1. A Solution to Land Area Calculation for Android
Phone using GPS
Abstract—This paper proposes an Android application to
calculate the land area of any shape using GPS. This application
provides the ability to locate user on the Google Maps, record
user’s walking path and calculate the area within this path.
Gauss-Kruger Projection is used to project the GPS coordinates
based on WGS-84 to plane coordinates. This application employs
the Trapezoid Method that breaks the irregular land shape into
small trapezoids to calculate the land area. Kalman Filter has
been used to improve the GPS accuracy. Test results demonstrate
that this application has a good performance with 3.64% average
error.
Keywords-component; GPS; Land Area; Android; Gauss-
Kruger Projection; Kalman Filter
I. INTRODUCTION
Since Google introduced the Android Operating System in
2008, it has occupied more than half of the smart phone market
by Quarter 3 of 2011 according to Gartner [1]. One reason for
its speedy spreading is the open source nature. Everyone can
utilize the Android SDK to develop any specific application.
This paper introduces an Android application that calculates
land area utilizing the GPS (Global Positioning System) sensor.
The demand for land area calculation is not limited to the
professionals, people who have similar needs can be the
potential users. For example, farmers want to know their land
area to make an efficient management plan. Workers have to
know the area of a mine to plan the explosion for the mineral
products. This paper proposed an efficient and convenient
application to calculate the land area using GPS for the
Android Phone. It records the GPS data of the user while the
user runs the application. Then, the land shape will be
presented on the Google Map visually. The Kalman Filter is
employed in this application to improve the GPS accuracy. As
a result, this application has a good performance with 3.64%
average error.
The rest of the paper is organized as follows. Part II
reviews some related works. Part III presents relevant
technologies that are used in this application. Part IV shows the
design of this application. Part V presents the experimental
results and gives validation and discussion. Part VI summarizes
this paper and gives future directions.
II. RELATED WORK
Location based service is one of the Android application
focuses. In paper [4], the author proposed an application that
can calculate land area using GPS. It recorded the location
points’ GPS data manually and stored the data in a light
database, and then the land area would be calculated by these
data. However, it just recorded the discrete points of land shape
steadily without showing the location of the points visually.
Another aspect of the author did not consider was the GPS
accuracy. Since the GPS data can directly affect the precision
of land area, it is very important to obtain the accurate GPS
data as more as possible.
In the area of applying Kalman Filter to GPS, the author of
paper [7] proposed an algorithm that uses the Kalman Filter
with Velocity Renovation to track location. It can improve the
GPS accuracy to 0.57m. In another paper [8], the author
adopted the Adaptive Kalman Filter in the robot tracking which
gave stronger tracking when the manoeuvre of the robot was
sudden changed. However, there is no research focusing on
how to combine Kalman Filter with land area calculation to
improve the land area calculation precision.
III. RELEVANT TECHNOLOGIES
A. Gauss-Kruger Projection
As WGS (World Geodetic System) system is widely used
in cartography, geodesy and navigation, it has become a
standard in this area. GPS uses the latest version (WGS-84) of
WGS as a reference coordinate system [2]. However, this
ellipsoid system is convex and not flattened which makes it
complex to calculate the area directly. Consequently, it is
necessary to project the GPS data to the plane coordinate
system. Gauss-Kruger Projection is one of the projection
methods.
Provided that the GPS coordinates of B (latitude (°)) and L
(longitude (°)), the plan system coordinates (x (m), y (m)) can
be obtained through the Gauss-Kruger Projection formulas [3].
B. Trapezoid Method
In this paper, the application records the coordinates of the
discrete points of the path when the user walks around running
this application. The shape of the land may be irregular.
Actually, the land shape is almost irregular in reality.
Mathematically, the normal way to calculate the irregular
shape area is to use calculus. However, considering the discrete
nature of the data and the difficulty of implementing calculus
in code, the most efficient method to calculate the area of
irregular shape in this case is breaking up the irregular shape to
small regular shapes. The Trapezoid Method has been
successfully used in paper [4] to calculate the land area.
Trapezoid Method breaks an irregular shape into many
trapezoids whose areas are easier to be calculated. Then adding
relevant area of trapezoids and subtracting relevant area of
trapezoids to obtain the total area of the irregular shape. The
concept of this method is shown by Figure 1.

