Unknown Source Localization Using RSS in Open Areas in the Presence of Ground Reflections Ryan J. R. Thompson, Ediz Cetin, and Andrew G. Dempster School of Surveying and Spatial Information Systems University of New South Wales Sydney, Australia
[email protected]; {e.cetin, a.dempster} @unsw.edu.au
Abstract-This work explores the localization of unknown RF transmitters
in
open
outdoor
areas
using
Received-Signal
Strength (RSS) measurements. The positioning accuracy in RSS is typically limited by the behavior of the path-loss environment. The
motivation
for
this
work
is
the
localization
of
RF
interference in the GPS LI band but as it is not legal to broadcast
in that band the scenario is explored with real experiments using
Wi-Fi devices. The Received Signal Strength Indicator (RSSI) output
of
a
commercially
available
Wi-Fi
chipset
was
characterized and found to be suitable for measuring path-loss by using passive monitoring of an access point and by applying a spline fit to the histogram of the incoming RSSI measurements. A
sensor network of 5 sensor nodes was then setup on an oval over 2 an area of 150m • To verify a two-ray path-loss model, RSSI was measured at a number of points at height combinations of 1.05m and 1.55m. The measured path-loss was found to be close to what was given by the two-ray path-loss model, with significant dips in the path-loss visible in the 1.55m height data. The position was then solved using the RSSI values at each test point using the log normal path-loss model. Increasing the sensor and transmitter height was found to significantly increase the positioning error. For the data recorded for nodes and transmitter at a height of 1.05m, the Root-Mean-Square-Error (RMSE) of the test points was 10m, and for the 1.55m case the RMSE was equal to 34m. With this model verified, Monte-Carlo simulations were used to evaluate the positioning performance that could be expected in the
GPS
L1
band.
It
was
observed
that
the
positioning
performance was poor if the transmitter was located too close or too far from the sensor nodes, depending on the heights of the transmitter and receivers and the sensor network topology. Hence, for robust localization to be achieved, another alternative approach to solving the positioning equations that takes into account the variations in the path-loss is required.
Keywords-path-loss; strength
I.
two-ray
model;
localization;
signal
INTRODUCTION
Due to the weak signal power of GNSS signals, they are vulnerable to sources of Radio-Frequency Interference (RFI). Any interference that disrupts the operation of equipment that utilizes these GNSS signals needs to be detected and geo located quickly to ensure safety and integrity. This work is part of the GNSS Environmental Monitoring System (GEMS) [1] being developed that looks to detect and geo-Iocate any sources of RFI in a timely and accurate manner over a wide area. One
978-1-4673-0387-3/12/$31.00 ©2012 IEEE
possible scenario for the application of this system is protecting the GBAS system [2] at an airport providing DGPS corrections and integrity information for vertical aided aircraft landings. Traditionally there are two methodologies for geo-locating unknown RF sources; those that use the Angle-Of-Arrival (AOA) of the incoming signals to triangulate the transmitter position [3], and those that use the Time-Difference-Of-Arrival (TDOA) of the incoming signals in multi-Iateration [4]. A geo location system that uses AOA will have expensive hardware and computational requirements due to the need for antenna arrays and beam-forming processing. A geo-Iocation system that uses TDOA requires very accurate timing synchronization between sensor nodes and will not be able to localize narrowband-type interferers, as the signals need to be wideband for achieving good estimation of time-delays. In a system that can calculate AOA and TDOA it will also be possible to calculate RSS measurements with little modification. The positioning accuracy in Received-Signal Strength (RSS) is typically limited by the behavior of the path loss. The work presented here concentrates on the use of RSS for localizing unknown RF sources in open outdoor areas where a ground reflection will make the path-loss measurements noisy [5]. Theoretical results from the two-ray path-loss model that take into account a reflection from the ground show greater variability when the transmitter and receivers have greater heights. This work aims to confirm this model with experimental results and look at the impact this will have on positioning accuracy when using the log-normal shadowing path-loss model solving for the transmit power and path-loss exponent along with position [6] in the L1 GPS band. This paper is structured as follows: In section 2 two path loss models that are used in RSS are compared. In section 3 the methodology used in testing and taking RSSI measurements from Wi-Fi devices is shown. In section 4 the results of field experiments are presented and analyzed. In section 5 a comparison is made between the path-loss for Wi-Fi and GPS L1 frequencies. In section 6 simulation results at the GPS L1 frequency are explored. Concluding remarks are given in section 7.
