MULTI-HOP POSITIONING

Relative Positioning Method for GPS Wireless Sensor Network

Masayuki Saeki

and Kenji Oguni

Tokyo University of Science, Yamazaki 2641, Noda-shi, Chiba, Japan

Keio University, Yagami 3-14-1, Kohoku-ku, Yokohama-shi, Kanagawa, Japan

Keywords: GPS, Relative positioning, Wireless sensor network, Displacement monitoring.

Abstract: This paper presents a relative positioning method, called “multi-hop positioning”, which is suitable for raw

GPS data collected by densely deployed L1 GPS receivers. The wireless sensor network employing an

affordable L1 GPS receiver has been developed by the authors for monitoring displacement of large civil

structures with high spatial resolution. In general, relative positioning of GPS sensors are performed

between a single reference point and sensor nodes. On the other hand, in the newly developed approach,

relative positioning is performed between all pair of sensor nodes in the network. Then, the best set of

relative position vectors is selected to determine the location of sensor nodes. Experiments have been

conducted using 53 sensor nodes equipped with an affordable L1 GPS receiver and the collected data are

analysed by using the proposed method in a post-processing manner. The results show that the success rate

of relative position estimate is considerably improved compared with the conventional approach.

1 INTRODUCTION

Displacement monitoring of large infrastructures

such as artificial island, embankment and reclaimed

land is very important. This work is operated for

controlling quality and ensuring safety. In general,

displacement monitoring is performed by survey

work or an automated monitoring system in which

accurate instruments are networked with cables and

the displacements are monitored remotely. Although

the automated monitoring system could replace the

survey work for reducing the monitoring cost, the

application examples are still limited. One of the

disadvantages of the current automated system is its

high cost. Very expensive instruments such as a

laser displacement meter or a high performance GPS

(Global Positioning System) receiver is employed to

detect the displacement in sub-centimetres accuracy.

For the dense displacement monitoring of large

civil infrastructures, a cost-effective system should

be developed. The combination of wireless sensor

network and an affordable L1 GPS receiver can be a

possible solution to this problem. Besides, the

wireless sensor network has big advantages not only

in cost but also in robustness and workability (Lynch,

2004). Therefore, we have been developing the

system of wireless sensor network using an

affordable L1 GPS receiver (Saeki, 2008). We call

this system GWSN (GPS Wireless Sensor Network).

This system consists of a central server and many

sensor nodes equipped with an affordable L1 GPS

receiver. Each sensor node collects raw GPS data

according to the command from the central server

and sends their data back to the server. The relative

positions of the sensor nodes from a reference point

are analyzed in the server. The displacements of the

sensor nodes are estimated as the change of position

from the initial state.

Since the sensor node runs using a small battery

and/or additional harvested energy, the total energy

consumption should be suppressed. Considering the

high energy consumption of the GPS receiver, the

observation time should be minimized. On the other

hand, to improve the accuracy of positioning, the

observation should be performed as long as possible.

Clearly this system has the trade-off relationship

between the accuracy and the energy consumption.

Therefore we have tried to develop a new relative

positioning method which gives accurate relative

position with short data length.

This paper presents a relative positioning method

suitable for the data collected by the densely

deployed GPS receivers with short data length. In

this method, the location of the sensor node is

361

Saeki M. and Oguni K..

MULTI-HOP POSITIONING - Relative Positioning Method for GPS Wireless Sensor Network.

DOI: 10.5220/0003798503610368

In Proceedings of the 2nd International Conference on Pervasive Embedded Computing and Communication Systems (PECCS-2012), pages 361-368

ISBN: 978-989-8565-00-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

estimated as a sum of the relative position vectors.

Relative positioning is performed between all pair of

sensor nodes in the network and the optimal sum of

relative position vectors is selected to determine the

location of sensor nodes. To assess the performance

of our method, experiments have been conducted

using 53 wireless sensor nodes. The collected data

are analysed by using the proposed method in a post-

processing manner. The results show that the

success rate of estimating the relative positions is

considerably improved compared with the

conventional approach.

2 RELATED WORK

GPS-less localization method for large networks of

wireless sensor nodes has been intensively studied

by many researchers. For example, Bulusu et al.,

(2000) evaluates the effectiveness of a simple

connectivity metric method for localization in

outdoor environments. Moor et al., (2004) presents a

linear-time algorithm for localizing sensor network

nodes in the presence of range measurement noise

and demonstrates the algorithm on a physical

network. These results show that the accuracy

depends on the scale of distribution and is not high

enough for monitoring displacements of large civil

infrastructures, which needs a few centimetres to

sub-centimetres accuracy.