2. In Figure 1, the irregular shape is formed by 7 points noted
as ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’ respectively. B is the
rightmost point (value in x-axis is the largest), E is the leftmost
point (value in x-axis is the smallest). For every point, draw the
perpendicular line to the x-axis. Any two adjacent points, their
perpendicular line and the x-axis form a trapezoid. For example,
EDD’E’ forms a trapezoid. ABB’A’ forms another trapezoid.
Then, the total area of this irregular shape can be obtained by
add and subtract relevant trapezoids’ area. The specific
equation for this case is followed:
ABCDEFG EDD'E' DCC'D' CBB'C'
ABB'A' GAA'G' FGG'F' EFF'E'
S S S S
S S S S
  
   
(1)
Figure 1 : Irregular Shape
In general, for any shape that has been formed by n points,
the first step is to find the leftmost and rightmost points. Then
add the area of trapezoids formed by the two points whose y-
value (value in y-axis) is greater than or equal to the y-value of
the leftmost and rightmost points. Finally, subtract the area of
trapezoids formed by the two points whose y-value is lower
than the y-value of the leftmost and rightmost points.
C. Kalman Filter
After did some tests for the GPS data that received by
mobile phone, the error of the GPS data was noted on the
Google Maps. To find how precise the GPS data was, a steady
point test has been done several times. This test just let the
mobile phone collect the GPS data for some steady points.
From the data analysis, the average error of the GPS module is
12 for MEIZU M9 smart phone. This error is relatively small
when the land area is large. However, the smaller the land area,
the more significant influence will be introduced by the GPS
error. There is a problem that GPS module cannot be modified
through Android platform. As a result, it is impossible to
directly improve the GPS module itself.
Since the white Gaussian noise is common in satellite
communications, the GPS signal is affected by this noise
significantly. Collected the GPS data for one steady point (-
6.257905, 53.385598) about 20 minutes by using MEIZU M9
smart phone, the results are shown as Figure 2 and Figure 3.
They obviously show that the distribution of GPS data is
almost normal distribution. In other words, the GPS data are
influenced by the white Gaussian noise.
Thus, white Gaussian noise has such significant influence
on GPS data. Finding an efficient way to filter out such noise is
essential to improve GPS accuracy. In 1960, R.E.Kalman has
introduced a new approach to filter out white Gaussian noise
[5]. This method is named as Kalman Filter. The proposed
application took advantage of Kalman Filter to improve GPS
accuracy.
Figure 2 : Longitude Probability for Steady Point
Figure 3 : Latitude Probability for Steady Point
Kalman Filter has two parts: one is the Time Update
Equations and the other is the Measurement Update Equations.
The former one is used to predict the current state which is
named priori state and get the estimate error covariance. The
latter one is responsible for correcting the priori state based
on observation or measurement. Once the Kalman Filter
finished one iteration, the output is the posterior state which
will be used as the input for the next Time Update Equations. It
will iterate again and again when a new measurement value
comes into it.
The discrete time process can be modeled by the linear
stochastic difference equation [6]:
1 1 1k k k kx Ax Bu w     (2)
Measurement can be expressed as [6]:
k k kz Hx v  (3)
In (2) and (3), 1kw  and kv are process noise and
measurement noise respectively. They are white Gaussian
noise and independent.

