Mobile Anchors

There are some localization schemes making use of mobile anchor nodes. In [13], it uses four anchor nodes which form a square to position sensor nodes.

Ideally, the centroid of the square is the sensor node which we want to localize and we can efficiently compute the coordinate of centroid of the square. In [14], it describes a localization scheme that a sensor node using mobile anchor nodes to localize itself based on Cramer’s rule. Each anchor node equipped with a GPS device broadcasts its current position periodically. It is a simple localization method, but broadcasting scheduling, chord selection, and obstacle tolerance would be important factors to affect the location accuracy.

Chapter 2

Related Work

In this chapter, we first review two existing most related localization methods for mobile wireless sensor networks. Then different localization approaches are compared.

2.1 MCL

The key idea of MCL is to represent the posterior distribution of possible locations using a set of weighted samples. Each step is divided into a prediction phase and filtering phase. In the prediction phase, the sensor node makes a movement and the uncertainty of its position increases. In the filtering phase, new measurements (such as observations of new landmarks) are incorporated to filter and update data. The process repeats and the sensor node continually updates its predicted location [2].

In Figure 1, initially, a sensor node unknown of its location generates five samples in the prediction phase. Then, some anchor nodes observe two samples and filter out three impossible samples. In order to maintain five samples, this sensor node must resample three predictive sensor nodes. Finally, the other anchor nodes observe two samples and filter out three impossible samples. Over and over again, a sensor node can compute its location by these samples.

Figure 1. The process of the MCL algorithm.

2.2 CDL [1]

The CDL algorithm is a centralized localization algorithm that is based on the color theory to perform positioning in mobile WSNs. It builds a location database in the server, which maps a set of RGB values to a geographic position.

And the distance measurements by sensor nodes are based on the DV-Hop [12].

When a sensor node receives anchors’ RGB values, it calculates its own RGB values. The node then sends its RGB values to the server so that the server can find the most possible location by looking up in the location database.

Prediction Filtering

Anchor node Sensor node

Predictive sensor node

Initial state &

prediction

Filtering

2.2.1 The Information Delivery of Anchors [1]

In this section, we introduce some notations that are defined in CDL:

¾ Each sensor i maintains an entry of (R_ik,G_ik,B_ik) and D , where k _ik represents the k^th anchor.

¾ D_avg is the average hop distance, which is based on DV-Hop [12].

¾ h is the hop counts between sensors i and j. _ij

¾ D represents the hop distance from anchor k to node i; _ik D_ik =D_avg×h_ik

¾ Range represents the maximum distance that a color (brightness) can be propagated.

¾ (R_k,G_k,B_k) is the RGB value of anchor k.

¾ (H_ik,S_ik,V_ik) is the HSV value of anchor k received by the i^th sensor.

The RGB values of anchors are assigned randomly from 0 to 1. After a sensor i obtains each anchor’s RGB value and hop count (h ), the RGB value is first _ik converted to the HSV value by equation (1) [15]:

) , ,

(H_k S_k V_k = RGBtoHSV(R_k,G_k,B_k) (1) With h , _ik D can be computed. The updated HSV value corresponding to _ik sensor i of anchor k is calculated by equation (2):

k

ik H

H = , S_ik =S_k, _ik ^ik V_k Range

V =(1− D )× (2)

The RGB value of sensor i corresponding to anchor k is then calculated:

) , ,

(R_ik G_ik B_ik = HSVtoRGB (H_ik,S_ik,V_ik) (3) The RGB value of sensor i is the mean of the RGB values corresponding to all

∑

=

where n is the number of anchors that sensor i received their RGB values.

2.2.2 The Establishment of Location Database [1]

A location database is established when the server obtains the RGB values and location of all anchors. The mechanism is based on the theorem of the mixture of different colors. With the RGB values of all anchors, the RGB values of all locations can be computed by exploiting the ideas of color propagation and the mixture of different colors. In the first place, the distance between each location i and anchor k is obtained:

dik=

( ^x

_i

^{− x}

_k

)

²

^{+ ( y}

_i

^{− y}

_k

⁾

² (5) where (x_i,y_i) is the coordinate of location i, and (x_i,y_i) is the location of anchor k. First of all, we have to calculate the HSV value of each location i corresponding to anchor k:

)

The RGB value of location i corresponding to anchor k can be derived by equation (8):

) , ,

(R_ik G_ik B_ik = HSVtoRGB(H_ik,S_ik,V_ik) (8) Then the RGB value of location i can be calculated by averaging all RGB values of location i corresponding to N anchors.

