## 4 Advanced Positioning Methodologies Using UWB and Wi-Fi RTT Signals
### Autonomous Calibration of Base Station Coordinates  
With the TOA and TDOA principles, UWB- and Wi-Fi RTT-based geometric positioning requires known coordinates of base stations, as shown in Equations (1)-(3). Hence, these systems need to calibrate the coordinates of base stations of either UWB or Wi-Fi RTT when they are deployed in the field. The calibration process is often cumbersome and labor-consuming. Furthermore, the requirement of calibrating the base stations limits the positioning systems only working within the coverage area of these calibrated base stations. Methods have been reported to estimate the unknown positions of base stations online by jointly integrating complementary data of multiple sensors [96, 97, 98, 99, 82]. These methods not only alleviate the tedious tasks of measuring and calibrating base station coordinates in advance, but also enable new applications such as dynamic expansion and deployment of UWB or Wi-Fi RTT base stations, for example, in unknown complex environments where it is difficult to calibrate the coordinates of base stations manually. The complementarity of different sensor data enables the inverse estimation and calibration of the coordinates of base station positions at the initialization stage. Alternatively, the unknown coordinates of base stations are directly incorporated as state variables to be estimated together with the state parameters of mobile tags' positions during the online positioning process. Refs. [96, 97] reported successive joint estimation methods for tightly coupling vision-UWB combinations, effectively handling unknown positions of three base stations as additional state variables. The first method [96] and second method [97] in volved joint estimation of the scale factor and positions of UWB base stations, requiring initial values for the additional states. The former method eliminated prior error considerations but enhanced the Levenberg-Marquardt algorithm by constructing an explicit square error function. It then added the UWB measurement's residual term to the reprojection error for tight coupling, as illustrated in Figure 6. The latter constructed a ranging error and prior error equation, where the scale factor and positions of UWB base stations were both included in the error equation, solving it through minimization using the Levenberg-Marquardt method. VIO was utilized for precise positioning during the initialization, and the trajectory in the world coordinate frame was established. The distances between base stations and the trajectory were determined by UWB ranging information, forming an optimization problem on the data window. The optimization process was terminated when the position uncertainty fell below a threshold, determining the positions of base stations. It should be noted that it increases the number of estimated states by introducing the positions of base stations as additional states, and it also generates geometric constraints on motion trajectories, which enhances the solution robustness. Alternatively, the authors of [98] reported a two-layer sliding window algorithm based on a single base station. The study constructed a cost function introducing positions of UWB base stations in the estimated state vector during the initialization process, and the positions of base stations were fixed upon completion of the estimation and were considered invariant known variables in the subsequent navigation process. Using Wi-Fi RTT ranging measurements, the authors of [99] reported the method of jointly estimating the positions of Wi-Fi routers and user carriers together. The authors of [82] created a map consisting of visual features and anchor points using a monocular camera and UWB base stations. As a vehicle explored the unknown space of interest, new base stations were continuously deployed, and their positions were estimated online together with the vehicle position. This approach formed a UWB base station constellation to fulfill the task of exploring unknown environments and constructing maps.