## 4 Results and Discussion
### Power Consumption Evaluation of the Three DKF Algorithms: Scenario 1
#### 4.1.2 Results from Laboratory Experiments
The presented results lead us to the conclusion that the simulation results align with the experimental results, validating our combined approach. The battery discharge performance of the three DKF algorithms is comparable, resulting in approximately equivalent node lifetimes for all implementations. The experimental results, depicted in Table 5, align with the simulation results, depicted in Table 4, with the exception of EDKF. Notably, from simulations (Figure 5), EDKF exhibits energy consumption over a one-day period that is eight times less than that of the other algorithms (ICF and SGG-ICF). This discrepancy arises from the fact that CupCarbon models solely the communication energy of the node, excluding the energy consumed by the MCU and sensor. Given that the ICF and SGG-ICF involve a communication frequency at least five times greater than that of the EDKF, their energy profiles appear similar but differ from the EDKF's. Figure 8 illustrates that, despite these differences, the battery discharge for all three algorithms is similar. Upon estimating the node's energy consumption from the State of Charge (SOC) of the battery, we find that there are no significant differences in the battery energy usage for all three DKF implementations over a period of one day. This similarity arises because the primary consumer of the node's battery energy in this case is the MCU rather than the communication unit. As all three DKFs maintain the ESP32 MCU in an active state continuously, their energy \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **Battery Voltage (V)** & \multicolumn{3}{c}{**SOC (\%)**} & \\ \cline{2-7}  & **Time (min)** & **0** & **1440** & **0** & **1440** & **Battery Energy Usage (\%)** \\ \hline \multirow{4}{*}{**DKF Algorithm**} & EDKF & 3.83 & 3.67 & 67.32 & 26.61 & 40.71 \\ \cline{2-7}  & ICF & 3.85 & 3.67 & 71.14 & 26.61 & 44.53 \\ \cline{1-1} \cline{2-7}  & SGG-ICF & 3.82 & 3.66 & 65.26 & 23.92 & 41.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Battery energy consumption from laboratory experiments. Figure 7: State of charge of sensor node’s battery for the selected DKF implementations: (**a**) EDKF, (**b**) ICF, (**c**) SGG-ICF. consumption is expected to be similar. Specifically, the energy consumed by the MCU (ESP32 core) in the active state (36.8 mA) far surpasses that consumed by the transceiver (nRF24L01+) during transmission (11.3 mA). We now turn our attention to the computation of the node's lifespan for all three DKF implementations when powered by a 3.7 V 2000 mAh Li-Po battery. Traditionally, lifespan estimation involves calculating the total energy of the battery divided by the average power of the node computed over an hourly period. Additionally, we have the opportunity to assess lifespan through the direct extrapolation of data from real deployed batteries used to power the nodes. Thus, we will employ two methods for estimating the node's lifespan, as summarized in Table 6.  
Method 1 utilizes the average power derived from power measurements presented in Figure 6 to calculate the node's lifespan. Method 2 leverages battery voltage measurements from Figure 7 and an approximate equation (cf. Equation (5)) to compute the State of Charge (SOC) of the battery at the beginning and end of the one-day experimental period. The energy usage for one day is then derived from the difference in SOC. With this energy consumption data, we calculate the time required to deplete the battery's energy. Results presented in Table 6 reveal that the lifespan of the sensor nodes for all DKF implementations is approximately 2 days using both methods of estimation. The slight disparity in node lifespans using the two estimation methods may be attributed to the use of the approximate polynomial in Equation (5) for estimating the battery's SOC. Another contributing factor could be the variability in the average power of the sensor node over one-hour periods due to asynchronous events, causing fluctuations in power consumption.