Many displacement monitoring systems using L1

GPS receivers are developed and demonstrated in a

real field. Gassner et al., (2002) developed a GPS-

based continuous monitoring system and applied it

to landslide monitoring. Shimizu, (2003) developed

a monitoring system and applied it to large open

quarries and landslide slopes. Seynat, et al., (2004)

developed the monitoring system, which uses a low

cost GPS receiver and a radio link, and applied their

system to volcano monitoring. These demonstrations

show that displacement monitoring using L1 GPS

receivers might be possible in terms of accuracy.

In order to deploy the sensor nodes densely

covering a large infrastructure, the cost for a single

observation point should be decreased further. So,

we have been developing the new displacement

monitoring system which combines the wireless

sensor network with an affordable L1 GPS receivers

connected to a small patch antenna which is

generally used for a mobile navigation (Saeki, 2008).

This combination enables us to decrease the cost of a

single observation point but brings about other

problems to be solved.

One of the problems is the energy consumption

of the GPS receiver. The sensor node of GWSN

keeps the GPS receiver off as long as possible to

save its battery. However, shortening observation

time results in the accuracy deterioration. To

overcome this problem, we have tried to develop a

new positioning method considering the condition of

dense sensor deployment.

The problem to determine the locations of many

GPS receiver simultaneously is known as network

adjustment (Han, 1995). In the network adjustment,

variance-covariance matrix between GPS sensors is

taken into account. However, it is so difficult to

estimate an appropriate variance-covariance matrix

in the application of a large infrastructure that

network adjustment might not be applicable.

3 GPS WIRELESS SENSOR

NETWORK

This section describes the outline of the present

system and the conventional relative positioning

method, and specifies the required technology.

3.1 Outline of the System

Figure 1 illustrates the schematic view of GWSN.

This system consists of a single central server and

many sensor nodes. The sensor node has a micro-

controller, a small wireless communication device, a

small battery and an affordable L1 GPS receiver.

The sensor nodes run according to the command

from the central server. After getting the command

to start observation, it turns on the GPS receiver

which outputs the raw binary messages to the micro-

controller every one second. The micro-controller

extracts the required data from the original binary

message and save them to the non-volatile memory.

The size of the original binary message is 266 bytes

and is compressed to 28 bytes in the present system.

After the sensor nodes collecting the data for several

minutes (e.g. 4 minutes), the central server orders

them to send their data back to itself. The locations

of the sensor nodes are analysed by the central

server in a post-processing manner.

In the prototype, a middle range series micro-

controller PIC16F877A (Microchip Technology

Inc.) is employed since any complex calculation is

not required. As an affordable L1 GPS receiver,

GT8032 (Furuno Electric co., ltd.) is used which is

capable of outputting L1 carrier phases in a Furuno

binary format. A small patch antenna is connected to

the receiver for saving cost. This kind of antenna is

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362

commonly used in an automotive navigation system

and never used for accurate positioning because the

measured carrier phases are very contaminated by

the antenna noises. The wireless communication

device of the prototype is MU1-1252 (Circuit

Design, Inc.) which uses the frequency band of 1252

MHz. The maximum distance of wireless

communication is 600 m with a line of sight at the

RF output power of 10 mW.

Figure 1: Schematic view of GPS wireless sensor network.

3.2 Conventional Relative Positioning

Method

In the present system, the relative position vector is

estimated by the static interferometry positioning

method which is widely used in a practical GPS

surveying to achieve centimetre-level accuracy.

3.2.1 Observation Equation

The relative position vector is estimated by

analysing the L1 carrier phases. In case of short

baseline, the DD (Double-Differenced) carrier

phases at time t, 





(



)

, is modelled as follows

(Hofmann, 2001),







(



)









(, ) + 





+





()

(1)

where ∗





represents the DD values for the GPS

satellites k, l and the sensor nodes i, j.  is the

wavelength of L1 carrier waves, 





(, ) is the DD

ranges between satellites and the nodes,  is the

relative position vector of a sensor node, 





is the

DD integer ambiguity and 





is the noise. Eqn. (1)

is linearized by substituting =



+Δ and

applying the Taylor Expansion with respect to 



Gathering Eqn. (1) corresponding to the different

sets of satellites forms the following simultaneous

equations.



(



)

= ()Δ +  + ()

(2)

where 

(



)

is the vector of the corrected DD carrier

phases, () is the design matrix. The unknowns in

Eqn. (2) are the correction terms for the position

vectors Δ and the vector  of DD integer

ambiguities. Solving Eqn. (2) through the least mean

square method gives a float solution in which the

DD integer ambiguities are estimated as float values.

