Improving node positions in the presence of location errors in geographic routing protocol

Abstract

In Wireless Sensor Networks (WSNs), a node location is usually estimated using GPS or network localization algorithms, but this estimation incurs some errors. In this work, we propose techniques to improve node locations and reduce the location errors. Location errors have an impact on location-based routing algorithms. Packets could be delayed in reaching the destination, or dropped due to exceeding the hop count. Altogether, this drains the energy resource of WSNs. Our techniques to reduce the location errors are as follows: First, a node identifies a subset of its neighboring nodes that have estimated Euclidian distances greater than the given communication range as OutLier (OL) nodes. A node can communicate with OL nodes because their unknown actual locations are within the communication range, but their estimated locations are not. We use, then, mathematical formulas to correct the OL locations to be within the communication range and thus close to their actual locations. This OL method works for a binary sensor model in which the radio signal strength cannot be measured, and the system works on the binary values Received or Not Received. If the sensor model can measure the radio signal strength, then in addition to the OL method, we can use a Received Signal Strength Indicator (RSSI) to calibrate the distance and to reposition the OL nodes. We call this approach OutLiers with Calibration (OLC). Finally, we incorporate our derived mathematical equations into our simulation. The simulation results show that OL and OLC reduce the miss probability of an actual next node, which means better location of the next node.

Keywords

Sensor networks location errors geographic routing

1. Introduction

Recent advances in Micro Electro Mechanical Systems (MEMS) technology [3] allow the design of smaller and lower cost computing sensor devices. A sensor device can perform local calculations and communicate with other sensors through a radio channel forming wireless sensor networks (WSNs). WSNs need to receive information from the physical world and fuse it together to achieve application goals. WSNs have many applications such as detection of a wildfire and an intruder, monitoring of a battlefield and animals, and so forth. A limited energy capacity is the main challenge of WSNs, and extending the lifetime of such a network is important. Typically, sensor networks encompass many nodes operated in a sensor-controlled environment. Each sensor node comprises wireless communication and sensor devices. Power, memory, and computational capabilities are usually severely constrained in each sensor node. Sensor networks often consist of a huge number of nodes. As these nodes are susceptible to failure, network topology may change with time. Sensor networks may consist of either identical or heterogeneous nodes. Within the heterogeneous structure, some nodes are more powerful than others at different resources [13].

Geographic (location) routing is a forwarding protocol that relies on geographic position information. It is on-demand routing and uses the Greedy Forwarding (GF) technique, where a sensor node forwards its holding packet to a neighbor in closest distance to a destination node. The location of a destination node is often known in advance, and most likely this node is the base station in WSNs. Neighboring nodes are nodes that are in communication range with a sender. The sender broadcasts messages regularly to get an updated list of its neighbors. In GF, both the control messages for topology maintenance and for the addressing scheme for sensor nodes are eliminated. This type of a protocol is very convenient for high node density WSNs where minimum information is exchanged with only immediate neighboring nodes [5,14].

The determination of a sensor location incurs a margin of error that can severely impact the function of a routing protocol that depends on it. The location of a node can be determined by a GPS receiver [15] attached to each node, or network localization algorithms such as triangulation methods [2]. Estimating the position of a node using these methods always incurs some errors. Throughout this paper, we call the estimated position a measured position. The real position of a node, however, is computed as if GPS or a localization algorithm is 100% accurate. The location error is defined as the distance between the real and measured position of a node. The worst scenario in routing in the presence of location errors is destination unreachable, where WSNs drop the forwarding packet due to crossing large numbers of hops, which exhausts the energy resources. Therefore, there is a need to find the next node nearest to the destination and thus save the energy of WSNs.

Accurately determining the positions of sensor nodes plays a key factor in sensor applications. Finding precisely the location of the detected object is based on the accuracy of sensor positions. There are different ways for a sensor network to estimate the location of a target object. One simple approach is to average the position of the nodes sensing the target [10]. [8] suggests a weighting scheme for sensor positioning that exploits the fact that if the sensor lies near the path of the object, the detection period will be longer. Another more sophisticated approach uses cooperative signal processing and Bayes’ Law [7]. In particular, Bayes’ law is used to quantify the probability of the target position, based on its recent history.

In this paper, we improve the estimated positions of nodes in order to select a better next node closest to the destination. Our solution is based on the observation that in the presence of location errors, the distance between a sender and a receiver (neighboring node) could be larger than the transmission range of the sender. Therefore, the sender concludes that the receiver must be at a closer distance to it, and then estimates a new position for the neighboring node. The other solution uses Receiver Signal Strength Indicator (RSSI) to correct the measured positions of next nodes. Our approaches perform better in terms of the miss probability of an actual next node closest to the destination.