1018
PATH-LOSS IN RSS POSITIONING
II.
A.
Log-normal shadowing model
The classical model used to define path-loss is the log normal shadowing model [7]:
P,
=
Po -1 On
iOg,,( :J
+c,
(1)
where Po is the reference transmit power measured at a distance do, Pd is the power measured at a distance d, n is the path-loss exponent which defines the rate at which the power falls, and if is the variance of the shadowing. In free-space the value of n is equal to 2, and in practice can vary depending on the surrounding environment. The variance of the shadowing if is also dependant on the surrounding environment and can increase significantly in complex environments.
B.
Two-ray reflection model
Another model that can be used to define path-loss is the two-ray reflection model. This model takes into account the impact a reflected signal from the ground has on the signal power.
Figure l. The geometry used for the two-ray reflection model.
Fig. 2 depicts the RSS values using (1) and (2) for a
transmitter with Po = OdBm, n=2, er=9, at a frequency of
1575.42MHz, with receiver and transmitter heights of 1m The RSS values given by the two-ray model move above and below the values given by the log-normal model as the reflected signal constructively and destructively combines with the Line-Of-Sight (LOS) signal. Also shown on Fig. 2, as a blue dot, is the distance of the first Fresnel zone. The first Fresnel zone distance can be defined as [5]:
(5)
In this model the path-loss can be defined as [S]:
r
where L = hI + h (2)
where d is the distance, A, is the wavelength of the transmitted
r
and � = hI - h
'
and describes where the
path-loss begins to decay due to the same mechanism as free space losses only. After this distance the path-loss eventually begins to decay at the same rate as the log-normal model with n=2.
signal, d+ 0d is the distance of the reflect path: I I
(3)
E
co
- 20
(j) (j) a:
-30
�
and r is the reflection coefficient. The reflection coefficient is different depending on whether the transmitted signal is vertically or horizontally polarized. In this work the transmitted signal is assumed to be vertically polarized and the reflection coefficient is given by
--
l�_ : :�:___�_�_ I I I
I
(�cr -COS(O)2) 2 sin(O) + (�cr -COS(O) ) sin(O) -
�
I I I I I1 III I I I I1 III
2RM LN
I I I II II
_1___ 1 1. .1 1. LI.LI___ 1.. _
-40
I I I I -1 - -1 I I
I I II III I I I II III I I I11111 I I I I T T TiITI- - - T - T i- I- I-, I I II III I I I I I III
10
r= ----��====
__
1
Distance (m)
Figure 2. A comparison between the path-loss for the log-normal and two ray reflection model. {circle: l st Fresnel zone distance}
(4)
III. where e is the incident angle of the ground reflection and £r is the relative permittivity of the ground material. Some typical values for £r include 1 for a vacuum, and 9 for grass. The geometry for the terms of the two-ray reflection model is shown in Fig. 1.
MEASURING PATH-LOSS USING WI-FI
The work presented in this paper is motivated by RFI localization in the GPS Ll band. However, the GPS bands are protected and it is not legal to transmit in these bands. An alternative approach to evaluate the performance of the RSS based localisation is to measure the path-loss in another band such as the ISM band using IEEES02.11 Wi-Fi devices. These devices provide RSSI outputs, that can be equivalent to RSS, that have been used by a number of authors for path-loss
1019
measurement and positioning purposes [8],[9]. The quality of the RSSI values given by these devices can be variable however [10]. After evaluating a number of different Wi-Fi adapters with different chipsets during this work, one based on the ZyDAS 1211b chipset [11] was found to give a usable RSSI output for the purpose of measuring path-loss. An investigation of the RSSI output performance of this chipset is described in the following section.