3.2.2 Integer Ambiguity Resolution

In order to achieve centimetre-level accuracy, the

DD integer ambiguities should be resolved as the

integer values. This solution is called fixed solution.

Denoting the float solution and the fixed solution as





and 



, respectively, the fixed solution 



estimated as the integer-valued vector which

minimizes the following objective function .



=



−



















−





(3)

where 





is the variance-covariance matrix of the

float solution 



In general, the fixed solution is validated by

checking the ratio 



/



where 



and 



are the

minimum residual and the second small one,

respectively. It is known that the larger ratio gives

the higher probability of selecting the correct DD

integer ambiguities. In the case that the ratio 



/



greater than 3, the fixed solution is empirically

considered a correct solution. On the other hand, the

solution might be wrong with the smaller ratio, and

the wrong DD integer ambiguities might give more

than several centimetres to meters error to the

estimated position. In the general usage of GPS, the

data is logged until the ratio exceeds 3 to guarantee

the quality of solution. However, in the present

system, the observation time is limited to save

battery energy.

3.3 Required Component Technology

As mentioned above, it is preferable to measure the

GPS data longer for estimating the correct relative

GPS satellites

Central server

battery

small patch antenna

Sensor node

wireless communication module

MULTI-HOP POSITIONING - Relative Positioning Method for GPS Wireless Sensor Network

363

position vectors while the longer measurements

results in the higher energy consumption. Since the

sensor node should run for at least several months

without changing battery, it is needed to develop a

method to estimate the correct relative position

vectors with short data length.

As considering the affordable cost of this system,

the sensor nodes are expected to be densely

distributed over a large infrastructure. This dense

deployment might be a great advantage of the

present system. Therefore, we have tried to develop

a new relative positioning method considering the

dense deployment of the sensor nodes. In the

conventional approach, the relative position vectors

are individually estimated for each sensor node. And

the advantage of the dense GPS deployment is not

taken into account.

4 MULTI-HOP POSITIONING

Float solution is estimated by solving Eqn. (2) with

the assumption that the noise is white. The

assumption could be true in some pairs of sensor

nodes but could be false in other pairs. If the

surrounding conditions of the sensor nodes are very

similar to each other, the noises also become very

similar. In the case, the noises can be cancelled out

in the double difference calculation and the residual

behaves as the white noise. On the other hand, when

the surrounding conditions of the sensors are

different from each other, the residuals of the noises

are not likely to be white. In this case, the accuracy

of the float solution becomes worse and the DD

integer ambiguities are not correctly resolved in the

minimization problem of Eqn. (3). This leads to the

wrong relative position vectors. Therefore, it is very

important to select a good pair of sensor nodes

whose noises are very similar to each other.

4.1 Basic Idea of the Proposed Method

Suppose that three sensor nodes are there and the

noises are different from each other but the noise of

node 3 has some similarities to those of node 1 and 2.

This situation often happens in actual observations

when many sensor nodes are deployed densely. In

such case, the relative position of node 2 from 1 is

likely to be estimated wrong and the ratio 



/



becomes small since the noises are not cancelled out

in the DD calculation. On the other hand, the relative

position of node 3 could be estimated correctly and

the ratio becomes larger than that of node 2. This

situation is schematically drawn in Figure 2(a). Two

relative position vectors and ratios are described on

the figure. In this example, node 2 is unsuccessfully

estimated.

Figure 2: Simple example of the relative position vectors

estimated by the conventional method (a) on the left side

and the proposed method (b) on the right side.

In the above situation, the relative position of

node 2 is estimated wrong from node 1. However, it

can be estimated correctly by summing up the

relative position vectors as described in Figure 2(b).

Since the noise of node 2 has some similarities to

that of node 3, some parts of noises can be cancelled

out. Then it must yield better float solution and it

gives higher probability of selecting the correct

integer ambiguities. Then, the relative position of

node 2 from node 3 can be estimated in accurate.

In a real situation, there are many candidates of

the paths because many sensor nodes are distributed.

And besides, the ratios 



/



might have similar

values. So there is a problem how to select the

optimal path with a convincing reason. To solve this

problem, we introduce the success probability into

the present approach. By comparing the success

probabilities evaluated for each path, the optimal

path can be selected convincingly.

4.2 Assumption of Success Probability

We assume that the success probability of resolving

the DD integer ambiguities is represented as a

function of ratio 



/



. And the success probability

of a path can be estimated as the products of the

success probabilities of the corresponding relative

position vectors. In this subsection, we empirically

estimate the function relating the success probability

and the ratio 



/



4.2.1 Experiment and Data Analysis

Figure 3 shows a look of the experiment conducted

on the concrete roof of a building March 3, 2008.