∑

=

location database by maintaining the coordinate(x_i,y_i) and the RGB value )

, ,

(R_i G_i B_i at each location i. Then the location of a sensor node can be acquired by looking up the location database based on the derived RGB value.

2.2.3 Mobility [1]

When a mobile node arrives at a new location, it sends an anchor information request to neighbor nodes. If the neighbor nodes have the anchors’ RGB values, they transmit packets that include the RGB value of each anchor and the hop count from the anchor to the node. After receiving the packets from neighbors, node i compares and calculates the D to the k_ik ^th anchor and get the smallestD . _ik With the RGB values and D to all anchors, node i can update its RGB values _ik using equation (1), (2), (3), and (4). The new RGB values are then transmitted to the server and the position of node i will be updated by looking up the location database.

2.3 Comparison of Different Localization Approaches

Some existing localization approaches are compared in Table 1. We take the following metrics into account: centralized or distributed, mobility, number of reference nodes, and mobile anchors. The proposed E-CDL, which will be described in Chapter 4, is also included in this table. The metric of centralized or distributed indicates it there is a central server taking responsibility for localization. Mobility indicates nodes in the network system are mobile or not.

Number of reference nodes indicates the number of reference points required in each approach. Mobile anchors indicate that if the landmarks are mobile or not.

Approach

Centralized or distributed

Mobility

Number of reference

nodes (anchors)

Mobile anchors

AhLOS [5] distributed low medium no

APS [7] distributed low medium no

Centroid [9] distributed no high no

HiLoc [10] distributed no low no

LPS [11] distributed low low no

MCL [2] distributed medium high yes

MoAP [14] distributed no low yes

CDL [1] centralized medium low no

E-CDL

(proposed) centralized medium low yes

Table 1 .Comparison of different localization approaches.

Chapter 3

Design Approach

In this chapter, we propose a novel method, called E-CDL, to enhance the location accuracy of the CDL algorithm. Since CDL is based on the DV-hop approach [12], correct estimation of the average hop distance is very critical to location accuracy. Besides, by employing mobile anchor nodes, we can decrease possible isolations of sensor nodes in the multihop environment [12]. We will discuss these enhancements as follows.

3.1 Average Hop Distance Estimation

The first scheme is described below. We propose two simple and quick schemes to enhance the average hop distance estimate. When a sensor node intends to route data to some destination, it would select a nearby node that is close to the destination. According to this characteristic, we analyzed the behavior of sensors and discovered that they would select the next hop located between 0.5r and r (r is the radio range). As shown in Figure 2(a), sensor node S should choose a neighbor node 1 which is located larger than half of the radio range, as the next hop. However, in Figure 2(b), if sensor node S choose a neighbor nodes 1, which is located less than half of the radio range, as its next hop, the following hop (node 2) must be larger than half of the radio range; otherwise it will result in the situation of Figure 2 (c), where node 1 and 2 both are within the radio range.

So it is expected that the candidate of the next hop should be located within the

area. We compute the expected value of the next hop distance as follows:

The advantage of this enhancement is that it is simple and quick for estimating the average hop distance. Unlike the DV-Hop scheme, it must wait until the convergence of the topology to obtain a better average hop distance estimate.

Figure 2. (a) Sensor node S chooses node 1, which is located within the gray area, as the next hop;

(b) Sensor node S chooses node 1, which is located less than half of the radio range, as the next hop; (c) Sensor node S chooses nodes 1 and 2 as its next two hops.

(a) (b)

We now present our second scheme to further enhance the average hop distance estimate. In Figure 3, it is obvious that the shortest path length (S→1→2

→3→4→D) is larger than the Euclidean distance, SD, especially when the node density is low [16]. Apparently if the node density is large enough, the shortest path length will be close to the Euclidean distance. We have verified this observation via simulation. The average hop distance will be adjusted based on the ratio of the Euclidean distance to the shortest path length. We will derive such a ratio via simulation offline.

Figure 3. S→1→2→3→4→D is the shortest path from S to D. The straight line, SD, is apparently shorter than the shortest path.

S D

1 2 3

4

3.2 Mobility

In order to further improve the location accuracy, we let anchor nodes as well as regular sensor nodes mobile in order to reduce possible isolations of sensor nodes in the multihop environment. As shown in Figure 4, sensor node movements can help reduce possible isolations of sensor nodes in the multihop environment. We put anchor nodes in the four corners of the square. And anchor nodes will move a radio range (r) along the square in every time slot. Some sensors may decrease their hop counts to anchor nodes, but other may increase.