A.
Logging RSS from Wi-Fi Devices
The most common method for making RSSI measurements is through measuring the signal strength of packets sent by access points in response to probe requests. This is called
'active scanning' [12] as the Wi-Fi client device is actively requesting probe responses from surrounding access points on different channels. This is shown in Fig. 3. However, this method can suffer from coverage and latency problems, as the probe request sent by the client must be strong enough to be decoded by the access point, and the access point must reply in time. Probe Requests
)))))) ((((((
Probe Responses
To compare the coverage performance of the active and passive scanning modes a USB Wi-Fi dongle with a Zydas 1211b chipset with a detachable antenna was placed in both active and passive modes one after another and 5 minutes of data recorded. An image of this device is shown in Fig. 5. For active scanning the manufacturer's drivers for Windows XP was used along with the application Network Stumbler [13] to record the RSSI values. For passive scanning mode, a modified version of the zd12IIrw [14] drivers was used under Ubuntu 9.04 along with the aircrack-ng [15] package, and tcpdump was used to capture the radiotap headers of the incoming Wi-Fi packets. Over 5 minutes, the active scanning technique was able to make RSSI measurements on 10,471 probe responses
from 11
unique
Service
Set Identifiers
(SSIDs). Over 5 minutes, the passive scanning technique on the other hand was able to make RSSI measurements on 4,958 packets from 11 unique SSIDs.
B.
Dynamic Test
As part of the Window's Windows Management Instrumentation (WMI) interface [16] it is possible to poll the Wi-Fi chipsets driver at a periodic rate to get the RSSI of the access point that the device is currently connected to. Using this technique it is theoretically possible to get more RSSI measurements from an access point than when using the probe request/response technique, which generally provides an RSSI measurement every 2 seconds. To evaluate the dynamic response of the Windows and Ubuntu based measurements the RSSI was measured as the antenna shown in Fig. 5 was rotated 90 degrees and back again.
Figure 3. The client-server interchange of packets when measuring RSSI in 'active' scanning mode.
---
Another method for making RSSI measurements is by placing the Wi-Fi device in a 'passive'[12] or 'promiscuous' monitoring mode. In normal operation a Wi-Fi device is programmed to make available packets that are addressed to its particular MAC address. In passive mode however the device can decode all incoming packets. As an access point transmits beacon packets periodically (up to 20Hz) for infrastructure purposes, the RSSI measurements can be taken from these instead. This method is shown in Fig. 4.
(((((( ))))))
Broadcast Beacons
Figure 4. The monitoring of the broadcast beacons from access-points in 'passive' scanning mode.
rotation
·ments.
The change in RSSI as the antenna was rotated is shown in Figs. 6 and 7. In both figures the measurement rate is 20ms. As can be observed, the response in the RSSI is markedly different between the Windows and Linux based set-ups. Another difference is that the WMI interface provides the RSSI value in dBm. The Windows based RSSI value measurement values appears to be filtered whereas the Linux based ones appears to be change rapidly. As shown in Fig. 7, the RSSI values measured in passive mode under Ubuntu change almost instantly. The RSSI values taken using the
1020
Windows driver are slow to react with some sudden jumps and appear filtered. It takes almost 10 seconds for the RSSI values to settle. From these results the use of passive mode is recommended for this chipset, and will be used in the field experiments which are described in the proceeding sections.
these vanatlOns must be caused by the device itself and not from a shadowing effect or from the access point, as the outljers only occur when the attenuation is high. Analysing how the histogram of the RSSI changes with attenuation, it is apparent that the highest RSSI values correspond to the true value, and the others are anomalous.