The paper is organized as follows: Section 2 reviews some techniques to cope with location errors in geographic routing protocols. Two different approaches are proposed to cope with location errors in Section 3. The performance evaluation of our proposals is given in Section 4. Finally, Section 5 concludes the paper.

2. Related work

Most of the research on WSNs that study variations of GF in their simulations or numerical experiments assume a perfect positioning of sensor nodes in a field. There are few works that address geographic routing in the presence of location errors [6,11] and that propose solutions to reduce them as possible.

Location errors of sensor nodes are commonly inherited from the equipped GPS devices or the implemented techniques in sensor nodes. Table 1 shows a comparison of embedded GPS devices that can be used in sensor networks [12]. The claimed position accuracy of these devices in clear weather ranges from 2.5 m to 5 m in radius. The average cost of these GPS devices is 70 dollars, which makes them an expensive choice for a large deployed sensor network. Therefore, a few sets of nodes in the sensor networks can be equipped with GPS devices to act as anchors for other non GPS sensor nodes and to determine their positions. The positions can be determined using localization algorithms such as triangulation methods [2]. Given the location errors in anchor nodes that determine non GPS nodes, the location errors in non GPS nodes will accumulate and become larger.

The estimation of a sensor node location using anchor nodes has been studied in the field of localization in WSNs. Several approaches have been proposed to solve this problem. All studies show a margin of error in the position estimation of a sensor node even though a perfect anchor position is assumed. [16] is an example of these studies. Figure 1 shows that as the number of anchor nodes increase, a better estimation of other node positions is achieved. However, this study assumes the perfect position of an anchor node. In practice, GPS is mostly used to determine the coordinates of an anchor node, as discussed before, which incurs an inherited error. This error will increasingly affect the position estimation of non anchor nodes.

It is worth mentioning that additional hardware like a GPS receiver is not the only way to know the coordinates of a sensor node. In additional to global coordinates, relative coordinates could be hard coded into a sensor node’s memory without extra hardware. This approach is useful for small WSNs, but not in large-scale ones since it becomes unfeasible and expensive.

Table 1
Embedded GPS modules/receivers

GPS Module Chipset Antenna Accuracy

Copernicus Trimble Trim Core ceramic patch 5 m

SUP500F Venus634 small ceramic patch 2.5 m

MN5010(uMini) SiRF Star III chip 3 m

LS23060 MediaTek MT3318 ceramic patch 3 m

DS2523T U-Blox 5 helical 2.5 m

EM-406A SiRF Star III ceramic patch z 2.5 m

GPS Module	Chipset	Antenna	Accuracy
Copernicus	Trimble Trim Core	ceramic patch	5 m
SUP500F	Venus634	small ceramic patch	2.5 m
MN5010(uMini)	SiRF Star III	chip	3 m
LS23060	MediaTek MT3318	ceramic patch	3 m
DS2523T	U-Blox 5	helical	2.5 m
EM-406A	SiRF Star III	ceramic patch z	2.5 m

Fig. 1.

Estimation error normalized with R using randomly heard anchors.

The most related works are [6] and [11], in [6] the authors propose the maximum expectation within transmission range (MER) that makes routing decision based on the error probability. It uses an objective function called revenue, where a next node that has a maximum expectation and within a transmission range (R) is selected. The objective function is computed as a product of measured progress to the next node and the probability that the real position of the next node is located within a certain distance from the difference between the measured locations (itself and the sender node). This probability is generated as a Rayleigh distribution.

[11], however, proposes the conditioned mean square error ratio (CMSER) algorithm. CMSER exploits the notion of maximum progress to destination, but gives more importance to the probability of success when node positions are affected by location error. The authors model the location error of a node as Gaussian white noise with zero mean and variance $σ^{2}$ , and used a Rician distribution to calculate the expected distance between neighboring nodes and the closest point to the destination inside the radius range of a sending node. The expected values are then used to calculate the mean square error (MSE) which is used in calculating CMSER. They showed the benefits of selecting a forwarding node with a minimum expected distance to be a good candidate.

Our approaches are different than others in that we employ the knowledge of R to identify OL nodes and then use mathematical equations to reduce the location errors. MER and CMSER approaches use R and probability theory to reduce the location error. Our approach turns out be to better in accuracy and beats MER and CMSER as shown in the simulation results.

