## 6 Performance Evaluation Strategy
### Tracking Error Estimation  
In order to evaluate the proposed algorithm and to assess its tracking accuracy, we devised a set of intruder mobility patterns (straight, random and curve), which are illustrated in Figure 2. We can observe in Figure 2, besides the intruder's path (represented as a slim dotted trajectory), some circles that highlight those sensors nodes that are activated at some instant of time, generating the appropriate reports for the sink. Crosses represent the sequence of estimations about the intruder's path made by the sink. Differences between real and estimated intruder trajectories are slightly more noticeable in Figure 2(b).  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Default Value** \\ \hline Number of Nodes & 200 \\ PHY/MAC & IEEE 802.15.4 / 2.4 GHz band \\ Traffic Type & CBR \\ Simulation Time & 500 seconds \\ Simulation Area & 200 \(\times\) 100 m\({}^{2}\) \\ Sensor Topology & Grid \\ Routing Protocol & MRLG \\ Transmission Range & 10 meters \\ Packet Size & 50 bytes \\ Traffic Load & 0.2 pkt/s \\ Intruder Speed & 4 m/s \\ Sink Speed & 4 m/s \\ \hline \end{tabular}
\end{table}
Table 1: Reference simulation parameters.  
To obtain an accurate measure of the overall error in determining the intruder's trajectory, the following actions are taken:  
1. Retrieve the exact intruder location at all times, based on the mobility pattern defined as input to the simulation.
2. Based on the intruder reports received at the sink, filter all signals, keeping only those that correspond to the sensors that have detected an intruder. The available data are: the number of sensors that detected the intruder, the location of each sensor, and the intruder report time advertised by each sensor.  
Figure 2: Illustration of the intruder tracking accuracy for different mobility patterns: (**a**) straight, (**b**) random and (**c**) curve.  
3. For each report received, obtain a new estimate for the intruder's location by relying on Algorithm (1), which creates information groups by combining the reports received at time intervals of fixed duration.
4. Calculate the mean value of the Euclidean distance between the sequence of known intruder coordinates and the intruder trajectory estimation during the entire test period.  
In our evaluations, the values adopted for the different tracking algorithm parameters were: \(interval=5\) s, \(max\_alfa=0.25\), and \(\beta=0.4\). Notice that, as shown in Figure 2, the filters and estimation techniques used in our proposed algorithm are able to achieve a noticeable performance in terms of trajectory estimation, even though simple binary sensors are used.  
Concerning the calculated error, notice that three different factors are combined: (i) the intruder location inaccuracy associated with the binary reporting provided by the sensors, which will typically be equal to 10 meters for the first report generated, since this is the sensor's detection range; (ii) the mean estimation error introduced by the chosen data aggregation algorithm, based on the information received; and (iii) the delay experienced by the different reports, when traveling throughout the WSN, until the sink is reached.