UNCERTAINTY IN TRILATERATION

Is RSSI-based Range Estimation Accurate Enough for Animal Tracking?

Ragnar Stølsmark and Erlend Tøssebro

Institute of Electrical Engineering and Computes Science, University of Stavanger, Stavanger, Norway

Keywords: RSSI, Trilateration, Localization, Uncertainty.

Abstract: Animal tracking is important to farmers. It is mainly performed using GPS receivers. Equipping only some

of the animals with GPS receivers and have the others use them as beacons for RSSI-based trilateration

could be beneficial. This article tests whether such a solution is possible from an uncertainty point of view.

First a range of RSSI measurements were performed. These measurements were used to create a formula for

RSSI as a function of distance. The RSSI standard deviation measured in the tests gave an indication of the

error, or uncertainty, related to using RSSI to calculate distance. The distance function and standard

deviation were then used as a basis for simulations that calculated the uncertainty of RSSI-based range

estimation. The simulations showed that the localization error related to distance estimation by RSSI was

too high for it to be an efficient solution, even with a device twice as accurate as the test device.

1 INTRODUCTION

Animal tracking is a concept which has been of

scientific and commercial interest for a long time.

Different studies have for instance tried to figure out

where birds stay during the winter and how far a

pack of wolves roam. New technologies, such as

GPS and satellites, have revolutionized animal

tracking.

Livestock tracking is of great interest to

agriculture. By using new technology it is possible

for a farmer to keep track of his livestock without

leaving the office. Livestock tracking has proven to

be especially effective in sheep farming. Sheep

farmers traditionally send their animals to graze in

the mountains during the summer. In autumn they

then need to recover their sheep. This is a tedious

and time consuming process. It is not easy to search

for the sheep in large mountainous areas without

roads. The fact that the sheep tend to walk in small

flocks rather than one large group does not help

either. Thanks to commercial solutions such as

Telespor, built on the Electronic Shepherd research

project (Thorstensen et al., 2004) , sheep farmers can

now remotely track their sheep.

These systems typically rely on GPS for

localization. There are a couple of weaknesses with

this approach. First GPS consumes a lot of energy.

This means that one either have to reduce update

frequency or equip the nodes with big batteries that

can last an entire season. Secondly, GPS satellites

produce a weak signal. Therefore it can be hard to

locate sheep in dense forests and other areas with a

relatively low GPS signal strength.

An alternative way to locate sheep or other

animals could alleviate these problems. Since there

are several sheep in a flock, it could be possible to

use RSSI (Received Signal Strength Indicator) to

measure the range between sheep. Some of the sheep

would find their position using GPS. The others

could find their own position by trilateration using

the range measurements from the GPS sheep.

The main topic of this paper is whether such a

method gives an acceptable uncertainty, or

localization error, or if RSSI simply is unsuitable as

a range measurement tool in this context. Acceptable

uncertainty means it should be possible to retrieve

the sheep in a reasonable amount of time.

The paper is organized as follows: Chapter 2

presents related work. Chapter 3 gives an overview

of trilateration and uncertainty. Chapter 4 contains

the results of both our RSSI and range

measurements as well as our simulation results.

Chapter 5 concludes the paper.

2 RELATED WORK

RSSI and localization in wireless sensor networks

have been the topic of many research projects, such

237

Stølsmark R. and Tøssebro E..

UNCERTAINTY IN TRILATERATION - Is RSSI-based Range Estimation Accurate Enough for Animal Tracking?.

DOI: 10.5220/0003834402370241

In Proceedings of the 1st International Conference on Sensor Networks (SENSORNETS-2012), pages 237-241

ISBN: 978-989-8565-01-3

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

as: (Awad et al., 2007); (Sichitiu et al., 2003);

(Barsocchi et al., 2009); (Paul and Wan, 2009) and

(Hyo-Sung and Wonpil, 2009). Many of these

algorithms focus on indoor localization (Awad et al.,

2007); (Barsocchi et al., 2009); (Paul and Wan,

2009) and (Hyo-Sung and Wonpil, 2009), even if

RSSI is not particularly suitable for indoor range

estimation due to walls and other obstacles that

affects the signal propagation (Akyildiz et al., 2002).

