# Positioning Energy-Neutral Devices: Technological Status and Hybrid RF-Acoustic Experiments
## 4 Experiments Demonstrating Opportunities and Challenges in Hybrid RF-Acoustic Positioning
### Conducted Experiments
#### 4.2.1 Ranging Audio  
As sound pressure is subject to the inverse square law, with sound pressure decreasing by 50% when the distance doubles, an experiment of interest is that of the investigation of how well the ranging method performs if the audio distance (\(\Delta x_{a}\)) is increased by moving the backscatter device in a linear, stepwise motion. The RF source and accompanying antenna are moved along, keeping the distance (\(\Delta x_{rf}<2\) m) and angle of the incoming RF wave (\(\alpha\)) similar in all test cases. This minimizes the potential influence of the RF source and receiver spacing. Nevertheless, since the receiving antenna of the anchor node is connected through an SDR with the centrally positioned processing unit, there is still some unavoidable influence of the increased RF distance. Figure 10 plots the CDF of the measured error for 10 distances ranging from 50 to 500 cm. For each distance, at least 150 measurements were performed. The error is the absolute difference of the calculated hybrid ranging measurement and a reference value measured with a laser-based instrument. The results show an initial steep slope and sudden increase in the outliers. This leads to the initial conclusion that at the acoustic level, the ranging performs well. Only at the 350 cm distance in Figure 10a can a more gradual increasing graph be observed. This anomaly can be addressed to path loss or reverberation in the acoustic or the RF medium, as better results are obtained with larger distances. However, the initial rapid incline of this graph shows that the system is capable of calculating the correct distance which rules out errors in the calculations or constructive interference at another fixed frequency. At the larger distances between the acoustic source and backscatter device, the method behaves as expected and increases with the interdistance (\(\Delta x_{a}\)). A detail of the acoustic CDF plot is depicted in Figure 10b. Here, it can be seen that  
most of the experiments have a P90 value below 20 centimeters. All except two have a median error within a 10 cm error, a favorable result for indoor positioning where outlier detection algorithms can be used to optimize the results. The 400 cm curves on both plots show that even for larger distances, excellent results can be obtained. For the largest two distances, a plateau can be noticed on the CDF plot. This plateau can be explained by the fact that, wrongfully, the index of the maximum correlation coefficient is used to estimate the distance, as can be seen in Figure 11. The red line on this correlation plot describes the actual distance, whilst the orange lines indicate the peak selected based on the overall maximum. In case of this sample set, adopting an advanced peak selection method would improve the distance error drastically. From Table 3, similar results can be deduced. The difference between the mean and P50 error can be attributed to the high outlier errors. How early these outliers occur is described by the P90 value. The last metric in this table is the mean value of the STARR. Here, the second highest correlation peak is divided by the highest which gives an index in how distinct the correlation peak is. \[mean\;STMR=\sum_{i=0}^{n}\frac{1}{n}\frac{max_{2}(f(t)\star g(t))}{max(f(t) \star g(t))} \tag{8}\]  
With \(f(t)\) as the received backscatter signal, \(g(t)\) is the transmitted chirp signal and \(max_{2}\) is the second highest value of the cross-correlation between these two. Values closer to 1 indicate that these peaks have similar heights and can often be caused by noise-induced backscatter signals. For ranging calculations with a high STARR, refined peak selection methods could have a great impact on the results.