Accommodation of NLOS for Ultra-Wideband TDOA Localization in Single- and Multi-Robot Systems Amanda Prorok ∗ , Phillip Tom´ e † , and Alcherio Martinoli ∗ ∗ Distributed Intelligent Systems and Algorithms Laboratory, School of Architecture, Civil and Environmental Engineering † Electronics and Signal Processing Laboratory, School of Engineering Ecole Polytechnique F´ ed´ erale de Lausanne, Switzerland. Email: firstname.lastname@epfl.ch Abstract—Ultra-wideband (UWB) localization is one of the most promising indoor localization methods. Yet, non-line-of- sight (NLOS) positioning scenarios can potentially cause signifi- cant localization errors and remain a challenge. In this work, we propose a novel, probabilistic UWB TDOA error model which explicitly takes into account NLOS. In order to validate our approach systematically in a real world setup, we leverage the utility of a group of mobile robots, and introduce our error model into a real-time localization framework run on- board the robots. We subsequently extend our framework by employing a collaborative localization strategy which enables the sharing of inter-robot, relative position observations. Our experimental results show how the novel TDOA error model is able to improve localization performance when information on the LOS/NLOS path condition is available. These results are complemented by additional experiments which show how a collaborative team of robots is able to significantly improve localization performance when no information on the LOS/NLOS path condition is available. Index Terms—Non-line-of-sight, ultra-wideband, mobile robots, collaborative localization I. I NTRODUCTION Accurate indoor localization is an enabling technology, with applications ranging from asset management and inventory tracking to assembly control for a variety of different in- dustries. Within the research community, the mobile robotics domain plays an important role with a vast and continuously growing body of contributions. Popular localization sensors employed on-board robots include cameras [18], ultra-sound sensors [6], laser range finders [19] and even infrared sen- sors [1], and are used independently or in combination with fixed landmark beacons [2]. Although such systems have proven accurate and efficient, their great disadvantage lies in the requirement for line-of-sight (LOS). Wireless localization systems alleviate the LOS constraint, in particular those re- lying on UWB technology because of their large frequency spectrum, and thus enable localization over large ranges and in dynamic environments [7]. Nevertheless, they simultaneously entail issues induced by the propagation through and reflection off obstacles, which need to be addressed in order to guarantee reliable localization. In this paper, we consider the problem of absolute lo- calization of a team of mobile robots for unknown initial This work was sponsored by the National Center of Competence in Research on Mobile Information and Communication Systems under grant number 51NF40-111400 of the Swiss National Science Foundation. x y R n R m θ nm θ mn r nm r mn r um r un r vn r vm B u B v Fig. 1. System of two robots (Rn and Rm) and two UWB base-stations Bu and Bv . The figure illustrates the robots’ relative range (rnm and rmn) and bearing (θnm and θmn) values. The ranges from the base-stations to the individual robots are shown (run, rum, rvn and rvm). pose estimates. We design an algorithm targeting miniaturized, computationally limited platforms equipped with noisy, low- power sensing modalities, and ultimately envision our solu- tion’s portability onto much smaller devices such as portable tags. Given its efficiency in solving localization problems for unknown initial conditions, and for accommodating arbitrary probability density functions, our method of choice is the par- ticle filter, building on the probabilistic framework of Monte- Carlo Localization (MCL) presented in [3]. Our localization strategy uses time-difference-of-arrival (TDOA) measurements from one or several pairs of UWB base-stations, and on- board dead reckoning information. Finally, as it is commonly known that multi-robot collaboration is able to compensate for deficiencies in the data owned by a single robot [3, 9], we extend our approach to include relative (inter-robot) range and bearing observations. We conclude our work by showing experimental results of the localization performance for both a single- and a multi-robot scenario. A. Related Work UWB has shown to be amongst the most promising localiza- tion techniques for indoor environments [7]. As a consequence, it has very recently been adopted by the robotics community. In [17], an UWB receiver is mounted on a mobile robot which uses a TDOA algorithm between pairs of anchor nodes to es- timate its own position. The robot’s self-localization algorithm is based on UWB measurements, yet it does not employ an UWB error model. The studies in [4] and [5] develop prob- abilistic models for biased UWB range measurements which are combined with on-board odometry data. Yet, both papers model NLOS biases within augmented-state particle filters that 978-1-4577-1804-5/11/$26.00 © 2011 IEEE