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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Target tracking is an important application of wireless sensor networks. The networks' ability to locate and track an object is directed linked to the nodes' ability to locate themselves. Consequently, localization systems are essential for target tracking applications. In addition, sensor networks are often deployed in remote or hostile environments. Therefore, density control algorithms are used to increase network lifetime while maintaining its sensing capabilities. In this work, we analyze the impact of localization algorithms (RPE and DPE) and density control algorithms (GAF, A3 and OGDC) on target tracking applications. We adapt the density control algorithms to address the

A Wireless Sensor Network (WSN) consists of a set of sensors distributed over an area of interest and capable of collecting information from the environment. Therefore, the correct localization of these events and the sensors themselves is necessary for a proper analysis of the gathered data [

The sensors also have limited service life; they use batteries as the only energy supply and recharging them is often impossible [

These two problems, namely localization and density control, play fundamental roles in target tracking applications, which is an important application of WSNs. For example, the SAUIM project aims at tracking an endangered species of monkeys in the jungle. The continuous and long-term tracking can help us to protect these animals, since it allows a thorough study of their habits. The success of that project depends on the network's ability to operate for as long as possible and on the tracking accuracy.

Although these problems are important, they are usually solved separately. However, deploying a sensor network demands to integrate different solutions for different layers, such as application, routing, medium access, density control, synchronization, and localization. In this integrated approach, Souza

A major contribution of this work is the adaptation of the density control algorithms (GAF, OGDC and A3) for the more general

The remainder of this paper is organized as follows. In Section 2, we present the related work. Section 3 presents the theory behind the localization and density control algorithms. Section 4 discusses modifications on the density control algorithms that we propose. A detailed discussion of our methodology and results is presented in Section 5. Finally, Section 6 brings our lessons learned and recommendations.

The localization problem has been widely discussed in WSN. Niculescu and Nath [

As far as the density control problem goes, Ye

Target tracking is one of the most importation applications of WSN. Schmitt

The original Kalman Filter works well with linear models when the error can be modeled as Gaussian noise [

Taking a broader approach, Gui and Mohaptra [

In this work, to provide an integrated evaluation, we adapt density control algorithms for the more general

In some applications, the nodes of a WSN must estimate their own positions. However, it is not always possible to equip all sensors with a GPS. Therefore, only a fraction of the nodes are equipped with such capability; these nodes are called beacons. Through the combination of the positions from the beacons and localization algorithms, the other nodes (called free nodes) are capable of estimating their positions. This process can be divided into three steps [

The distance estimation can be done through Received Signal Strength Indicator (RSSI) or some variation of Time of Arrival (ToA) [

After estimating the distance to a minimum set of beacons, a free node is capable of calculating its position. Methods like trilateration or multilateration can be used. Trilateration is essentially a geometry problem: estimate the position of the free node based on the coordinates of three references and the distances from these references to the free node. Although it is intuitive, trilateration does not work in practice due to the imprecision on the distance estimations. Multilateration, on the other hand, uses a larger number of reference nodes to create an overdetermined system of equations; this system is solved with optimization methods, such as Least Squares.

The last stage of the localization system is to use a localization algorithm; this work evaluates two of these algorithms: the Recursive Position Estimation (RPE) [

RPE is divided into four stages, as depicted in _{i}, y_{i}_{i}

RPE makes the number of reference nodes grow rapidly; this is its main strength. However, there is a side effect: the localization errors are also propagated quickly [

DPE is a variation of RPE. The main difference is that DPE uses only 4 beacons, arranged in a cross-like structure. The use of such structure guarantees that the recursion has only one origin, as depicted in

For the sake of our argument, let us consider that the distance estimation is perfect, which would allow us to use trilateration. To use trilateration, a node must know its distance to three reference nodes. If a circle is drawn from the node to each beacon (where the radius is the distance between them), the three circles will intersect at the node' location. Now let us consider the case where we use only two reference nodes. In this case we would have two intersection points for the circles, where one is the right position of the node and the other is not. Since we know the direction of the recursion (a DPE feature), the correct intersection is the farther from the recursion origin, as depicted in

Density control consists in turning off as much sensors as possible for as much time as possible while keeping the network's functionality. This work evaluates

The idea behind this algorithm is that minimizing the intersection between the sensing areas of all sensors in the network implies optimal use of energy. This algorithm assumes that each sensor knows its position. In a nutshell, the algorithm is based on the mathematical proof that the minimal coverage disk intersection of three sensors is achieved when they are arranged as an equilateral triangle of sides √3

A topology is periodically created. Any node can start the algorithm (the choice is based on the remaining energy level). The algorithm starts with a node

Zhang and Hou [

GAF consists in creating a virtual grid on the sensing area. Once a free node starts to know its position, it can determine its cell on the virtual grid. Nodes in the same cell are considered equivalent. The cell size is dimensioned such that any nodes in two adjacent cells can communicate. Therefore, the radio range must be greater than or equal to

Nodes can operate in three modes: active, discovery and sleeping. All nodes start in discovery mode, which means that they are looking for equivalent nodes. Once the equivalent nodes have been identified, they follow an application-dependent protocol to decide which nodes will sleep and which node will stay active. After some time, sleeping nodes return to the discovery mode and the active node gives the opportunity to another node.

