Chapter 5 Evaluations
5.2 Evaluation of the DAG Measurement
5.2.2 Simulation Parameters
The values of log-normal shadowing model parameters are chosen from the ranges of their typical values in indoor environments [23]. Pr(d0) is obtained by the experiment in an indoor environment. The parameters and corresponding values used in this simulation are summarized in Table 5.1. They do not exactly reflect the details of a real environment, but are representative of the range of environments in which the algorithms may be applied.
Fig. 5.1. Solid circles mark the training data points.
Table 5.1. Parameters and their values used in the simulations of incremental beacon placement.
used to evaluate and compare the performances of various measurements used to design beacon deployment. However, according to the fact that the locations of training data are known, for the simulations with pattern matching localization, only the data points which are not in the training data set are chosen to examine the mean localization error.
Therefore, following equation is used to examine the mean localization error in the respectively. In each of simulation rounds, initially 20 beacons are randomly placed in the terrain. After examining the localization errors on the terrain, the location without a beacon that has highest measurement value is chosen to place an additional beacon.
Then the mean localization error is re-examined. Fig. 6 shows the flow chart to illustrate the flow of incremental beacon placement. There is a random factor in the initial state (i.e., random beacon placement). To characterize the statistical significance of our simulation results, each simulation executes for 10 times with different random initial beacon placements.
5.2.5 Simulation Results
Fig. 5.3 shows the final placements of Max, Grid, DAG, and Greedy. According to the centralized-distributed improvement on localization, the Grid measurement overly expects the ability of a beacon node to reduce the localization error in neighboring region. Therefore, many beacon nodes will be designed to place at locations with no any benefits on localization. This overestimation flaw of Grid causes a locally dense placement behavior that extremely squanders on beacon resource.
Fig. 5.2. Flow chart of incremental beacon placement.
Fig. 5.4 and Fig. 5.5 show the simulation results of incrementally placing beacons on connectivity based localization and pattern matching localization respectively. The averages and 95% confidence intervals are plotted in the figures.
Fig. 5.3. The final beacon placement of Max, Grid, Greedy, and DAG in a 2-dimentional space.
Fig. 5.4. Performance of the measurements to incrementally place beacon nodes with connectivity based localization.
As shown in Fig. 5.4, Grid provides better performances than Max at early placement stage. That confirms the idea of considering regional localization error. However, because of the locally dense placement behavior, Grid quickly starts to converge and provides the saturated localization performance much worse than Max. Although Greedy and GWG have similar trends on reducing localization error, DAG performs about two times better than Greedy at saturated state. DAG surpasses other three methods at early placement stage and provides the saturated performance same as Max (around mean error of 4 meters) with less additional beacon number to save 30%
beacons. Moreover, for the device shortage scenario, it reduces 76% localization error compared to Max when only half of the beacons at saturated state (around 150 beacons) are placed. This phenomenon also exists in the pattern matching localization as shown in Fig. 5.5. DAG can reduce 25% usage of beacons and reduce 61% localization error with half of the placed beacons at saturated state.
5.3 Evaluation of the ABDS algorithm
To evaluate the performance of ABDS, STROBE, E-STROBE, and Gribben’s method are also implemented in the simulated wireless sensor network to be compared with ABDS. The simulated network is composed of 100 beacon nodes uniformly deployed in a square area of size 100 m × 100 m in a grid manner. Beacon duty scheduling algorithms are performed on each beacon node. The environmental condition (noise distribution) is same across simulations of various beacon duty scheduling algorithms. Simulation methodologies are described in following sections.
5.3.1 Energy Model
In addition to the signal propagation model in Section 5.1 and corresponding values in 5.2.2, an energy model is introduced to simulate the energy usage of beacon duty scheduling algorithms. We use the same energy model in [16], as summarized in Table 5.2. This energy model only characterizes the energy usage of the radio transceiver and does not model the energy usage of local computation, because typical computational costs are much lower than communication costs and thus negligible [15], [16], [17], [24].
Table 5.2. Parameter settings of the energy model in the simulations of beacon duty scheduling algorithms.
specifically designed for range-based localization methods. The input for localizing a blind node is the estimated distance from beacon nodes, which is derived from Eq. (5.1) and given by
Accordingly, the scheduling algorithm cannot be applied on proximity-based localization. It was evaluated on MLE [22], which is
implemented on MLE in another simulation for the comparison with Gribben’s method.5.3.3 Parameter Setting of Algorithms
Due to the fact that all beacon nodes are active to exchange information for making decision at decision stage and only a fraction of beacon nodes are active at execution stage, system lifetime is sensitive to the ratio of time of execution to time of decision.
Higher ratio can result in longer system lifetime. However, a long time of execution stage can bring the system low response to variations. Accordingly, these scheduling algorithms need to set a same time of execution stage for fair comparison. Table 5.3, Table 5.4, and Table 5.5 summarize the parameters in ABDS, STROBE, E-STROBE, and Gribben’s method, and corresponding values set in the simulations.
Table 5.3. Parameters of ABDS and corresponding values.
Table 5.4. Parameters of STROBE and E-STROBE, and corresponding values.
Table 5.5. Parameters of Gribben’s method and corresponding values.
5.3.4 Performance Metrics
During the simulations, as in [16], following metrics are measured periodically for a snapshot interval 100 seconds.