Other work related to target localization in the indoor environment is [4]. The author proposed a rapid site survey of RSSI in the indoor environment. The offline generated radio map is used later for comparison and matching to locate target position. This study assumes a knowledge of sensor location, but an unknown location of the object being detected. However, our study is about the location errors in the sensor nodes themselves and ways to improve them. Since these sensor nodes are stationary, there is no need to generate a radio map for all possible locations of such a target, as in [4]. On the other hand, we use a signal attenuation model to infer the distance between two stationary sensor nodes and use this information to improve sensor node locations.

[1] extends the positioning service using an agent-based approach to discover and localize different pervasive objects. It uses cheap technologies, such as Bluetooth, Wi-Fi, and RFID, that have embedded positioning support. In our approach, however, we focus on the accuracy of sensor node position, which can be improved by using the information in the exchange messages between neighboring nodes. The accuracy of node location affects the geographic routing protocol if used in WSNs.

3. Improving the geographic routing algorithm in the presence of location errors

In this section, we discuss our proposed methods: 1) geographic routing with position corrections of outlier nodes (OL) and 2) routing with position corrections of outliers and position corrections of inside nodes using a distance calibration (OLC).

Fig. 2.

An example of detecting an outlier and correcting its measured position.

The OL method exploits the fact that if nodes are distributed with location errors, then there is a chance that the measured distance of a neighboring node is greater than R. The sending node then identifies this node as an outlier in the context of the measured distance and corrects the outlier location to a point on the line crossing both the measured locations of the sender and receiver. The point is distanced R from the sender’s measured location. In the end, we hope that the new location of the outlier node is close to its real location.

Figure 2 depicts the OL approach and how to find the point on the line. As can be seen, sender node i with real and measured locations $p_{i}$ and $p_{i}^{'}$ , respectively, can communicate with neighbor node j with real and measured locations $p_{j}$ and $p_{j}^{'}$ , respectively. In this scenario, sender i computes the Euclidean distance $D_{i j}^{'}$ of the measured locations $p_{i}^{'}$ and $p_{j}^{'}$ . If sender i discovers that $D_{i j}^{'}$ is greater than R, then receiving node j qualifies as an outlier with respect to this calculated distance, and sender i finds a better location that is close to its real position. This new location is $p_{j}^{″}$ which is calculated to be distanced R from $p_{i}^{'}$ and on the line between $p_{i}^{'}$ and $p_{j}^{'}$ .

The x-coordinate and y-coordinate of the corrected location $p_{j}^{″}$ are calculated as $\begin{array}{l} (1) & x_{j}^{″} = \{\begin{matrix} \frac{(x_{j}^{'} - x_{i}^{'} C^{2}) \pm C (x_{i}^{'} - x_{j}^{'})}{1 - C^{2}}, & if C \neq 1, \\ \frac{1}{2} (x_{i}^{'} + x_{j}^{'}), & if C = 1, \end{matrix} \\ (2) & y_{j}^{″} = \{\begin{matrix} \frac{(y_{j}^{'} - y_{i}^{'} C^{2}) \pm C (y_{i}^{'} - y_{j}^{'})}{1 - C^{2}}, & if C \neq 1, \\ \frac{1}{2} (y_{i}^{'} + y_{j}^{'}), & if C = 1, \end{matrix} \end{array}$ where C is the fraction of Euclidean distances defined as $\begin{matrix} (3) & C = \frac{D_{i j}^{'} - R}{R} \end{matrix}$

There are two possible values for each $x_{j}^{″}$ and $y_{j}^{″}$ , respectively, but one value from each of them is selected to satisfy the following $\begin{matrix} (4) & D_{i j}^{'} = R + D_{j}^{'} \end{matrix}$ where $D_{j}^{'}$ is the calculated distance between $p_{j}^{″}$ and $p_{j}^{'}$ .

In our second approach, however, we want to reduce the location error of a node by exploiting the radio communication signal. RSSI is a measurement of the power strength of the received radio signal. Generally, the emitted radio signal will be attenuated as moving away from a target source with a path-loss exponent n. The signal strength model used for the distance radio model [9] can be quantified as $\begin{matrix} (5) & {RSSI}_{i} = - 10 n {log}_{10} (D_{i j}^{c}) + A + x_{σ} \end{matrix}$ where ${RSSI}_{i}$ is the received signal strength at node i in decibel milliwatts (dBm), A is the received signal strength in dBm at a reference distance of 1 meter, and n is a coefficient parameter that depend on path-loss. The typical value of n is 2 [9], but it can range depending on other factors. $x_{σ}$ is a Gaussian noise with zero mean, and $D_{i j}^{c}$ is the corrected Euclidean distance from sender i and receiver j.

