## 4 Simulation Results and Discussion  
This section discusses the simulation experiments developed to assess the effectiveness of the proposed architecture. The simulation parameters used in this section are based on previous work [14; 29], studying observation-driven communication in WSNs, which determined that the optimal scheduling strategy parameters which allow estimate performance become comparable with full measurements under a moderate transmission rate. In particular, using the same simulation details, we compare the TET mechanism [14] with the proposed TETSO algorithm. The following section uses the notation and development presented in the recent literature on state estimation problems [29]. The following are considered as an object's position and velocity,  
\[x_{k}=\left[ \begin{array}{cc}0.8&1\\ 0&0.95\end{array} \right]x_{k-1}+w_{k}\,.\]  
The sensor measures the position and velocity based on the observation model stated as follows,  
\[z_{k}=\left[ \begin{array}{cc}0.7&0.6\end{array} \right]x_{k}+v_{k}\,.\]  
In this simulation, the represented outcomes are calculated over a Monte Carlo (MC) simulation of 100 runs with \(N_{SP}=30\) particles. The object's velocity and position in each simulation iteration change randomly to provide a fair experimental benchmark. The parameters used in this simulation are shown in the Table 1.  
This simulation compares the five following filters: (1) Full-rate estimation of the Kalman filter (KF); (2) Open-loop event-based estimation of KF; (3) Full-rate estimation of particle filter (PF); (4) Event-based estimation of particle filter with binary decision; and (5) The results of proposed TETSO architecture. KF, which is suitable for linear systems and Gaussian white noise [30], is an efficient recursive algorithm that estimates unknown variables based on measurements observed over time and is used to estimate unknown variables optimally when they are not directly measurable but indirect measurements are available [15; 31]. PF is a Bayesian-based estimation algorithm based on conditional probability density, developed by [PERSON] et al. [32] for addressing applications that are nonlinear and non-Gaussian. Without making assumptions about the state space model or the state distributions, PF provides a mechanism for producing samples from the \begin{table}
\begin{tabular}{l l} \hline \hline \(N_{SP}=30\) & \\ MC simulation = 100 & Max iteration = 200 \\ \(c_{1}=1.4962\) & \(c_{2}=1.4962\) \\ \(V_{1}=0\) & \(X_{1}=0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of Parameters Used Throughout the Simulation. appropriate distribution. The values \(c_{1}=c_{2}=1.4962\) have been considered for the TETSO, and the number of particles within the swarm, \(N_{SP}\), is set to be 30. The multi-objective problem consists of three objectives, and the repository of previously discovered solutions is 100 in size. The completion criterion for the particle swarm optimization is the maximum number of iterations, set to be 200. The reported results are calculated over various communication rates. The matrix consisting of a pair of sets of \(\Pi_{L,k}\) and \(\Pi_{W,k}\) is considered, where \(\Pi_{L,k}\) includes a set of \(m=6\) numbers selected randomly at each iteration \(k\) from 0.001 to 10 (i.e., \(0.001\leq\Delta_{j,k}\leq 10\)), and \(\Pi_{W,k}\) is determined by Equation (7) where \(K_{k}\) is chosen randomly at each iteration from the range 1.0001 to 2. As mentioned in the previous section, constraints 1 and 2 are satisfied by the \(\Delta_{j,k}\) values for the proposed TETSO. In this experiment, we consider multi-objective optimization, which is concerned with optimization problems that involve more than one objective function to be optimized simultaneously; thus, no single optimal solution may exist. Therefore, the algorithm provides a set of Pareto optimal solutions. In multi-objective optimization problems, all the components of the Pareto optimal solution set are believed to be satisfactory designs.