In a room it can be effective however, and also a

good alternative since GPS is not available. In

(Awad et al., 2007) they used a neural network to

estimate the distances based on RSSI. This worked

well, however the distances in their experiment were

below 5 m, making it inapplicable to animal

tracking. They used an exponential function to

predict distance from RSSI. Using regression, they

found it to be a suitable function.

In (Sichitiu et al., 2003) the researchers

performed RSSI measurements using IEEE 802.11b

network cards. These measurements show a good

correlation between RSSI and distance. The

measurements were performed at relatively short

distances, the longest being 40 meters. This makes

the topology and terrain less of a factor. They also

simulated the accuracy of their RSSI-based

localization algorithm. They were able to get a low

uncertainty. The main problem with applying their

simulation to long range applications is that their ±

25 m RSSI accuracy is too optimistic. The

experiments in this paper show that ±100 m is closer

to the truth.

Researchers have also tried using RSSI to locate

cattle in grazing fields. In (Huircán et al., 2010) they

were able to locate animals by having a high beacon

density, with only 80 m between beacons. This

makes their solution expensive for animals that

reside in a large area. To cover an area of 5000 x

5000 m, which is not unusual for sheep grazing in

the mountains, would require approximately 3900

beacons.

3 TRILATERATION AND

UNCERTAINTY

Trilateration is a well-known method for

localization. A good introduction to the topic can be

found in (Yang and Liu, 2010). To be able to

unambiguously locate an object in two dimensions

using trilateration, the following information is

necessary:

1. The position of at least three other objects.

2. The distances between the object being located

and each of the other objects.

Figure 1: Trilateration with two beacons. The object could

be located in both shaded areas.

If these are known, one can solve a set of

equations to find out the position of the last object.

Although the position of three other objects is

enough to locate an object, the accuracy improves

with every extra distance and location combination

that is known.

Applying RSSI-based trilateration to livestock

tracking is not trivial. There are especially two

problems that arise from relying on trilateration

based on other animals’ positions. The first problem

is that one needs the position of at least three other

animals. This means that at least four animals must

be fairly close to each other and three of them must

find their positions via different means. To achieve

this, the flock must be dense compared to the

maximum range of the transceivers used to send

messages between the animals. Some of the sheep

must also have a different localization method.

Localization is possible with fewer than three other

known positions, but it will lead to reduced accuracy

due to separate uncertainty areas, as illustrated in

figure 1.

The second problem is the uncertainty of the

final position estimate. The uncertainty comes from

two sources, the position of the other objects and the

distance to those objects. If the other objects were

localized via GPS their position should be fairly

certain. GPS receivers typically have an accuracy of

10 meters under normal conditions. The distance

uncertainty depends on the accuracy of the distance

measurement tool.

RSSI is generally reduced with increasing

distance and easy to obtain if both animals carry

transceivers. Therefore it is a good candidate as a

distance measurement tool. Distance is however not

the only thing affecting RSSI. Terrain, obstacles,

vegetation, antenna orientation and weather also

plays a role. With that in mind the objective of this

paper is to determine if RSSI is a suitable tool for

livestock tracking. That means to test if it can

provide acceptable uncertainty in a realistic terrain.

SENSORNETS 2012 - International Conference on Sensor Networks

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4 TEST SETUP AND RESULTS

To test whether RSSI can be used as a range

estimator for tracking of sheep and other animals,

several RSSI measurements were performed. The

results from these measurements were then used in a

set of simulations designed to test the accuracy of

RSSI-based trilateration.

4.1 RSSI Measurements

The RSSI measurements were performed outdoors

in varying environments similar to those where

sheep typically graze. Hills, forests and flat open

ground, were all present in the areas where the

measurements were carried out. The radio

equipment used in the tests was Waspmotes,

wireless sensor network motes from Libelium. They

are equipped with an 868 MHz XBee transceiver

connected to an antenna capable of transmitting a

315 mW signal. During the tests they were never

able to transmit a signal over more than 2 km. The

average achieved range during testing was 505 m

with a standard deviation of 170 m. The RSSI

measurements were carried out separately from the

range tests.

