# An Efficient Single-Anchor Localization Method Using Ultra-Wide Bandwidth Systems
## 1 Introduction  
Location-awareness technologies play an important role in many applications, such as logistics, autonomous vehicles, medical care, and smart factories [1; 2; 3; 4]. The Global Navigation Satellite System (GNSS) is the most common position service provider, while its accuracy is affected by urban multipath components (MPCs) and non-line-of-sight (NLOS) propagations in indoor environments. To meet the demand for high-accuracy localization services, both the academia and industry are devoted to developing an alternative indoor localization method [5; 6; 7; 8]. Radio frequency (RF) signals are widely used for indoor localization, such as Bluetooth, Wi-Fi, and radio-frequency identification (RFID)-based localization systems [9; 10; 11; 12]. However, it is challenging for these RF technologies to achieve sub-meter level accuracy and robust localization. Methods based on the received signal strength indicator (RSSI) can cause meter-level localization errors [13]. On the other hand, Bluetooth-based and Wi-Fi-based technologies generally determine the agents' positions by means of the location fingerprints (LF), which has low precision and high complexity. There is also an angle-of-arrival (AOA)-based localization method using Bluetooth signals, but it has only meter-level coverage [14]. The ultra-wideband (UWB) signal can enable high-accuracy localization considering its following unique advantages [15]: (i) sub-nanosecond-level time stamps; (ii) strong resistance to MPCs; and (iii) high throughput and transfer rate [16; 17; 18; 19]. Most UWB indoor localization systems are based on time-of-flight (ToF) and time-difference-of-arrival (TDOA) [20; 21; 22; 23]. In such systems, many UWB transceivers, often called anchors, are applied to multiple corners of a scene to create a large coverage. Generally, three or four anchors can realize two-dimensional or three-dimensional localization of agents, respectively. The anchors allocate different time slots for different agents, and at each time slot they measure the ToF or TDOA from one agent and calculate the agent's position via trilateration. This ToF- or TDOA-based localization method requires both high-cost system deployment and the exchange of a large number of messages, resulting in high system complexity and complicated message collision avoidance operations. Besides, the TDOA-based method requires strict clock synchronization between the anchors. Improved communication strategies can reduce the number of message exchanges. Multi-agent localization technology is required in many scenarios [24; 25; 26], and it is also necessary to improve the efficiency of multi-agent localization [27; 28]. TDOA-based localization methods can reduce the number of message exchanges between nodes while completing ranging and localization [29; 30; 31; 32]. A passive extended double-sided two-way ranging method is proposed in [33], which is a passive asynchronous localization strategy that uses extended two-way ranging to improve ranging accuracy. The proposed method requires fewer messages through indirect distance measurement by passive listening. Sequential TDOA is proposed in [34], where the anchors are triggered sequentially to send periodic signals. This approach supports an unlimited number of agents as well as high update rates, and it enhances covertness because agents are not \"visible\" as they do not send signals. In general, these improved TDOA-based methods still require message collision avoidance techniques, which leads to low time efficiency. Responding (quasi-)simultaneously by multiple agents to the anchors can reduce the number of message exchanges if the agent signals are orthogonal either in time or frequency. When the agents send UWB signals to anchors, each anchor can extract the superpositioned responses in one channel impulse response (CIR) estimate and further obtain all the arrival time-stamps from the agents [35; 36].