The OLC algorithm checks first if a neighboring node is an outlier, as described above, and then applies the OL equations. If it is not an outlier, then sender i at real location $p_{i}$ calculates the distance $D_{i j}^{c}$ by measuring the RSSI coming from neighbor j at real location $p_{j}$ . If $D_{i j}^{c}$ is greater than $D_{i j}^{'}$ then sender i calibrates the coordinates of the neighboring nodes to be distanced $D_{i j}^{c}$ from the sender’s measured location $p_{i}^{'}$ and on the line reaching $p_{j}^{'}$ as shown in Fig. 3. If $D_{i j}^{c}$ is less than $D_{i j}^{'}$ , however, then the OL equations are applied again. As in OL, we hope again that the new location is close to the receiver’s real location. The new coordinates are calculated as $\begin{array}{l} (6) & x_{j}^{″} = \{\begin{matrix} x_{i}^{'} + \frac{D_{i j}^{'}}{\sqrt{m^{2} + 1}}, & if x_{j}^{'} - x_{i}^{'} > 0, \\ x_{i}^{'} - \frac{D_{i j}^{'}}{\sqrt{m^{2} + 1}}, & if x_{j}^{'} - x_{i}^{'} < 0, \\ 0, & otherwise, \end{matrix} \\ (7) & y_{j}^{″} = \{\begin{matrix} y_{i}^{'} + \frac{D_{i j}^{'}}{\sqrt{\frac{1}{m^{2}} + 1}}, & if y_{j}^{'} - y_{i}^{'} > 0, \\ y_{i}^{'} - \frac{D_{i j}^{'}}{\sqrt{\frac{1}{m^{2}} + 1}}, & if y_{j}^{'} - y_{i}^{'} < 0, \\ 0, & otherwise, \end{matrix} \end{array}$ where $\begin{matrix} (8) & m = \{\begin{matrix} \frac{y_{j}^{'} - y_{i}^{'}}{x_{j}^{'} - x_{i}^{'}}, & if x_{j}^{'} - x_{i}^{'} \neq 0 or y_{j}^{'} - y_{i}^{'} \neq 0, \\ 0, & if x_{j}^{'} - x_{i}^{'} = 0, \\ \infty, & if y_{j}^{'} - y_{i}^{'} = 0 . \end{matrix} \end{matrix}$

The detail operation of OLC is described in Algorithm 1.

Fig. 3.

An example of the measured position correction of a neighboring node using RSSI calibration.

Algorithm 1:

OLC

4. Simulation evaluation

In order to understand the effects of different network metrics on our proposed algorithms, simulation experiments were executed using C++ programming language to validate the performance of OL and OLC in comparison with MER and CMSER. We assume in our sensor model that all sensor nodes have the same fixed communication range R during the mission time. A sensor node communicates with its neighboring nodes and receives messages, after which OL, OLC, MER or CMSER are run to reduce the location errors of the neighboring nodes. The results show that our methods reduce the miss probability of selecting the actual closest neighbor node to the destination.

4.1. Simulation setup

The simulation setup includes a number of nodes distributed uniformly over an area forming a node density of λ (nodes/m²). This distribution incurs location errors derived from a normal distribution $~ N (0, n_{σ}^{2})$ . The communication range R is computed using RSSI as described above, where RSSI creates a white noise derived from $~ N (0, x_{σ}^{2})$ . The typical mean value of R equals 250 m, which is considered the nominal transmission range of IEEE 802.11. All λ, $n_{σ}$ , and $x_{σ}$ are controlled variables changed for the experiments. The simulation run was carried out 1,000,000 times.

4.2. Simulation results

Four experiments are conducted to evaluate OL and OLC against MER and CMSER in terms of the miss probability of a correct next node. We define the miss probability as the fraction of times a sender forwards a packet to a wrong next node divided by the total forwarding times. The miss probability provides an indication of the goodness of such algorithm. A high miss rate means that a packet will be frequently forwarded to a wrong next node. Therefore, more routing will occur and a large amount of the node’s energy resource will be consumed.

Fig. 4.

The miss probability as a function of the node density λ with $n_{σ} = 30$ m, $R = 250$ m, and $x_{σ} = 0.02$ dBm.

In the first experiment, we evaluate OL, OLC, MER, and CMSER algorithms in terms of the miss probability of a correct next node as a function of different values of a node density λ with $n_{σ} = 30$ m, $R = 250$ m, and $x_{σ} = 0.02$ dBm. Figure 4 shows the results of this experiment. As expected, for all algorithms, as λ increases, the miss probability also increases. This is very obvious since having larger values of λ increases the magnitude of confusion in selecting the correct next node within the existence of location errors, and hence increases the miss rate. It can be seen, however, that OL achieves better than CMSER, but much better than MER in terms of reducing the miss probability. OLC has the lowest miss probability for all given values of λ. It reduces up to 100% and 130% of the miss probability compared with MER and CMSER, respectively.