Table 1: RSSI measurements.

Distance Avg. RSSI Std. Dev. # tests

71.4 6.8 25

100

89.7 11.0 25

200

100.3 8.5 25

300

104.8 9.1 20

400

97.6 1.8 5

500

115.0 1.4 5

600

124.0 1.4 2

The RSSI tests were performed in the following

manner: A beacon node was first setup. This beacon

node would reply to any request received from the

mobile node carried by the person performing the

test. The tester could then read the RSSI at the

mobile node. For each test location, 5 RSSI readings

would be done at a distance of approximately 50 m.

The tester would then perform 5 readings at 100 m,

200 m, 300 m and so forth, until no signal was

received. Table 1 summarizes the results of these

measurements. The RSSI in the Waspmote range

from 61 db, when the antennas are placed next to

each other, to 130 db, when there is almost no

signal. As predicted, table 1 shows significant

variations in the RSSI at equal distances due to

geographical differences. The small variation at the

three longest distances is due to the fact that there

was only one of the five beacon placements that

were able to transmit a signal that far.

4.2 Simulation Setup

The simulations ran in a Java simulator written

specifically for these tests. The simulator would first

uniformly distribute the sheep flock over an area of

5 x 5 km. This size was chosen because it represents

a typical grazing area for a flock of sheep. The

simulator equipped all the sheep with transceivers

that had the same range (505 m) and standard

deviation (170 m) measured during the range tests.

Some of the sheep would also be equipped with GPS

receivers. These receivers have an accuracy radius

of 10 m in the simulations. All of the animals knew

which sheep were within their radio range, and the

exact position of those sheep. The sheep without

GPS receivers calculated the uncertainty of their

own position estimate based on the position of sheep

with GPS within radio range. This uncertainty was

calculated in the following manner: For each

neighbor with GPS, the known distance to that

neighbor would be used to calculate a minimum and

maximum RSSI value. The function used for

converting distance to minimum (-) and maximum

(+) RSSI was:



(



)

= 9.431 + 17.2 ∗ 

(



)

±2σ

(1)

where σ = 6.7823 when dist < 100 m

and σ = 9.5448 otherwise.

This function was based on the results from the

RSSI measurements. With increasing distance there

was more variation, therefore a higher standard

deviation was used for distances over 100 m. These

two values would then be translated to a minimum

and maximum distance representing the uncertainty

of the distance estimate using an inverse function:



(



)

= 5.211 ∗ 

(.∗)

(2)

The uncertainty area corresponding to each GPS

neighbor is therefore doughnut shaped. The total

uncertainty area is decreased with every additional

GPS neighbor. Every simulation scenario was

repeated 100 times and the results are an average of

the values in those runs.

Table 2: Average uncertainty area among non-GPS nodes

GPS % 50 sheep 100 sheep 150 sheep 200 sheep 250 sheep

1889539 1714458 1555184 1376825 1260480

1726486 1390939 1119644 879674 701482

1530232 1104071 773226 563953 421873

1382559 904196 584406 409051 285684

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239

4.3 Simulation Results

Two metrics have been chosen as the main success

criteria, average uncertainty area and average

extremity distance. The uncertainty area is defined

as the area a node can be in given it knows the

location and an approximate distance to a set of

other nodes. A smaller uncertainty area means less

area has to be searched and the animals can therefore

be retrieved faster. The second criterion is the

extremity distance. It is defined as the length of the

longest straight line possible to draw within a

bounding box surrounding the uncertainty area. This

metric is important since one of the main purposes

of animal tracking is to be able to find the animal

quickly when searching for it in the real world. The

problem with just looking at the uncertainty area is

that the area can be quite small and still have a large

extremity distance. An example of such an area

would be a very thin rectangular shape. This would

result in a lot of time spent walking from one end of

the area to the other. The simulations have been

performed with different flock sizes and different

GPS/non-GPS ratios (20-80% GPS). The average

uncertainty and extremity distance will decrease

with a denser flock. Therefore it is interesting to test

at which flock size these reach acceptable levels and

also if what can be considered normal flock sizes

(between 50-250 animals) have an acceptable

uncertainty. In the tests the ratio of animals having

an acceptable uncertainty and extremity distance

were also measured. The limits for these two metrics

were set to 40000 m

and 300 m, respectively. These

limits have been set so that animals within those

limits can be found in less than an hour.

