Robot localization faces the classic chicken or egg problem where it has to either know the location of the robot or the map to localize itself. In most applications this can be using Simultaneous Localization and Mapping(SLAM) through measurements via sensors. Most applications of SLAM involve taking measurements that contain both range and orientation information about its environment. But Range-Only SLAM localization faces an ambiguity because it receives only range measurements from its sensors. Hence in order to implement localization we would need to know atleast an approximate initial location of the landmarks. Previous approaches to this issue involves basic trilateration, probabilistic methods, least squares approximation, multiple hypothesis methods using the Extended Kalman Filter. This however does provide a delay the localization. In order to overcome this there are multiple hypothesis methods that initialize the problem in real time. However, this is computationally expensive and all of these methods do not cope well with multipath noise. Multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths leading to false range measurements.In this research we explore the problem put forward with the use of radio beacons when applied to RO SLAM and multipath noise that has a non Gaussian distribution. In particular, the use of the particle filter approach that copes with multipath noise as compared to the Extended Kalman Filter that is only applicable to noise that has a Gaussian distribution. This thesis proposes a method using particle filters to perform SLAM and is then compared to the established methods through simulations.