Phase-difference-based 3-D Source Localization Using a Compact Receiver Configuration Hui Chen, Tarig Ballal and Tareq Y. Al-Naffouri Computer, Electrical and Mathematical Science & Engineering King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900 Email: {hui.chen; tarig.ahmed; tareq.alnaffouri}@kaust.edu.sa Abstract—Source localization has many important applica- tions, especially in tracking and navigation. Trilateration, trian- gulation, and multilateration are three widely-used techniques for localization depending on the available information. The main drawbacks of these methods are the requirements of a large number of anchors and an elaborately designed layout. To accomplish the localization task with minimal resources while maintaining reasonable accuracy, we propose a 3-D source localization method with a compact infrastructure (prototype realized with 4 anchors located within an area of 2.5×20 cm 2 ) by utilizing only phase-difference information. The proposed method first estimates the direction-of-arrival (DOA) of the target and then finds the candidate 3-D location along on the DOA by minimizing a cost function. This system is compared to the other two similar setups based on simulations and the experimental tests are carried out using acoustic waves. The results show that the proposed approach can achieve 3-D location error of 2.77 cm for a target at 0.5 m without synchronization between the transmitter and the receivers. The relatively small system size and sufficient location accuracy provide possibilities in controller tracking for virtual reality applications. I. I NTRODUCTION Location information is important for many applications such as patient tracking [1], robot navigation [2], wireless sensor network (WSN) [3], gesture recognition [4] and so on. Sensor network based localization is one of the important methods to obtain the location of a target using a base station (BS) network; a summary of techniques can be found in [5]. Trilateration can be implemented using measurements of the distance from the target to the BS. The distance can be esti- mated using received signal strength (RSS) [6], time of flight (TOF) [7], or round-trip TOF [8]. Triangulation algorithms are used in systems that can utilize the direction of arrival (DOA) information of the signal to the BSs [9]. When the BSs are synchronized, multilateration algorithms can be applied using time difference of arrival (TDOA) information [10]. Although deploying sensor networks yield sufficient lo- calization accuracy, the number of BSs required in these methods increases the complexity and the cost of the system. As an alternative, a localization solution using a single base station is of great utility. Several positioning systems using single BS were designed in [11]–[13]. These systems are still unsatisfactory either because of their poor accuracy or the large system size. To solve the mentioned high complexity and large size issues while accomplishing the localization task with satis- factory measurement accuracy, we proposed a system using phase-difference measurement and a compact receiver config- uration. The definition of compact has two aspects: a) Minimum hardware resources, i.e., the system functions with at most 4 anchors without synchronization between the transmitter and the receivers; b) Minimum efforts for deployment. The small size of the receiver array (2.5 × 20 cm 2 for the proposed system) enables the integration of all the components in one board. This plug-and-use feature prevents calibration errors in system deployment. And the small size of the array can be easily installed on a virtual reality headset to track the 3D locations of the controllers. Due to the small distance between the anchors, TDOA information is no more helpful in finding 3-D location. This system estimates the DOA and absolute range of a target by using only the phase-difference information which will be explained in the next section. The proposed methods can be applied to both acoustic and radio frequency signals with possible application in indoor localization, human-computer interaction, robot navigation, and so on. This paper is organized as follows. Section II states the localization model and explains the 3-D localization algorithm. Section III analyzes how locating performance is affected by the system parameters and gives suggestions on tracking application. Section IV presents simulation and experimental results. In section V, we derive the conclusions of the whole work with suggestions of future directions. II. THE PROPOSED LOCALIZATION ALGORITHM A. Localization and Signal Models The localization model is shown in Fig. 1. A transmitter periodically sends signal blocks which are received by a planar receiver array on a base station. Each block consists of sinusoidal pulses with frequencies of f 1 ,f 2 ,...,f N , where N is the number of frequency components. These pulses have the same duration t p and are transmitted sequentially inside each block. The transmitted signal block can be expressed in the continuous time (t) domain as x(t)= N  i=1 a i (t) cos(2πf i t + ρ i ), (1) 251 978-9-0827-9705-3 EUSIPCO 2020