, 1__ � ____ L ____ , , , (f) (f) a:
-40
-
-45
-
-50
80 en 60 (f) a:
10
20 30 Time (s)
40
50
20 �-----L--�UL----� 550 600 650 700 750 Measurement (20ms)
Figure 6. The RSSI values from the Windows NDIS interface while rotating the USB adapter's antenna.
Figure 9. The raw RSSI values at two different attenuations.
The anomalous values do not occur as regularly as the true values. In order to find the true RSSI value, a spline fit is applied to the histogram of the RSSI values over an observation period and the location of the global maximum is used as the true RSSI value. In Fig. 10 the shape of the spline fit is shown for the values corresponding to the attenuation of 16dB shown in Fig. 9.
(f) (f) a:
50
---- +
- - ---l - - - - -1- - - - - I- - -
45L-----��--L-----L-----L-� 20 5 15 10 Time (s) Figure 7. The RSSI values from the modified zd l 2 l l rw Linux drivers while rotating the USB adapter's antenna.
1000 C.
(J)
Characterizing RSSI Values
C
:J
To characterize how RSSI changes with RF power the USB Wi-Fi adapter was connected directly to an access point through a variable attenuator as shown in Fig. 8. The access point was set to transmit beacon packets every 20ms, allowing 50 RSSI measurements to be taken per second. The modified zd1211rw drivers provide the RSSI as an unsigned integer with values ranging from 0 to 128. The attenuation was varied from 3 to 89dB and the RSSI measured at each step. Wi-Fi Access � Point
..,... / t-----. / variable
I
8
I I I - - - - -,- - - - - � - - - - -,- , , ,
I
I
I
I
500: - - - - -:- - - - - � - ----:-o
,
- �
-
.. , - - _....--'--
65
70
75 RSSI
80
85
Figure 10. The spline fit of the histogram of RSSI at l6dB attenuation
In Fig. 11 the response of the RSSI as the attenuation is increased is shown before and after using the spline fit of the histogram for 10 seconds of RSSI values. The RSSI falls linearly as the attenuation is increased and can be fit with a linear model:
USB Wi-Fi dongle
attenuator Figure 8. The setup for characterising the RSSI from the USB Wi-Fi dongle.
The values of the measured RSSI are shown over time at two different attenuation levels in Fig. 9. The RSSI appears to follow a Gaussian distribution but there are also outliers and unexpected behaviour which has been observed from the RSSI values from various different Wi-Fi chipsets [10). This behaviour occurred with the Windows based setup as well. As the Wi-Fi device is connected directly to the access-point
RSSI (x) = 101.114-1.072(x)
(6)
where x is the amount of attenuation in dB. As can be observed in Fig. 11, the fall in dB is slightly steeper than what would be expected at 1.072dB per dB of attenuation The fit has an RMSE of 1.022dB. For the raw values at higher power levels the RSSI begins to jump around. With these
1021
adjustments, the RSSI can be used for taking reliable measurements of the signal strength. Without this fix, the RSSI will not be accurate for strong signal strengths, which would be when the access point is located within a close distance.
(C) 2012 DigitalGlobe, GeoEye, Sinclair Knight Merz, Cnes/Spot Image; Map data (C) 2012 Google, Whereis(R). Sensis Pty Ltd.
In Fig. 13 the value of the RSSI from three of the sensor nodes is shown at one of the test locations. Although noisier than the measurements taken when the devices was connected to the access point through an attenuator, the values do not drift over short periods of time.
-35
C/) C/) a:
E
,-----�--�---�___i ----- - - - I- - - - - - - 1 - - - - - - - L 1
1
--
-40
81 82 83
CO � -45
o
20
40 60 Attenuation (dB)
(f) (f)
0:
80
-55
Figure II. The fall in RSSI before and after the spline calibration technique.
IV.
A.