By employing mobile anchor nodes, we can reduce possible disconnections and the isolation problem of sensor nodes can be relieved. Therefore, the location accuracy can be improved. Finally, we summarize the E-CDL algorithm in Figure 5.

Figure 4. Sensor node movements can help reduce possible disconnections in the multihop environment.

move in

Sensor node

Start

1. Anchor nodes move a radio range r.

2. Anchor nodes deliver their RGB values and coordinates information to the sensor nodes and server

Location database is constructed by the server using Eq. (5), (6), (7), (8) and (9)

Each node obtains an average hop distance to each anchor node by (7r/9)×R

Sensor nodes update RGB values using Eq. (1), (2), (3) and (4)

Sensor nodes transmit the updated RGB values to the server

The server receives the RGB values from sensor nodes

The server calculates the coordinate of each sensor node by looking up the location database

Compute the ratio (R) of the Euclidean distance to the shortest path length offline.

To the server To sensor nodes

Chapter 4

Simulation Results and Discussions

In this chapter, we evaluate the proposed E-CDL algorithm. Besides, we have also implemented CDL [1] and MCL [2] for comparison.

4.1 Simulation Model

Our simulation model is a mobile WSN where all nodes are put in a 500 m × 500 m area and anchor nodes are placed in four corners. The simulation parameters are defined as follows:

z Sensor maximum speed (v_max): The maximum speed of sensor nodes.

z Sensor minimum speed (v_min): The minimum speed of sensor nodes.

z Anchor density (A ): The average number of anchor nodes in the radio _d range.

z Sensor density (s ): The average number of sensor nodes in the radio range. _d z Radio range (r): The radio transmission range.

z Ratio (R): The ratio of the Euclidean distance to the shortest path length.

z CDL1: An enhanced CDL that sets the average hop distance to 7r/9.

z CDL2: An enhanced CDL that adjusts the average hop distance by R.

z CDL3: An enhanced CDL with mobile anchor nodes.

z E-CDL: CDL with the three enhancements.

We adopted the modified random waypoint model [2], in which nodes randomly choose their speed during each movement instead of choosing a speed for each destination. With this model, the average speed can be maintained at

addition, we assume the radio range is a perfect circle [2] and sensor nodes are uniformly distributed in the area. The simulation parameters are shown in Table 2.

In addition, we compute the location error(ε)by,

(

Xest −Xa

) (

² + Yest −Ya

)

²

ε =

where

(

Xest,Yest

)

is the estimated position and

(

Xa,Ya

)

is the actual position.

Parameter Value

Area size 500×500 m ²

Node speed Randomly choose from [Vmin,Vmax].

Radio range (r) 50 m

Pause time 0

Number of samples maintained

(MCL) 50

Measurement period 50 t_u

Time slot length (time unit) t_u

Anchor speed (E-CDL) r t_u

Table 2. Simulation parameters [2].

4.2 Simulation Results

Based on Figure 2, our first enhancement is to set the average hop distance to 7r/9. In Figure 6, the location error has been reduced from 0.22r (CDL) to 0.15r (CDL1) in average.

0

Our second enhancement is to compute the ratio of the Euclidean distance to the shortest path length (called hop distance adjusting ratio) offline for different source and destination pairs. Based on the sensor density (s_d= 10), we randomly generated different distribution of sensor nodes and compute the ratio(R) which is about 0.9. We used this ratio to adjust the average hop distance. In Figure 7, the location error has been reduced form 0.22r (CDL) to 0.13r (CDL2) in average.

0

The last enhancement is to employ mobile anchor nodes. By allowing four mobile anchor nodes to move around the corners, the location error can be

reduced from 0.22r (CDL) to 0.17r (CDL2) in average.

Finally, compare E-CDL, CDL, and MCL. These three range-free localization approaches are designed for mobile WSNs. Note that E-CDL is a CDL with the three enhancements. Figure 9 shows that location error of E-CDL (0.1r) is better than CDL (0.22r) and MCL (0.44r). Because MCL would exploit past information, its location error improves over time [2], and E-CDL and CDL perform stable over time [1].

0

Figure 9. Location accuracy comparison via simulations. s_d =10,v_max =r

In Figure 10, we can see that sensor density is a significant parameter in

But if the sensor density is low, sensor nodes might not be uniformly distributed in the local area and the average hop distance would be inaccurate. Hence, when the sensor density is below 8, the location accuracy of E-CDL is close to CDL.