3. Time Update Equations (Predict) [6]:
1 1
ˆ ˆk k kx Ax Bu
   (4)
1
T
k kP AP A Q
  (5)
Measurement Update Equations (Correct) [6]:
1
( )T T
k k kK P H HP H R  
  (6)
ˆ ˆ ˆ( )k k k k kx x K z Hx 
   (7)
( )k k kP I K H P
  (8)
More information and explanations about Kalman Filter
equations and operation can be found in paper [6].In above
equations, ˆkx
is the priori state vector that is predicted by the
Kalman Filter, and 1ku  is control input. A is transition matrix,
B is control matrix. kP
is the covariance for ˆkx
. kK is the
Kalman gain that is used to correct the priori state. H is named
measurement matrix. I is identity matrix. Q is assumed to be
the process noise covariance, while R is assumed to be the
measurement noise covariance.
Usually, Q can be obtained through empirical analysis. But
the R is determined by the GPS module in the smart phone. It
can be attained to analyze the GPS data. According to the GPS
data that collected from the MEIZU M9 Smartphone, the
measurement noise variance of longitude is 9
1.55 10
 in
square degrees and the measurement noise variance of latitude
is 9
1.82 10
 in square degrees. This application adopted the
9
1.00 10
 in square degrees as the measurement noise
variance, which still gives good performance. The GPS data
has two parts: longitude and latitude. This two dimensional
vector has two dimensional normal distribution. As a result, the
marginal distribution is also normal. It is possible to apply
Kalman Filter to each dimension
L
L
 
  
and
B
B
 
  
, which
makes it easy to implement in Android Platform. Here, the L is
longitude, the L is the increment of the longitude. Similarly,
the B is latitude, the B is the increment of the latitude.
IV. DESIGN
The design concept and mechanism of this application is
shown by Figure 4. Firstly, the application should get GPS data
from GPS module of Android smart phone. Then, Kalman
filter will be used to reduce the white Gaussian noise. Thirdly,
the filtered GPS data will be shown on the Google Maps. Then,
Gaussian-Kruger Projection will be applied to project GPS data
to plan system coordinates. Finally, the land area will be
calculated by using Trapezoid Method.
Some HCI (Human Computer Interaction) issues have been
taken into account. The GUI (Graphical User Interface) was
simple and easy to use for every person and outdoor activities.
Since the GPS module is one of the most power-consuming
devices in a smart phone, it is necessary to strike a balance
between power consumption and performance. Therefore
empirically, the minimum distance for obtaining GPS notice is
set to 2 metres.
Figure 5 and Figure 6 give the demonstration of the
application operation. Google Maps have been used to provide
the interface to visualize the shape of the land area. The start
point of the user is marked by a blue pin. The path of the user
is recorded by a yellow line, while the green line is marked
between the start point and the current point when user clicks
the “Calculate the Area” button. The area within these two
lines will be calculated and the results will be shown. This
application demonstrates three kinds of data. One is the
distance that the user has walked in real-time. The second is the
area of the land, and the final one is the GPS accuracy in
meters which is returned by GPS satellites. The blue arrow is
used to show the current location of the user when the user
clicks the “Current Location” in Menu. Some basic functions
such as Unit Changing and Map View have been added in this
application.
Figure 4 : Design of Application
Figure 5 : Application Screenshots – 1

4. Figure 6 : Application Screenshots - 2
V. RESULTS AND VALIDATION
In this part, three experiments will be presented; the first
two are to test performance of Kalman Filter, the last one is to
test the land area calculation. The performance of Kalman
Filter was tested by steady point and manoeuvre path. Eleven
land shapes have been chosen to test the area calculation.
A. Kalman Filter Experiment for Steady Point
The first experiment was conducted to validate the Kalman
Filter for the steady point. Applying the Kalman Filter in this
application, MEIZU M9 smart phone was used to collect the
GPS data for the point (-6.257905, 53.385598) by 841
measurements. This point was randomly chosen, the true GPS
data was obtained manually on Google Maps by clicking the
exact point. The results are shown in Figure 7 and Figure 8.
The green line is the true location GPS coordinate, while the
red line is the GPS data using Kalman Filter and the blue line is
the GPS data without Kalman Filtering. The red line follows
the blue line; however, the red line (Kalman Filter) is closer to
true value (green line) than the blue line, which means the
Kalman Filter worked as expected. More specifically, at the
500th measurement and 600th measurement, the raw latitude
(blue line) is influenced by white Gaussian noise significantly
referring to Figure 7. However, latitude (red line) using
Kalman Filter is more stable and closer to the true latitude. In
Figure 8, the raw longitude (blue line) is affected worse by
white Gaussian noise. But the longitude (red line) using
Kalman Filter is also closer to the true longitude. Finally, the
Kalman Filter improves the GPS accuracy up to 1.97m seeing
the Figure 9. The left green point is true point and the right red
point is the Kalman Filter Point.
B. Kalman Filter Experiment for Manoeuvre Path
The second experiment was designed to validate the
Kalman Filter for manoeuvre path. Using the same smart phone
MEIZU M9 and the proposed application, the manoeuvre path
started to walk from the road in the Dublin City University.
This road is relatively straight without large curve as the white
line in Figure 10. The blue pin mark in Figure 10 indicates the
start point. The blue line indicates the GPS data using Kalman
Filter while the red line indicates the raw GPS data without
Kalman Filter. Improvement on GPS accuracy caused by
Kalman Filter is obvious by comparing these two lines.
According to Figure 10, Figure 11 and Figure 12, the red line is
influenced by the white Gaussian noise significantly that
jumped around the true path. But the blue line is much
smoother than the red line and much closer to the true path.
Figure 7 : Latitude of Steady Point using Kalman Filter
Figure 8 : Longitude of Steady Point using Kalman Filter
Figure 9 : True Point and Kalman Point of Steady Point Experiment