-50
1.256
FIELD EXPERIMENT
Experimental Setup
To explore the path-loss in an open outdoor environment a sensor network of 5 sensor nodes was created using laptops with the Wi-Fi adapters described in Section V with an access point used as a rover. The experiment took place on an oval 2 field with an area of over 150m . All of the devices were attached to 1/4 wavelength dipole antennas of the same make in an attempt to normalize the antenna radiation patterns. RTK GPS was used to measure the positions of the sensors and the rover at each position. At survey marks located around the field, the RTK GPS provided positioning accuracy in the range of 1O-30cm. The rover was moved to different locations and the RSS values were collected at a number of test points with the transmitters and receivers at a height of 1.05m. The process was then repeated with transmitter and receiver heights of 1.55m. In Fig. 12 an image of the oval where the experiment took place is shown. The green markers are the locations of the sensor nodes. The southernmost sensor node was placed closer to the centre to allow test points outside the geometry of the sensor network to be taken.
1.256
1.256 1.256 Time (s)
x
10
9
Figure 13. The RSSI values measured at different sensor nodes SI, S2, and S3, over time with the transmitter located at one of the test points.
B.
Path-loss Behaviour
The RSSI values taken at a height of 1.05m was used to create a log-normal model of the path-loss environment. The resulting equation to describe the path-loss was:
Pd = 2.809-1O·3.041·loglO (d)+0'
(7)
where cr is equal to 2.964dB. The test points, along with the log-normal fit, and the path-loss given by the two-ray model is show in Fig. 14. There are some points that do not follow the log-normal model, but in general the RSS values fall linearly with distance. There is some variation which occurs with the dips in the two-ray model. Overall the RSS values also appear to fall in value at a faster rate then what is implied with the two-ray model and the cause of this is not known. •
Points
-- 2 RM -- LN
C/) C/) a:
-
50
-60
II I I II
I
I I I
Distance (m) Figure 14. The path-loss behaviour for the 1.0501 data set.
1022
In Fig. 15 the path-loss behavior is shown for the data collected at height of 1.55m. The resulting log-normal path loss model took the form:
initial guess. The true position, Po, and n are used as the initial guess, but due to the non-convex shape of the cost function it is not guaranteed to converge to the global minimum.
Pd = 16.93-10·1.846·10glO (d)+0'
In Fig. 16, the Cumulative Distribution Function (CDF) is shown for the position errors for the 1.05m and 1.55m data when solving using the log-normal path-loss model. For the data at 1.05m the size of the first Fresnel zone distance is small and the path-loss values behave smoothly for most of the recorded data points. In Fig. 17 the behavior of the position estimates relative to the true locations is shown. At this height, the positioning performance is quite good. For the 1.05m data the RMSE of all of the points was close to 10m
(8)
where cr is equal to 3.063dB. Due to the increased height of the transmitter and receivers, the first Fresnel zone distance is located after a significant number of the observation points. A large dip is visible at a distance of 35m and this follows the dip given by the two-ray reflection model. Although the RMSE of the fit for 1.55m is of similar magnitude to the fit for the 1.05m data, the distribution of the residuals are a lot less normalized.
(after removing divergent points). For the experimental data at
1.55m the distance of the first Fresnel zone is larger and there are dips in the path-loss due to the ground reflection as shown previously in Fig. 15. This makes it more difficult to solve for position as there are locations where no sensible path-loss exponent value for the points can be found, causing a significant degradation in positioning performance. For the 1.55m data the RMSE of all of the points was close to 34m (after removing divergent points). At a height of 1.55m there are also more divergent points. This is shown in Fig. 18.
0.8
Distance (m) Figure 15. The path-loss behaviour for the 1.55m data set.
C.