Since there are no obstacles over the site, it is

considered as an ideal condition. In the experiment,

Node 1

2.0

1.1

ode 2

Node 3

Node 1

2.0

1.5

Node 2

Node 3

(a) (b)

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four sensor nodes are deployed in the different

manner. Two GPS antennas are fixed on the flat

plane of thin concrete block (ID1 and ID2) and the

other antenna is mounted on the concrete block with

different height (ID3). Another antenna is fixed at

the tripod (ID4). These various antenna conditions

are set for causing different antenna noises. For

example, the antenna noises of ID1 and ID2 are so

similar that the noises are effectively cancelled out

in the DD calculation. On the other hand, the

antenna noises of ID1 and ID4 are apparently

different and cannot be eliminated in the analysis.

Figure 3: Photo of the experiment conducted for collecting

raw GPS data with the different antenna conditions.

The raw GPS data are sampled for 24 hours at

1Hz sampling rate and are saved on a laptop. The

data is analysed in a post-processing manner. In the

analysis, relative position vectors of ID1-2, ID1-3

and ID1-4 are estimated.

In the analysis, the data with the length of 240

seconds is picked up from the continuous data and

analysed by means of the conventional relative

positioning. If the estimated location of sensor node

is within 3 centimetres from the most possible

position, this estimation is counted as a success. The

same operation is applied to the next data shifted

from the previous data by 1 second. These processes

are carried out 86400 times for each sensor node.

The estimated results are classified depending on the

value of the ratio 



/



. The success probability,

which is defined as the ratio of the frequency of

successes to trials in this paper, is estimated for each

class.

4.2.2 Success Probability of a Single Vector

The success probabilities obtained from the above

analysis are plotted in Figure 4. The marks of

triangle, circle and square represent the results of

ID1-2, ID1-3 and ID1-4, respectively. Three curves

are the corresponding success probability functions

which are estimated by the least square method. In

this paper, the success probability function 

(



)

assumed to be the following function.



(



)

=1.0−



(4)

where  is the ratio 



/



,  and  are the unknown

parameters to be estimated.

Figure 4: The relationship between the success probability

and the ratio 



/



As shown in Figure 4, the success probability of

ID1-4 has smaller values compared to that of ID1-2

especially at the small ratio 



/



. This means that

the success probabilities depend on the conditions of

antenna noises as well as the ratio. In the following

simulations, the curve corresponding to the case of

ID1-4 is used because it mostly represents a realistic

condition among them.

4.2.3 Success Probability of a Path

In the proposed method, a relative position vector of

sensor node is obtained by connecting other relative

position vectors. The success probability of the path

can be evaluated by multiplying the success

probabilities of the corresponding relative position

vectors.



(



)

=(



)(



)⋯(



)

(5)

where 



is the ratio 



/



of relative position vectors

constituting the path.

4.3 Optimal Path Finding by Dijkstra’s

Algorithm

The optimal path should be reasonably selected from

the numerous candidates by searching the path with

the maximum success probability. In the proposed

ID4

ID2

ID1

ID3

100

1.0 1.5 2.0 2.5 3.0

ratio, J/J

Success P

obabili

ies [%]

MULTI-HOP POSITIONING - Relative Positioning Method for GPS Wireless Sensor Network

365

method, Dijkstra’s algorithm is used as a search

algorithm (Wiitala, 1987). This algorithm is widely

used in many applications such as network routing

protocols or mobile navigation systems to find the

shortest (or lowest cost) path efficiently.

Dijkstra’s algorithm is applicable to the present

problem with a small modification. In the proposed

method, the optimal path is searched not for the

shortest length but for the maximum success

probabilities.

5 DEMONSTRATIONS

In order to investigate the performance of the

proposed method, we conduct two experiments and

analyse the data using both the conventional and the

proposed method. This section describes the details

of experiments and the results.

5.1 Experiment Described in Section 4

The data, collected in the experiment described in

the previous section, are analysed. In this analysis,

the sensor node ID1 is set to be a reference point and

the relative positions of the other sensor nodes are

estimated by using the conventional and the

proposed method. The data length is set 240 seconds

and the estimation is carried out 86400 times in the

same manner as mentioned in the section 4.2.1. If

the estimated position is within 3 centimetres from

the most possible position, the estimation is counted

as a success. And the success rate is estimated by

dividing the frequency of successes by trials. Table 1

shows the comparison of the success rates. The

success rate of ID2 slightly decreases but the other

success rates of ID3 and ID4 are improved. Overall,

it is said that the success rates are improved by using

the proposed method.

Table 1: Comparison of the success rates estimated by

analysing the data collected in the experiment described in

section 4.