5. Figure 10 : Manoeuvre Path – 1
Figure 11 : Manoeuvre Path – 2
Figure 12: Manoeuvre Path - 3
C. Land Area Calculation Experiment
The third experiment was designed to verify the land area
calculation that proposed by this paper. Practically, this
application has been tested in Dublin, Ireland. Eleven land
shapes including regular and irregular shapes have been chosen,
the results are shown in Table 1. It is not easy to get the ground
truth of the land shapes from the authorities. Thus, the “True
Area” results were obtained by calculation from land shapes’
GPS coordinates. These coordinates were obtained from the
Google Maps manually according to the land shapes. The
column “Calculated Area” is the land area calculated by using
this application. Obviously, the average error is 3.64% which
provides a robust performance in this case. One thing should be
noted is that the No.5 land shape got a very small error, while
the No.9 land shape got a relatively very high error. One reason
may be the fluctuation of GPS signals.
This experiment was done on several days under sunny
weather condition. Since the GPS signals are affected by the
weather and time, the signals can vary heavily on a day—to-
day basis. More experiments should be done in the future under
different time and weather conditions to check the performance
of this application. Moreover, GPS signal is affected by
different buildings. Different regions should be chosen to test
the performance such as countryside and build-up city.
VI. CONCLUSION AND FUTURE WORK
The land area calculation has been implemented as an
Android application in this paper. Kalman Filter has been
employed to improve GPS accuracy. According to the tests, the
average error of the land area calculated by this application is
less than 3.64%. In summary, there are some benefits of this
application. This application can run on any Android phone
with GPS module. It provides a relatively high accuracy in
calculation. However, it also has some shortcomings. The
accuracy of the first GPS signal is very important and can exert
significant influence on the subsequent GPS data especially for
using Kalman Filter. The time to wait for the first GPS signal is
varied from half of a minute to few minutes. This application
cannot be used in indoor and underground environment.
The future version can be improved by using other sensors
and resources. It can utilize the network or Bluetooth to
provide indoor localization. Built-in ephemeris can be used to
reduce the waiting time for the first GPS signal.
Table 1 : Land Area Calculation Experiment Results
Land
Number
True
Area(m²)
Calculated
Area(m²)
Error(m²) Error(%)
1 6500 6708.43 208.43 3.21%
2 3135 3280.92 145.92 4.65%
3 1150 1108.08 41.92 3.65%
4 1325 1355.52 30.52 2.30%
5 11770 11758.28 11.72 0.10%
6 21104 21473.48 369.48 1.75%
7 34841 36340.19 1499.2 4.30%
8 4875 5113.83 238.83 4.90%
9 3250 3486.09 236.09 7.26%
10 1326 1381.82 55.82 4.21%
11 662.5 637.95 24.55 3.71%
Average Error 3.64%
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