0 0.2 0.4 0.6 0.8 1

2 4 6 8 10 12 14 16 18 20

Sensor Density

Location error (r)

MCL CDL E-CDL

Figure 10. Impact of sensor density on location errors via simulations. (v_max =r).

We also evaluated the impact of anchor density on the location error of E-CDL. From simulation results, the location error of E-CDL with four anchor nodes in the corners is about 0.1r. If we place more anchor nodes (A_d =0.5), the location error stays within 0.09r. Therefore, we only placed four anchor nodes in the corners for localization.

Chapter 5

Experiments

5.1 Experimental Setup

We have implemented and evaluated E-CDL on the MICAz Mote Development Kit [3]. The MICAz is a 2.4GHz, Zigbee compliant Mote module used for enabling low-power, wireless sensor networks [3]. The MICAz uses the nesC language [17] on the TinyOS platform. It can be used for residential or building monitoring and security, and hospital health-care systems. We can easily construct a localization system with this kit. We conducted several experiments in a 20 m × 20 m area with seven motes. And, we chose three motes as anchor nodes and four as sensor nodes. Sensor nodes were randomly deployed in the area; however, there are two ways to deploy anchor nodes: (1) anchor nodes deployed randomly and (2) anchor nodes deployed in the corners. We will compare these two schemes in section 5.2.

5.2 Experimental Results

5.2.1 Anchor nodes deployed randomly

In this experiment, we first implemented the CDL algorithm with sensor and anchor nodes randomly deployed. In Figure 11, the location error of CDL is about 4.76 m. To enhance the localization accuracy, we computed the hop distance adjusting ratio (R) offline for different distribution of source and destination pairs.

In Figure 12, the location error of CDL2 is about 3.17 m which is better than that

Figure 11. Location errors of CDL via experiments with random anchors.

location error: 3.17 (m)

Figure 12. Location errors of CDL2 via experiments with random anchors.

5.2.2 Anchor nodes deployed in the corners

In this experiment, we placed anchor nodes in the corners [16]. In Figure 13,

adjust the average hop distance. In Figure 14, the location error of CDL2 is about 1.87 m. This demonstrated that the location error of CDL has been reduced from 4.76 m to 2.38 m and that of CDL2 has been reduced from 3.17 m to 1.87 m by placing the anchor nodes in the corners. Therefore putting anchor nodes in the corners can improve the location accuracy.

location error: 2.38 (m)

---02

Figure 13. Location errors of CDL via experiments with anchor in the corners.

location error: 1.87 (m)

---02

5.3 Comparison of Simulation and Experiment Results

In Chapter 4, the location errors of E-CDL from simulation results are about 0.1r, which is apparently better than the location error (0.21r) from experimental results. This is because the sample size for experiments was small and sensor nodes were stationary. In this situation, sensor nodes might not be uniformly distributed and might result in possible disconnections. In the future work, we will use a large sample size and mobile sensors to further validate the location accuracy of E-CDL.

Chapter 6

Conclusions and Future Work

6.1 Concluding Remarks

Localization is a critical issue in mobile WSNs. With the aid of location information of sensor nodes, for instance, the efficiency of routing can be improved. In this thesis, we have presented an E-CDL algorithm which is an enhanced color-theory-based dynamic localization algorithm, which uses three enhancements to improve the location accuracy of the original CDL algorithm.

The basic idea of the enhancements is more accurate estimate of the average hop distance and with the assistance of mobile anchor nodes that are placed in the corners. Simulation results have shown that the location error is about 0.1r when the sensor density is 10 and the maximum speed is r t_u . However, the experimental results show that the location error is only 0.21r. This is due to a limited sample size. In addition, the location accuracy of E-CDL is 50% - 55%

better than that of CDL, and 75% - 80% better than that of MCL. In summary, E-CDL is an efficient range-free and centralized localization scheme and is therefore very suitable for health-care and hospital monitoring systems.

6.2 Future Work

We have proposed three enhancements to further enhance the original CDL algorithm. However, routing is not considered in the thesis. Therefore, we are going to combine our localization method with a routing algorithm to propose an efficient location-aware routing algorithm. In addition, in the experiments,

might not be uniformly distributed and might result in the possible isolations of sensor nodes. We will use a larger sample size and mobile nodes to further validate the location accuracy of E-CDL. Finally, we will implement our algorithm combing with a routing algorithm in a heath-care system to further evaluate the effectiveness of E-CDL in real systems.

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