# Loosely Coupled GNSS and UWB with INS Integration for Indoor/Outdoor Pedestrian Navigation +
## 5 Evaluation of UWB Data
### Analysis of Range Measurements  
As previously stated, during the measurement campaign, the data acquisition and the processing were made all in the same python environment allowing both raw data and positioning estimation to be stored. Considering only the Pozyx UWB system, several data were acquired and stored like the ranges between the tag and the anchors network, the received signal straight RSS, the inertial measurements (acceleration, rotation rate, magnetic force) and finally the position estimation from our algorithm with the relative timestamp. The positioning update rate achieved by the Pozyx system depends on several parameters like the length of the preambles, the bitrate, the number of anchors, the communication protocols and the kind of raw data acquired. The manufacturer states that, with only four anchors and one tag, the best parameters combination allows a positioning update rate of around 140 Hz to be reached. Due to the complexity in characterizing the update rate with such variability, in the present work only the time variation for all the tests performed which have the same parameters and settings is reported. Figure 6 gives a good indication of the delay that can be expected in positioning estimation showing a mean time variation value of 0.24 s with a maximum of 0.34 s and a standard deviation of 0.03 s. Therefore, it is possible to summarize that the systems update rate is around 4 Hz which is useful for pedestrian navigation purposes and it is also under the update rate of the low-cost GNSS receivers used in this work. Figure 5: Number of measured ranges by the moving tag during the acquisition time for five different tests (**a–e**). Ranges are both in LOS and NLOS conditions. What is important to observe is that in the 0.2 s, the systems acquired in sequence all the data useful to perform the positioning and in particular a maximum of 8 range measurements from the anchors placed around the environment. In order to perform the positioning in real time, the ranges measurement timestamp has been packed (merged) in the positioning update rate therefore we are not able to observe their rate of acquisition. Thanks to the user continuous total station tracking, a reference ground truth of the walking path was acquired. The obtained data are East, North and Altitude position in the cartographic reference system. Knowing also the position of the anchors in the same reference frame, it is possible to derive the real ranges for all positioning time, thanks to the following geometric range model:  
\[R=\sqrt{\left(E_{msc}^{i}-E_{tag}^{t}\right)^{2}+\left(N_{msc}^{i}-N_{tag}^{t} \right)^{2}+\left(U_{msc}^{i}-U_{tag}^{t}\right)^{2}} \tag{20}\]  
where:  
\(E_{msc}^{i}\), \(N_{msc}^{i}\), \(U_{msc}^{i}\) are the East, North and Vertical components of the \(i\)-th anchor. \(E_{tag}^{t}\), \(N_{tag}^{t}\), \(U_{tag}^{t}\) are the East, North and Vertical components of the moving tag at the time \(t\). As these ranges are synchronized and aligned with the UWB raw ranges acquired in real time, it is possible to analyze the behavior of the system in all the environment crossed during the path. UWB sensors manufacturers usually declare the ranging capabilities of their system that usually don't reflects complex scenarios and real case applications. Therefore, computing errors of the range measurements acquired during a kinematic test both indoors and outdoors provide accuracy and precision of the system in a more realistic scenario. The two-way ranging algorithm implemented by host system software Pozyx is the single sided two-way ranging (SS-TWR) which involves the measurement of the round trip time of a message sent from a tag to an anchor and received back after a certain delay and the measurement of the replay time. Both times are measured independently by the two devices involved in the communication using their respective internal clock.