Abstract— In this paper we present a novel approach to estimating the trajectory of a robot by means of inexpensive passive RFID tags and odometry in unknown environments. We show how trajectory estimation, a prerequisite of mapping RFID transponder positions without a reference positioning system, can be achieved using a particle filter. The presented technique is based on a non-parametric model of spatial relationships between RFID measurements. It overcomes the noisy nature of RFID measurements and the absence of distance and bearing information. The accuracy of our method is investigated in a series of experiments with a mobile service robot.