I I , I --- �---- �---- '----4-
0.6 x
Positioning Results
Using the Levenberg-Marquardt[17] technique, the positioning equations based off the log-normal shadowing model were solved using the RSS values taken at each test point. As this paper addresses unknown sources, the transmit power Po was solved along with the path-loss exponent nand the position (simplified to (x,y) in 2D)[6]. The set of positioning equations and the RSS measurements can be represented by: d = f(O) + e
i:L
I I
I I
I I I
I
I _rT .,...I ---i- - - - --i- - - - -1- - --
0.4 0.2
--
--
0
10
20
h = 1 . 05m h = 1 . 55m
40
30
Position error (m)
50
60
Figure 16. CDF error comparison of positioning results at height of l.05m and 1.55m.
(9)
where d is the vector of RSS estimates, f(O) is the set of positioning equations evaluated at 0, and e represents the measurement error. In this application, the Levenberg Marquardt algorithm is used to minimize the least-squares cost function e to get an estimate of the position estimate
iJ: (10)
I *- El ILl � ---- 0--�, -------I *" El I
-40
-----
-60
------
:
,
+/�,
- - - - �L - - �-
-50
0= argo minCe)
(11)
where C-I is the covariance matrix of the measurements. The Levenberg-Marquardt is an iterative solver that requires an
1023
o
--t-
--
50
x (m) Figure 17 The positioning error for selected test points for the l.05m data. (*: position estimate, 0: sensor nodes, sqr: actual positions)
80 ,-----�----�--, 60
I _____
L _____ L _____ L _____
I GJ !.!.40 I� I I o I I >- 20 - - - - - � ,!- - - - �o- - - - - � I J I I 10 I� rI o � � I -+ I I : n _____L____� _ 20L-____-L______�� _____
__1___
_____
_____
-
-----
-60
-20
-40
o
40
----
-50
-100
20
--
-----
0
-----
50
100
x (m)
60
x (m) Figure 20. The position error for a test-point. (*: position estimate,
sensor nodes, sqr: actual position)
Figure 18. The positioning error for selected test points for the 1.55m data. (*: position estimate.
0:
sensor nodes, sqr: actual positions)
E. D.
Effect of Ground-Reflections
The variations in the path-loss caused by the ground reflections increases the positioning error. Under the same conditions and using the same equipment increasing the height of the transmitter and receivers was found to dramatically increase the error of the position estimates. In Fig. 19 the RSS values are highljghted that were used in computing the position solution shown in Fig. 20. At this test point the RSS values do not decrease monotonically with distance. As a result the minimization algorithm finds a solution that has a large position error. In trus situation a more advanced technique will be required. This behavior makes positioning difficult for transmitters or receivers that are placed higher, making RSS less robust depending on the heights of the transmitter and receivers.
Dilution of Precision
For the test points located outside the geometry of the sensor network, the position error becomes greater and has a greater risk of being divergent. This can be explained by the increase in the Dilution Of Precision (DOP) as the transmitter moves away from the sensor network[6l. Solving for Po along with n dramatically increases the rate the Cramer-Rao Lower Bound (CRLB) increases as the transmitter moves away from the sensor network. The CRLB sets a lower bound on the variance of any unbiased estimator and is defined as the inverse of the Fisher Information Matrix (FIM): (12)
df where H(O)=-. dO CRLBB (0) = [I(OWl
Distance (m) Figure 19. The path-loss model and points used as a specific test point. {line: fitted path-loss model, dots: path-loss from data, triangles: RSS at test point}.
0:
(13)
In Fig. 21 the CRLB is plotted for the sensor network used in the field experiment with n=2 and 0'=3. At location (0,0), n=2, 0'=3, for example, the viCRLB is equal to just 12.S7m. At the location shown in Figure 22, the vi CRLB is equal to 74.S0m, a significant increase. At the edges, the exponential like behavior of the increase in the CRLB is visible. In Fig. 23, the solution given by the Levenberg-Marquardt solver is shown for the test point shown in Fig. 22. As can be observed, the values of Po and n have been overestimated in this case, resulting in a position estimate with a large error.
