM) 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. 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, α) of a landmark position expressed in polar coordinates when r and α are independent, and the marginal probability p(r) of the PDF is constrained to be uniform.