## 7 Results and Discussion
### Antenna Beam Path Optimization  
Having obtained all the data from our antennas and completed one full antenna cycle from beam 1 to 52, we can begin optimizations to smooth out the results that we obtain and allow for even higher levels of optimization. Instead of applying the weights on our RFID tags, we can instead use our antennas and their corresponding RSSI values to determine the rough location and improve the result from our reference tags. To do this, we sacrifice finer accuracy (usually around 10 cm) and instead compensate with range (more than 2 m from the reader). This distance creates a buffer for smaller margins of error and allows the use of fewer RFID cards to obtain the course location of the target tag via the 1-Nearest Neighbor approach; we can then optimize the results and map them out using the antenna clusters and sectors instead. Starting with our clusters, in order to determine the sector of highest correlation with our reference tags, we create nested Euclidian vectors. The first is the vector matrix of each cluster \(C\) and each sector having the same Euclidian vector matrix. \[C= \begin{bmatrix}C_{1}\\ C_{2}\\ \vdots\\ \vdots\\ C_{8}\end{bmatrix} S= \begin{bmatrix}S_{1}\\ S_{2}\\ \vdots\\ \vdots\\ S_{6}\end{bmatrix}  \tag{12}\]  
Thus, in order to determine the location of the target tag, we first choose the highest correlation of the Euclidian value cluster. This will give the closest distance from the core. We perform a similar operation with the sectors and whichever pair of sector and cluster yield the highest values, which become the target RFID tag location point. Then, we cross-reference with our standard LANDMARC approach in order to validate the results, and if the selected antenna beam is in the neighborhood of our target tag, then we designate the localization event. As the graph below shows, the narrowing optimization is based on sectors and clusters. The main aim of single antenna use for RFID localization is to improve the following features that preexisting models are unable to provide: \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Reference Tags** & **Positioning Accuracy** \\ \hline
4 & 99.1 \\ \hline
9 & 93.4 \\ \hline
16 & 89.7 \\ \hline
25 & 78.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The accuracy of tags in 1-Nearest Neighbor approach. 1. Widen the range of effective scanned area;
2. Maintain low RFID reader overhead;
3. Use a single fixed antenna. Our system stands out by using a single antenna and also relying on successive antenna beam shifting in order to predict the final results. Regarding its limitations, firstly, there are some blind spots from the antenna diagram as we can clearly see in the core that some areas are not covered by the antenna. Moreover, because only one beam can be active at one time, this means that we cannot obtain simultaneous real-time values as compared to conventional models that use multiple antennas in their setup. Thus, when predicting the model, a good amount of accuracy is traded off, especially working with the sector. Due to their irregular calculation scheme, they can only be fully utilized once a complete cycle (beam 1 through 52) of changing antenna beams has been completed. This means that other systems operate faster than ours because, on average, one complete antenna beam cycle will cost, on average, 0.4 s; hence, overall, we can obtain all results after more than 40 s. The core and sectors are used for LANDMARC location prediction whenever their beams are finished and data are collected. Then, the overall location is checked twice with the results. Therefore, the location refresh rate is refreshed much faster depending on the user configuration. Below, we present a list of the refresh times depending on how many sectors and clusters are being used altogether. Distance was increased or decreased to analyze the change in the relative positioning accuracy [3].