1024
,ICRLB
FRESNEL ZONE DISTANCES
TABLE I.
ht
l.5sm l.ssm l.ssm
1.ssm 3.0m 10m
300 200 100 o
76.97m 148.67m 476.98m
I I I
30
I
I
E
50 0
I
-50
>-
c:J
,0 , , I o ,0 I ' ,., ---�-------- �-------- �� :0 : : - - - � - -----..a- � - - - - - - - - � I I I - - - � - -.� .!.� - - - � - - - - - - - - � .. . .r>I -..�I - - - - - - - - I - - - - - - - - I .. ---+-------- ,-------- �-
-60
, ,
�I , ,
I I I I I --
WiFI
GPS L1 c,----,----,---;-----,--' -,--; --
+
,
I I I I I I I I I I I I I I_J I ________ '- __ 1 __ 1 l _1_ 1 J _I J 1 __ , I I I I I I I I I I I I I , I I I I I I I I I I I I I I I I I I I I
•• ••
-100
Distance (m)
•
• ••
-150
..
-50 x
I
I
a
50
Figure 24. The path-loss using the two-ray model. (circles - 1st Fresnel zone distance).
VI.
(m)
Figure 22. The position error for a test-point. ( *: position estimate, sensor nodes, sgr: actual position)
0
A.
CD
GPS Ll BAND
Small Area Sensor Network In a GBAS installation at one particular airport [18] the
2- -20
antennas for the reference stations have a height of 1.55m and have typical separations of 100m. One possible topology for the interference localization network is to have 6 sensors in a star configuration with one sensor located in the center that closely surrounds the GBAS reference antennas. The radius of the network is set to 500m and is shown in Fig. 25 with the sensor nodes represented by the circles. In Table II the RMSE after 10,000 simulation runs is shown for different transmitter locations and heights. Divergent points (taken as 6v'CRLB) are removed from the calculation of RMSE.
-40
Distance (m) Figure 23. The resulting log-normal path-loss model (Po=149.90, n=8.69) and points used as a specific test point. (line: fitted path-loss model, dots: path-loss fyom data, triangles: RSS at test point).
V.
SIMULATIONS AT
In this section the positioning performance is explored in the GPS Ll band by using the two-ray model to generate the RSS values with added noise. Based on the RMSE of the fits from the Wi-Fi data the value of the shadowing noise added (Gaussian shaped) will be equal to 3dB.
0:
E C/) C/) 0:
:�
-40
:g" (/) -50 (/) a:
-----:- --� I I
GPSL1 50.01m 96.34m 291.61m
I
-
-
Figure 21. The CRLB surface using the model fit for the 1.55m data for the sensor network used in the field experiment.
Distance
Wi-Fi
hr
COMPARISION BETWEEN
GPS Ll AND WI-FI
TABLE II.
In the GEMS system[1], the interference signals will be at the GPS Ll frequency of 1575.42GHz, not at the 2.4GHz frequency of the Wi-Fi used in the field experiment. The different frequencies will have an impact on the path-loss behaviour and the location of the first Fresnel zone distance. The distance of the first Fresnel zone distance at different heights and wavelengths is shown in Table I. In Fig. 24 the path-loss is shown for Wi-Fi and GPS Ll for transmitter and receivers at a height of 1.55m. At this height the Fresnel distance is 16.96 metres further for Wi-Fi compared with GPS Ll. As a result, positioning with RSS will perform better at GPS Ll when compared with Wi-Fi.