Conventional Proposed

ID1 to 2 100.00 99.94

ID1 to 3 99.91 100.00

ID1 to 4 94.99 95.70

5.2 Experiment using 53 Sensor Nodes

5.2.1 Experimental Condition

Next, we conduct an experiment using 53 sensor

nodes to make sure that the proposed method works

well in case of dense deployment. In this experiment,

53 sensor nodes are arranged every two meters in a

grid on the rooftop of a building as shown in Figure

5 and 6. Some of GPS antennas are intentionally

located in the vicinity of the obstacles (the outdoor

equipment of air-conditioner shown in the right in

Figure 5 and the white building behind the sensor

nodes). This deployment of the antenna is for non-

uniform signal environment and corresponding

variety of the antenna noises. The raw GPS data are

collected for 4 minutes and gathered to the central

server via wireless communication.

Figure 5: Photo of the experiment conducted for collecting

GPS data using densely deployed GPS receivers.

Figure 6: Arrangement of 53 sensor nodes in a grid.

5.2.2 Results of Analysis

In the analysis, the conventional and the proposed

approach are performed setting every sensor node as

a reference point because the results of analysis

depend on the choice of the reference point. So, the

position of each sensor node is estimated 52 times in

this analysis. Table 2 shows the worst five success

rates which are estimated using the conventional

approach and the success rates of corresponding

sensor nodes improved by the proposed method. All

Sensor node

GPS antenna

From West to East

GPS Antenna

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sensor nodes listed up on the Table 2 locates near

the obstacles which cause different antenna noises.

The different antenna noises decrease the success

rates. However, the success rates obtained using the

proposed method are all improved to 100.00% in

this analysis. The multi-hop positioning method

works well especially in case of dense deployment

of sensor nodes because it is easier to find out the

best pairs of sensor nodes which include almost the

same antenna noises.

Table 2: Comparison of success rates in case of the

experiment using 53 sensor nodes.

Conventional Proposed

ID29 43.40 100.00

ID13 69.81 100.00

ID36 86.79 100.00

ID17 88.68 100.00

ID09 90.57 100.00

One of the worst cases in case of applying

conventional method is obtained if the sensor node

of ID17 is set a reference point. The estimated

locations are shown in Figure 7. The success

probabilities calculated by Eqn. (4) are also plotted

in the figure. In this estimation, 6 relative position

vectors are mistakenly determined and the success

probabilities are relatively small in the vicinity of

obstacles. Since the antenna of the sensor node of

ID17 is fixed among the white building and the

outdoor equipment of air-conditioners, the antenna

noises are considered to be very different from the

others.

Figure 7: Locations of the sensor nodes estimated by the

conventional method with the reference point ID17.

The results obtained by the proposed method

with the reference point of ID17 are shown in Figure

8. We can easily see that the proposed method

outputs better solution. All relative positions are

correctly determined and the success probabilities

are improved greater than 0.99 even though the

reference point seems to be set under the noisy

condition. Figure 9 describes the optimal path

determined by the search algorithm. The number of

connections of the relative position vectors is at

most 11 in this case.

Figure 8: Locations of the sensor nodes estimated by the

proposed method with the reference point being in the

worst condition (ID17).

Figure 9: The optimal path found out by the search

algorithm in case of setting ID17 the reference point.

6 CONCLUSIONS

This paper presents the relative positioning method,

called multi-hop positioning, which is suitable for

the data collected by the densely deployed GPS

sensors. We introduce the success probabilities into

the estimation of relative position vectors. The

relative position of sensor nodes from a reference

point is calculated as a sum of relative position

vectors. The optimal path, which connects the

relative position vectors, is selected by the Dijkstra’s

algorithm with maximizing the success probability.

We demonstrate the proposed method analysing the

experimental data. One experiment is carried out for

24 hours using 4 sensor nodes and the other

experiment using 53 sensor nodes. The analytical

results show that the success rates of estimating the

correct relative position using the proposed method

0.997

0.988

0.870

0.999

0.524

1.000

0.998

0.992

0.956

0.990

0.999

1.000

0.665

0.493

0.998

0.970

0.000

1.000

0.960

0.904

0.999

1.000

0.938

0.987

1.000

0.690

1.000

0.987

1.000

0.997

0.482

0.971

0.999

0.835

0.999

0.998

1.000

0.961

0.999

0.997

0.992

0.998

1.000

0.981

GPS Antenna

Estimated position

1.000

0.993

1.000

0.997

1.000

MULTI-HOP POSITIONING - Relative Positioning Method for GPS Wireless Sensor Network

367

is considerably improved compared with the

conventional approach.

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