Table 3: Average percentage without GPS neighbours.

GPS % 50 sheep 100 sheep 150 sheep 200 sheep 250 sheep

72.1 51.7 38.1 27.8 20.5

51.4 27.7 14.6 7.7 4.7

37.0 15.8 6.8 2.6 1.1

28.3 9.2 2.7 1.0 0.5

Table 3 displays the average percentage of non-

GPS animals that did not have any GPS neighbors.

Their uncertainty and extremity distances will

not be counted towards the averages reported in

table 2 and 4. Scenarios that have over 20 % without

GPS neighbors are not suitable for RSSI

trilateration. The animals are too sparsely deployed

in these scenarios.

Table 2 show the average uncertainty area in the

different simulation scenarios. It generally improves

with more GPS nodes. All scenarios have too much

uncertainty, even with 80 % of the nodes having

GPS. This is because RSSI as a range estimator is

not accurate enough.

Table 4 displays the average extremity distance.

The situation here is the same as with the uncertainty

area. Even the best scenario has, on average, over

twice the extremity distance considered adequate.

Table 5 show the percentage of sheep that got an

acceptable uncertainty and an acceptable extremity

distance. This increased with a higher beacon

density, but even with 200 GPS beacons only 2.2 %

of the non-GPS sheep where able to get below the

acceptable uncertainty limits.

The RSSI measurements were performed with

only one type of wireless device. To test the effect of

having more accurate RSSI measurements and

consistent antenna range, simulations were run with

half the measured standard deviation. The extremity

distance of these simulations are shown in table 6.

The distances are slightly more than half of those

measured in table 4. It is still not a good enough

solution, since on average only 59.5 % of the non-

GPS nodes have an acceptable uncertainty even

when 80 % of 250 sheep are equipped with GPS.

Table 4: Average extremity distance among non-GPS

nodes [m].

GPS % 50 sheep 100 sheep 150 sheep 200 sheep 250 sheep

2060 1952 1850 1736 1656

1959 1745 1558 1389 1244

1837 1556 1301 1132 1001

1747 1410 1146 980 850

Table 5: Average percentage of non-GPS nodes having an

acceptable uncertainty area and extremity distance.

GPS % 50 sheep 100 sheep 150 sheep 200 sheep 250 sheep

0.1 0.2 0.4 0.5 0.5

0.3 0.4 0.6 0.8 1.1

0.3 0.7 1.2 1.1 1.6

0.2 0.9 1.3 1.8 2.2

Table 6: Average extremity distance among non-GPS

nodes [m] with only half of the measured standard

deviance.

GPS % 50 sheep 100 sheep 150 sheep 200 sheep 250 sheep

1232 1133 1046 989 918

1137 981 845 727 625

1076 856 689 560 447

934 726 542 422 354

5 CONCLUSIONS

RSSI-based trilateration using GPS beacons is not

suitable for animal tracking. The uncertainty is too

high, even with RSSI measurements twice as

accurate as those obtained during tests. In those tests

SENSORNETS 2012 - International Conference on Sensor Networks

240

factors like placement of the node relative to the

animal’s body, weather conditions and antenna

orientation were not considered. These factors could

increase the RSSI variability significantly, making it

even harder to locate the animals. The variability in

RSSI measured in the tests comes from the impact

the terrain and other non-distance related factors

have on the signal propagation. Topography

becomes more important over long distances,

making animal tracking a particularly poor

application for RSSI-based distance estimation. A

system that does not need to rely on RSSI for

localization would therefore be preferable. Such a

system could make use of the fact that most animals

travel in groups. Therefore if one knows the location

of a group and the group’s members, it is possible to

locate all members. The group’s location could be

established using GPS and the members could be

determined by detecting the recipients of a wireless

broadcast of a membership message. This approach

could save energy and increase robustness compared

to a GPS-only approach.

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