## 6 Simulation Results  
A simulation in MATLAB was used to validate the proposed algorithm. In the simulation, the environment was set up with two minimums in the space (only one is the global minimum). \(K_{est}\) and \(K_{sd}\) are tunable parameters and set as \(K_{est}=5,\text{ and }K_{sd}=50\left(\text{m}^{-1}\right)\). The initial available energy bound is set to be \(E_{bound}=12\) (watt-second (ws) or Joule). Figure 22 shows the sequences of nodes being explored in iteration steps by setting different energy thresholds \(E_{T}\). By trials of different simulation runs, it can be concluded that:  
* When the \(E_{T}\) is large (in this scenario, 3 ws < \(E_{T}\leq 12\) ws), the algorithm is conservative, so it has only searched a small area that excludes the global minimum;
* When the \(E_{T}\) is in the mid-range (in this scenario, 0.5 ws < \(E_{T}\leq 3\) ws), the algorithm drives the camera to the global minimum. When the \(E_{T}\) is small (in this scenario, 0 ws \(\leq E_{T}<0.5\) ws), the algorithm is aggressive. Although it has searched a large number of areas that include the global minimum, it does not have enough energy to move the camera back to the best location explored in the previous stages. The two tunable parameters \(K_{est}\) and \(K_{sd}\) are selected randomly in the simulation. These parameters are used in the models to estimate the noise spatial distribution in the environment. As stated in Section 4, the positive parameter \(K_{est}\) indicates that the weight of an explored node in the estimation function is based on its Euclidean distance from the node to be estimated. The larger \(K_{est}\) in Equation (4) implies that Euclidean distance has a smaller influence on the weight. In other words, with increasing \(K_{est}\), the estimation result of an unexplored node is more different than that of an explored node nearby. As a result, the algorithm is more likely to search nodes around the local minimum. Similarly, \(K_{sd}\) is proportional to the magnitude of the standard deviation in the stochastic modified process. A smaller \(K_{sd}\) causes a smaller standard deviation and thus a more deterministic evaluation of an unexplored node, which discourages the algorithm to explore areas that are away from the local minimum. Figure 21: Reduction of nodes from the ideal to the realistic camera operational space. Therefore, by increasing \(K_{est}\) or decreasing \(K_{sd}\), we should expect that the algorithm has a higher tendency to exploit over explore. In this paper, we developed a parameter to present the degree of exploration in a simulation by measuring the average distance between the new explored node to the nearest previously explored node. \[Avg\_Dis_{new}=\frac{\sum_{i=1}^{M}\min_{j\in S_{index-exp}}(\overline{ED} \Big{(}P_{j}^{exp},P_{i}^{new}\Big{)})}{M} \tag{87}\]  
where \(M\) is the total number of iterations in a simulation, and \(P_{i}^{new}\) is the position of the new explored node at the \(i^{th}\) iteration. \(S_{index-exp}\) is the index of explored node set as defined in Equation (6) and \(\overline{ED}\) is the Euclidean distance between two nodes as defined in Equation (7). In a simulation, a large value of the parameter \(Avg\_Dis_{new}\) means new explored nodes in each search iteration are generally far away from previously explored nodes, and the algorithm succeeds in exploring a large area. A sensitivity test was performed by varying \(K_{est}\) and \(K_{sd}\) to show how these two parameters affect the searching process in the same simulation environment. Table 2 presents the sensitivity analysis of \(K_{est}\) by keeping a constant \(K_{sd}\) = 50 (m\({}^{-1}\)), while Table 3 presents the sensitivity analysis of \(K_{sd}\) by keeping a constant \(K_{est}\) = 50 (No unit). All analysis tests are based on the same scenario in Figure 22 with \(E_{bound}\) = 20 (ws) and \(E_{T}\) = 2 (ws). Tables 2 and 3 show that by decreasing \(K_{est}\) or increasing \(K_{sd}\), the algorithm explores more areas, as indicated by the parameter \(Avg\_Dis_{new}\).