## 4 Evaluation
### Simulation Setup  
In order to evaluate the efficiency of the DMMS, we have employed a real-world topology to provide a rigorous assessment. Specifically, we have chosen to adopt a Wireless Mesh Network (WMN) installation scenario located within the city of Barcelona [42], as visually depicted in Figure 5. Within this context, our scenario was limited to 25 Access points as shown in Figure 6a within a \(5\times 5\) grid topology where each distinct grid cell dimension measures 100 \(\times\) 100 m with the Acess point, as shown in Figure 6b. All Access points operate in the 2.4 GHz radio frequency range and use the IEEE 802.11n access network. Notably, each grid node acts as both an Access point and router to enhance the mesh network's operational capabilities. In terms of wireless propagation, the channel models used combine the constant speed propagation delay model and the log-distance path loss model.  
In our scenario, we have on MP and one stationary consumer, with producer equipped with a streaming video application. Consumer continuously sends requests for data to an MP for 100 s with a frequency of five Inputs per second using a Constant Bit Rate (CBR) consumer application. Based on the clustering algorithm, Nodes 6, 8, 16, and 18 are designated as Anchors for the DMMS and rendezvous servers for multi-RV KITE. We set a 100 ms delay for updating the producer's coordinates (attachment information) on all Anchors in the DMMS and RVs in multi-RV KITE. The MP moves freely within the grid topology according to the GM mobility model, where it changes its velocity and direction  
Figure 5: WMN topology of the city of Barcelona, Spain with Wi-Fi Access points (cyan dots).  
in each epoch based on previous movements to emulate the flight pattern of a real-world UAV. We conducted 100 runs for each MP speed, with the MP's movement speed ranging from 1 m per second to 30 m per second. We implemented the KF algorithm using C++ for the producer's coordinate location prediction. The next location coordinate is predicted every \(\Delta\)T = 500 ms using the same parameters as described in the previous section. Figure 7 shows the true trajectory of the MP at a speed of 30 m/s in blue and the estimated trajectory using the Kalman filter in red. The rectangle and triangle represent the start and end positions of the producer, respectively.  
Figure 6: (**a**) An extract of Barcelona WMN topology; (**b**) the corresponding 5 \(\times\) 5 topology used with rendezvous Anchor in red.  
Figure 7: Comparison of the actual trajectory of the producer with the estimated trajectory using the Kalman filter.  
To assess the performance of the location prediction model, we use the Root Mean Square Error (RMSE), a widely used metric for measuring the average magnitude of errors between predicted positions and actual positions. RMSE values are non-negative, with smaller values indicating better prediction accuracy.  
The formula for calculating RMSE is typically:  
\[\text{RMSE}=\sqrt{\frac{1}{N}\sum_{k=1}^{N}{(\hat{x}_{k}-x_{k})^{2}-(\hat{y}_{k }-y_{k})^{2}}}\]  
where \((\hat{x}_{k},\hat{y}_{k})\) represents the predicted coordinates, \((x_{k},y_{k})\) represents the real coordinates, and \(N\) is the total number of predictions.  
Table 3 presents the average RMSE value of the KF model, averaged over all 100 runs for each producer speed. The KF model demonstrates accurate tracking of the producer's position. However, the RMSE value increases with the producer's speed. This is attributed to the KF's reliance on predicting the future state based on the current state. As the producer's speed rises, predicting its future position becomes more challenging due to rapid changes in location, leading to accumulated prediction errors and higher RMSE. It is noteworthy that the RMSE value of the KF is influenced by the noise in the measurements. Higher levels of measurement noise can result in an elevated RMSE value.