SIMULATED POSITIONING RESULTS
ht
t-position
,ICRLB
RMSE
10m 3m 1.55m
(250,250) (250,250) (250,250)
130 130 130
114.64 64.17 77.384
10m
(500,500)
667
551.29
3m 1.55m
(500,500) (500,500)
667 667
201.47 846.39
In Fig. 25 the distribution of the posltton estimates is shown for a number of the simulation runs. At the transmitter location of (250,250) with a height of 10m, the position
1025
estimates resembles the true location and have a RMSE of 114.64m. Even for this closely spaced sensor network the positioning error is large and not suitable for robust localisation performance: the aim is for error in the range of 510m. In Fig. 26 the distribution of the position estimates is shown for a number of simulation runs for a point located outside the sensor network at (900,900). The transmitter again has a height of 10m. At this location, the distribution of the position estimates is more spread out. There is also a noticeable bias trend towards the centre of the sensor network.
-� -
500
I
0:
I
I
+ +,'*;
I
:0
I I I I I 1 -' - L ---- _1-- - - -1'1\- --------V I I I I
o
1
1
I
I
-400
-200
- t- -----1-- -
-500
I I I - -0- ----1 -- - - -jo
x
(m)
200
Heieht
Position
-vCRLB
RMSE
10m 3m l.55m
(2500,2500) (2500,2500) (2500,2500)
1303 1303 1303
905.93 1016.2 1037.2
10m
(5000,5000)
6675
11157
3m l.55m
(5000,5000) (5000,5000)
6675 6675
15311 11102
In Fig. 27 and Fig. 28 the distribution of the posItIon estimates are shown for a test point at (2500,2500) and (7500,7500). The distribution of the position estimates in the simulation runs look similar to the results found for the small area sensor network with a radius of 500m, after being scaled by a factor of 10. The -vCRLB values are also scaled by a factor of 10. Due to increased distance between the transmitter and receivers the path-loss is much more uniform at the test locations as the Fresnel point has been cleared significantly. The RMSE values are also more uniform for the different heights as well.
- - - -:- - - - -Q- ----:- ---- �I
400
Figure 25. The distribution of the position estimates for a number of simulation runs with transmitter at (250,250).(*: position estimate, 0: sensor nodes. sqr: actual position)
I
g
500
>.
o �OO
I I I I , ____ 1 ___ -' __-if. "",! _ -* 1 _ t_ -' __ *' -+ '-+ : I I I j 1
1
P
1 --
I o
500
1000 x
1500
1
1
-� ----�----�---- �----�--
1
-
----
-4000
1
0
----
-2000
----
0
(m)
----
2000
--
4000
Figure 27. The distribution of the position estimates for a number of simulation runs with transmitter at (2500,2500). (*: position estimate, 0: sensor nodes, sqr: actual position).
2000
15000 �-----,---,
(m)
1
Figure 26. The distribution of the position estimates for a number of simulation runs with transmitter at (750,750). (*: position estimate, 0: sensor nodes. sqr: actual position).
B.
-- - O�1 - - - � - - - � - - - � �O 1
x
I I I I I -0- - - -j----1 - - - T - - - -i - I I I I I 1 1 1 1 0 o
-2000
-6000
�---�---�----�---�---�--
-500
-�----t----�----{----�--
�OOO
1 1 - - - .I.- - - -' --
� - - -�-
0
>.
1500C=�-� ��= 1 -�-� �1 -� � � �1 -�-� � �� 1 -�-� �1�+� = , I I I I 1000
SIMULATED POSITIONING RESULTS
TABLE III.
Wide-Area Sensor Network
The small area topology described in the previous section has trouble localizing transmitters located outside the sensor network. The area of an airport is large and the interference source is likely to be located away from the GBAS reference antennas. To provide greater coverage the sensor nodes can be placed further apart. To explore this scenario 6 sensors in a star network with a radius of 5000m with one sensor located in the center is used in the simulation runs. The results of the simulation runs are shown in Table III for different transmitter heights and positions.
10000
: ------:- - - - - -t*- - - - - � - ----
5000
: - - - - - 0 - - +4:* �- - - , -----
o -5000
1
1
I
I
1
I
cL l'
•
+,� +
: ++ -IQ): +: :- - - - - Q - - - - -:- - - - - - � - ---:0 :0
1
0:
1
: - - - - -