Fig. 5.

The miss probability as a function of the location error represented by a Gaussian noise $n_{σ}$ with $λ = 0.0005$ nodes/m², $R = 250$ m, and $x_{σ} = 0.02$ dBm.

Fig. 6.

The miss probability as a function of the transmission range R with $λ = 0.0005$ nodes/m², $n_{σ} = 30$ m, and $x_{σ} = 0.02$ dBm.

Figure 5 reports on an experiment where the miss probability changes with respect to a location error represented by a Gaussian noise $n_{σ}$ with $λ = 0.0005$ nodes/m², $R = 250$ m, and $x_{σ} = 0.02$ dBm. The value of $n_{σ}$ varies from 0 m (0%) to 50 m (20%) of the transmission range R. As $n_{σ}$ expands, all approaches become more likely to miss the correct next node. However, OLC outperforms the others in terms of the reduction in the miss probability. OL still achieves less miss probability than CMSER but performs much better than MER. The reduction in the miss probability, here, indicates a good re-estimate of the sensor node location.

The study of a miss probability with respect to the variable transmission range R with $λ = 0.0005$ nodes/m², $n_{σ} = 30$ m, and $x_{σ} = 0.02$ dBm is illustrated in Fig. 6. It is not surprising that as R increases, the number of neighboring nodes of a sender also increases. Therefore, the confusion in choosing the correct next node becomes larger. Again, OL achieves a better reduction in the miss probability than CMSER, but much better than MER. OLC, however, greatly outperforms all others.

In the last experiment, we compute a miss probability in terms of a RSSI noise $x_{σ}$ with $λ = 0.0005$ nodes/m², $n_{σ} = 30$ m, and $R = 250$ m. Figure 7 illustrates that increasing $x_{σ}$ has an impact on OLC, where the miss probability has larger values as $x_{σ}$ expands. This is due to the large error in the calibration process. Nevertheless, the miss probability is slightly reduced in all OL, CMSER, and MER because of the reduction in the number of neighboring nodes of a given sender. This reduction occurs due to asymmetric communications, caused by RSSI noises, between nodes. In the asymmetric communication, a receiving node, for example, can receive a packet from a sender, but the sender could not hear back from the receiver. Therefore, the receiver cannot be a neighbor of the sender, and as consequence, the reduction in the number of neighbors will occur. However, for much larger values of $x_{σ}$ , OL and CMSER start to perform better than OLC.

As discussed previously, $x_{σ}$ has a relationship with the calculated distance. Just to give an insight into the impact of $x_{σ}$ on this distance, if $x_{σ} = 0.15$ dBm with mean equals 250 m, it causes a distance error of approximately $\pm 10$ m. Therefore, as $x_{σ}$ increases, the distance error also becomes larger.

As shown in all experiments, the OLC approach has a greater impact on the reduction of the miss probability for given system parameters. OL, however, shows a lesser improvement in terms of the miss probability. Improving sensor node location makes geographic routing more accurate in delivering a data message to the designated destination node along shorter route. And thus, it reduces the energy consumption of the overall sensor networks.

A good re-estimation of node position using OL and OLC enhances the selection of the actual next in the routing process, and thus reduces the miss probability of selecting this node. OL and OLC require the knowledge of R and RSSI, respectively, to identify OL nodes and re-estimate the position of such nodes. MER and CMSER, however, use error probability to determine the best candidate node to be a relay node. Using this probabilistic model accounts for more miss probability than in OL and OLC, which are based on identifying OL nodes and Euclidean calculations for node repositioning.

Fig. 7.

The miss probability as a function of the RSSI noise $x_{σ}$ with $λ = 0.0005$ nodes/m², $n_{σ} = 30$ m, and $R = 250$ m.

5. Conclusions

In geographic routing in the presence of location errors, selecting a next node based on improved position estimations using an RSSI calibration and an outlier correction, as we proposed, has shown to be better in terms of the reduction in the miss probability for different parameter settings. In the practical deployment of sensor nodes in a field, there is always an error in the position of a sensor node no matter how careful we are to eliminate this error. Most studies show that the location error is a Gaussian noise with zero mean and some variance $σ^{2}$ . Our proposal improves the estimated position and reduces the location error of sensor nodes. Therefore, a better next relay is selected, and the overall energy consumption of WSNs is reduced. Saving energy plays a key role in extending the lifetime of WSNs and making them function for as long as possible.

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