Xu

A3 uses an approximated solution of the Minimal Connected Dominating Set (CDS) problem, which is NP-Hard. This algorithm does not require the nodes to know their positions; it uses only the RSSI-based distance estimations to create a sub-optimal CDS tree. Any node can start A3 through a Hello Message; that makes the neighbors see it as a parent node through a Parent Recognition Message. Then, the parent node creates a list of its children and sorts the list by distance in descending order. This list is transmitted to the children; each child waits for a time proportional to its position on the list. If a child receives a Sleeping Message from another node in the list, it enters stand-by mode. In other words, if a node

Wightman and Labrador [^{2}). In low densities (e.g., <0.05 sensors/m^{2}), it needs around 41% of active nodes. In addition, the number of messages sent is shown to increase linearly with network density.

Among the density control algorithms that we evaluated, only OGDC aims to keep the sensing coverage of the network; both GAF and A3 attempt to build a topology that ensures communication coverage. Given that we are interested in target tracking applications, we suggest a few modifications on GAF and A3 such that they build a network capable of sensing the entire area of interest. For both algorithms the adjustments are merely computational and do not result in higher costs.

If we use a cell size of

In the original algorithm [_{s}_{s}

It is necessary to modify the density control algorithms such that it is possible to specify the minimum number of sensors that must cover all points of the area of interest (

The modifications that needed to have _{s}

For

To tune GAF to accept

Rewriting the equation in function of _{s}

In the original algorithm, the time a node sleeps after receiving a child recognition message is proportional to its position on the list, which is sorted in descending order by distance. Our first modification discussed in Section 4 changes this criteria to the distance to the sensing perimeter. To make

In OGDC, the sleeping time is proportional to the distance between the sensor's position and the ideal position. The mechanism we use for adding the residual is adding a period of time proportional to the residual to the time the sensor waits. Consequently, sensors with lower residual behave like in the original version of the algorithm. However, a sensor with high residual (

The time a sensor must sleep now depends on the inverse of the residual. Thus, a sensor with a smaller residual value sleeps for less time and has a higher probability to participate in the network. In addition, the tie-breaker criteria for sensors in the same cell becomes the residual (instead of the node ID in the original version). Again, these modifications have no impact on the communication and processing costs of the algorithm.

The A3 Algorithm assembles a topology where the enabled nodes are the ones farther away from the parents. The modification presented in Section 4 suggests that the distance from the children to the parents' sensing perimeters can be used as the sorting criterion. To use the residual error in this process, we suggest a radical conceptual change (but computationally simple). The idea is to create a topology that minimizes the residual; the sorting criterion is the residual of each node. In other words, each sensor that starts the process essentially selects its

The experiments are performed in the Sinalgo simulator [

Time is discrete in Sinalgo and is based on rounds. We use the approximation that a round is equivalent to 10 ms. The duration of one simulation can go up to 100,000 rounds (or 1000 s). The simulation terminates if that limit is reached or if the 3-coverage remains below 60% for a time larger than a density control round. A density control round is the time it takes for a density control algorithm to execute again. We set this time to be 7500 rounds (or 75 s) in our experiments.

The imprecision on the distance estimation between two sensors

Random walk [

In the results discussion, we consider the following metrics:

Both OGDC and A3 run in rounds that we define as density control rounds (not to be confused with simulation rounds). In the context of density control algorithms, a round is the time interval between two executions of the algorithm. In the end of each round, all nodes return to a state where a new topology can be created. As a consequence, we observe a periodic drop on 3-coverage for OGDC and A3. That does not happen with GAF because each node sends periodic messages to the sensors in the cell to determine if there is a node responsible for that cell. The result is that GAF shows smaller discontinuities, as shown in

Our results show that OGDC is the algorithm that performs best at maintaining 3-coverage, no matter what localization mechanism is used.

To determine which localization algorithm leads to a better 3-coverage with OGDC, we compare their behaviors.

Our results show that the choice of the localization algorithm impacts on the quality of target tracking, which is independent of the density control algorithm, as shown in

The choice for the density control algorithm depends in fact on the network density. In low densities (e.g., 0.05 sensors/m^{2}), OGDC and A3 have similar performance; there is an overlap of the confidence intervals of both mean tracking error and mean tracking time, as shown in ^{2}, OGDC is clearly superior in terms of tracking time while the three algorithms show equivalent results when it comes to tracking error. Finally, as the density gets even higher (e.g., 0.2 sensors/m^{2}), compared to OGDC, GAF gives smaller tracking errors and similar tracking time.

Our results show that A3 is not a scalable solution for target tracking; it only performs well (in comparison to OGDC and GAF) in low density networks. Therefore, we do not recommend its use for target tracking applications. When used with DPE, GAF results in slightly smaller mean tracking error than OGDC and is equivalent to A3. However, it is outperformed by OGDC in terms of mean tracking time. Given that the difference on tracking error between GAF and OGDC is small (about 0.5m) and OGDC keeps the network alive for longer than GAF, we conclude that OGDC is the best choice for target tracking applications among the three algorithms.

