## 6 Experimental Results
### Localization  
In the operating phase of _LOSNUS_, the transmitter positions obtained by the calibration process are used for device localization by TDoA. Locating is started by sequentially firing the transmitters with the well-defined protocol. For every transmitter a frame including its unique transmitter coding frequency is sent. Such signals are then received by ultrasonic receivers of the devices and processed by binary cross correlation. An example of a correlation result is shown in Figure 16. A typical correlation result includes several peaks. The first peak of each transmitter coding is considered to be the LoS, which gives the correct ToA values. These ToA values are then evaluated using the proposed locating algorithm.  
23 positions have been measured on the belt with a spacing of 50 mm. At each position, 20 measurements have been taken. The start and the end positions are also the reference positions used within the calibration. In the first step, the correct temperature has been estimated using Equation (29) using the fact that the reference position cannot move. This is shown in Figure 17 where the mean deviation of the 20 measurements at the reference point is shown for different temperature values. The correct temperature is 24.8 \({}^{\circ}\)which is in close agreement with the manually measured temperature of 24.9 \({}^{\circ}\).  
The measurements are shown in Figure 18. The two green star symbols are the reference positions from the calibration. The black plus symbols are the interpolated reference positions modeling the linear belt. At each position, a group of 20 measurements can be seen where the spread is a result of the DOP and the uncertainty of the TDoA measurement. The distance of the mean to the reference positions is due to the temperature uncertainty and calibration uncertainty. Anyhow the result is remarkable where standard uncertainty for this measurement is reported as \(\left\|\mathrm{P-(x,y,z)^{T}}\right\|=4.7\;\mathrm{mm}\;\underline{\pm}\;1.3 \;\mathrm{mm}\). A graphical visualization of the uncertainty components is shown in Figure 19a. In this case b(k)  
Figure 16: Correlation results of a complete _LOSNUS_ sequence showing ToA for individual transmitters and an example for a Non Line of Sight (NLOS) signal for Tx1.  
calculated according to Equation (18) shows the systematic component of the uncertainty, _i.e._, the mean distance between the points and the reference position. The value of \(\sqrt{\mathrm{u}^{2}(\mathrm{P}(\mathrm{k}))}\) is the standard deviation of the measured points at position k. This value is closely related to the DOP by the standard deviation of the ToA measurements and the DOP for the transmitter/receiver combination used. Due to the large and accurate reference path used the component \(\sqrt{\mathrm{u}^{2}(\mathrm{b}(\mathrm{k}))}\) is rather small.  
Figure 17: Determination of temperature using reference positions.  
Figure 18: Measurement on linear belt at 23 positions with 20 measurements each. Temperature = 24.8 \(\mathrm{\SIUnitSymbolCelsius}\) taken from Figure 17.  
What is also interesting to point out is that the final result did not contain any outlier (no postprocessing was performed on the input data). This is also a remarkable as at about 0.6 m on the belt the signal for transmitter six is lost. This is shown in Figure 19b.  
Reproducibility under different environmental conditions was verified as well. Again temperature identification shown in Figure 20b and results shown in Figure 20a are good. The reported standard uncertainty is \(\|\mathrm{P}-(\mathrm{x},\mathrm{y},\mathrm{z})^{\mathrm{T}}\|=6\:\mathrm{mm} \pm 2.2\:\mathrm{mm}\). The deviations between the two results, although small, are due to the finite sample size. In addition modeling does not take into account all possible effects.