Mean localization error: The mean localization error is computed by Eq. (3.1) according to currently active beacon nodes at the instant.
Percentage of active beacon nodes: This is the percentage of total beacon nodes
that are actively sending beacon signal at any given instant of time (either in decision stage or execution stage).
Other two metrics not a function of time are used.
System lifetime: A beacon duty scheduling system is dead if the moving average of
mean localization error exceeds an error threshold. The system lifetime is the time elapsed since the start before the system has died.
Mean active ratio: This is the mean active beacon ratio in the duration of system
lifetime.
In addition, we take the snapshot of active beacon node distribution to understand the outcome of beacon duty distribution produced by various scheduling algorithms.
5.3.5 Simulation Results
ABDS, STROBE, and E-STROBE on connectivity based localization
ABDS, STROBE, and E-STROBE are simulated on connectivity based localization. The error threshold for ABDS is set to be 12 m. The density threshold for STROBE and E-STROBE is set to be 4 (4 active beacon nodes in a coverage) to control the mean error to be under 12 m. Snapshots of the distribution of active beacon nodes in ABDS, STROBE, and E-STROBE are shown in Fig. 5.6. Because STROBE and
E-STROBE only consider the local density of neighboring active beacon nodes, the nodes that should take active beaconing duty are randomly selected out from candidates.
As a result, some beacon nodes at the location with minimum benefits on localization (such as very close to other active beacon nodes) are designed to be active. This phenomenon results in the holes of active beacon distribution and waste of power resource as described in Section 5.2.
Fig. 5.6. Snapshots of active beacon map of ABDS, STROBE, and E-STROBE on
beacon nodes with less node resource. Fig. 5.7 plots the mean localization error of these three algorithms and Fig. 5.8 plots the active beacon ratio. Table 5.6 summarizes the corresponding system lifetime and mean active ratio. As shown in Table 5.6, ABDS reduces 10 % beacon usage (mean active ratio) and prolongs 54% lifetime compared to STROBE. E-STROBE considers an energy threshold independently after checking the density threshold in its scheduling strategy. A beacon node may be turned off even it should be active to maintain the density threshold. As shown in Fig. 5.7 and Fig. 5.8, this method incrementally decreases the active ratio and increases the mean error with the consumption of energy. Therefore, it quickly makes the system dead.
Table 5.6. Performance comparison of ABDS, STROBE, and E-STROBE.
Fig. 5.7. Mean localization error of ABDS, STROBE, and E-STROBE on connectivity-based localization.
ABDS and Gribben’s method on MLE localization
Because Gribben’s method is specifically designed for range-based localization approaches, ABDS and Gribben’s method[15] are compared in the simulations on MLE localization. The error threshold is set to be 22 m. Snapshots of the distribution of active beacon nodes in ABDS and Gribben’s method are shown in Fig. 5.9. The location impact of beacon nodes is also considered in Gribben’s method, so it does not activate beacon nodes very closely.
Fig. 5.8. Active beacon ratio of ABDS, STROBE, and E-STROBE on connectivity-based localization.
However, this method does not consider real noise distribution in its model. As a result, it cannot adapt the real environment very well. As shown in Fig. 5.10 and Fig. 5.11, Gribben’s method activates too many beacon nodes and thus shortens the system lifetime. Table 5.7 summarizes the system lifetime and mean active ration of ABDS and Gribben’s method. ABDS provides 38% longer lifetime and 12% fewer beacon usage.
Fig. 5.9. Snapshots of active beacon map of ABDS and Gribben’s method on MLE localization.
Fig. 5.11. Active beacon ratio of ABDS and Gribben’s method on MLE localization.
Table 5.7. Performance comparison of ABDS and Gribben’s method.
Chapter 6 Conclusions
In this thesis, in order to efficiently schedule beacon duty cycle, we designed a measurement to the effectiveness of beacon locations. We face the improvement distribution on localization performance in the coverage of an additional beacon. We propose DAG to adapt the non-uniform improvement distribution to avoid the overestimation and locally dense placement occurred in the method of Grid. Our approach adopts Cauchy distribution to generate a centralized weight distribution. The weights are applied to cumulate regional localization error. The purpose is to more precisely measure the effectiveness of beacon locations and thus design better beacon deployments (with fewer beacon nodes deployed). To evaluate DAG, we compare it with the classical Max, Grid, and Greedy methods in the experiments of incremental beacon placement. The experiments were carried out in a simulated indoor environment built by the log-normal shadowing model. The results demonstrate that the placement of additional beacons with the employment of DAG can reduce 30% beacon usage. When only half of these beacons at saturated state were placed, DAG reduces 76% localization error.
ABDS for scheduling beacon duty cycle is then designed by the usage of DAG.
ABDS attempts to achieve following design goals.
• Maximize system lifetime
• Distributed algorithm
effectiveness to reduce localization error. This impact of beacon location is not considered in previous scheduling algorithms. In ABDS, neighboring beacon nodes exchange information to compute the DAG measurement and find out the efficient beacons. As a result, the requirement of localization error can be satisfied by fewer active beacon nodes and the system lifetime can be prolonged. Compared to previous method, ABDS can reduce 10% beacon usage and provide 54% longer lifetime.
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