The results in

Our version of A3 that considers the residual while creating the network topology performs better than the original version. With RPE, our modification yields greater mean tracking time and smaller mean tracking error. However, that advantage applies only to the tracking time when DPE is the localization algorithm; the modified algorithm produces statistically equivalent results in comparison to the residual-unaware version.

Adapting OGDC to use the residual does not result in significant difference; we observe overlap of the confidence intervals for both tracking error and tracking time, with both localization algorithms. Consequently, we cannot confirm nor deny the hypothesis that incorporating the residual into OGDC results in better tracking performance.

Our results show that increasing the number of sensors capable of sensing the target does not increase tracking precision. In addition, increasing

This work provides an empirical foundation to determine which combination of localization and density control algorithms should be used in a target tracking application. We have made extensive simulation of several combinations of such algorithms and we firmly believe our contribution is an important one.

We started by evaluating the combined impact of localization algorithms (DPE and RPE) and density control algorithms (OGDC, GAF, and A3) on the maintenance of 3-coverage of a network. In such scenario, the network can be used for target tracking applications. We also evaluated how the combinations of those algorithms affect both tracking error and tracking time. Finally, we investigated if tuning the density control algorithms with parameters like

Previous results show that DPE is better than RPE for target tracking applications [

A3 performed well in sparse networks and poorly in dense networks. Since it has a serious scalability issue, A3 is not recommend for target tracking applications. GAF's advantage is that it does not turn off the whole network from time to time, as opposed to OGDC and A3. As a result, while most sensors still have energy and when the network density is high, GAF manages to track the target more often than OGDC. However, as time goes by and the sensors start to run out of battery, OGDC is better at keeping the 3-coverage and consequently manages to track the target for longer time. Therefore, we conclude that among the density control algorithms we evaluated, OGDC is the most suited for target tracking applications.

We also investigated whether modifying the density control algorithms to be residual-aware increases the tracking performance. The impact is negative on GAF, positive on A3 and neutral on OGDC. Since we do not recommend A3 for target tracking applications and incorporating the residual into OGDC and GAF yields no gain in performance, we do not recommend such practice for density control algorithms in target tracking applications.

Finally, we observed how increasing

Current work leads to some interesting future directions. Our results are based exclusively on simulations; it is necessary to validate them with actual sensors. All the scenarios we evaluated had a single target and fixed sensors. It is important to evaluate the tracking performance with mobile sensors and multiple targets. Finally, our analysis considers that 3-coverage is necessary for target tracking. However, there are less precise tracking methods that do not require so. It is interesting to extend our analysis to such methods. We are also working on defining the theoretical performance bounds when such algorithm combinations are integrated.

This work has been partially supported by the following institutions: (1) the Brazilian National Council for Scientific and Technological Development (CNPq) and the Amazon State Research Foundation (FAPEAM), grants 575808/2008-0 (Revelar, CNPq/CT-Amazonia) and 2210.UNI175.3532.03022011 (Projeto Anura, PRONEX CNPq/FAPEAM 023/2009); (2) Instituto de Telecomunicações, Next Generation Networks and Applications Group (NetGNA), Portugal; (3) and by National Funding from the FCT - Fundação para a Ciência e a Tecnologia through the PEst-OE/EEI/LA0008/2011.

Stages of

Stages of the Directed Position Estimation. (

Overview of

Geography-informed Energy Conservation for Ad Hoc Routing.

Overview of

Sensing coverage with the original version of GAF.

Determining GAF cell size with respect to

Methodology.

Localization, Density Control and 3-Coverage. (

Localization and 3-Coverage of OGDC. (

Choosing the Localization Algorithm. (

Choosing the Density Control Algorithm. (

Distribution of Tracking Error Over Time with OGDC.

Impact of

Use of Residual in Density Control.

DPE-OGDC | no | 5.6083 ± 0.2305 | 0.6347 ± 0.0098 |

DPE-OGDC | yes | 5.5105 ± 0.2157 | 0.6491 ± 0.0137 |

RPE-OGDC | no | 6.0508 ± 0.3209 | 0.5630 ± 0.0136 |

RPE-OGDC | yes | 5.6463 ± 0.2207 | 0.5770 ± 0.0252 |

DPE-GAF | no | 5.3350 ± 0.2343 | 0.5535 ± 0.0111 |

DPE-GAF | yes | 5.2835 ± 0.2290 | 0.3538 ± 0.0149 |

RPE-GAF | no | 6.8673 ± 0.4966 | 0.4943 ± 0.0204 |

RPE-GAF | yes | 8.0791 ± 0.4672 | 0.2332 ± 0.0130 |

DPE-A3 | no | 5.5008 ± 0.2736 | 0.4436 ± 0.0067 |

DPE-A3 | yes | 5.4096 ± 0.2507 | 0.4837 ± 0.0144 |

RPE-A3 | no | 8.1320 ± 0.8846 | 0.4078 ± 0.0131 |

RPE-A3 | yes | 6.5698 ± 0.4677 | 0.4580 ± 0.0033 |