Journal of Global Positioning Systems (2005)
Vol. 4, No. 1-2: 245-257
Inverse Diffraction Parabolic Wave Equation Localisation System
(IDPELS)
Troy A. Spencer ¹, Rodney A. Walker ¹, Richard M. Hawkes ²
¹ Cooperative Resarch Centre for Satellite Systems (CRCSS), QUT University, Brisbane, Queensland, Australia
e-mail: [e-mail]; Tel: + 61 7 38641772; Fax: [phone]
² Navigation Warfare, Electronic Warfare and Radar Division, Defence Science Technology Organisation (DSTO), Edinburgh, South Australia,
Australia
Received: 22 April 2005 / Accepted: 13 July 2005
Abstract. While GPS is a relatively mature technology,
its susceptibility to radio frequency interference (RFI) is
substantial. Various investigations, including the Volpe
Report (Volpe, 2001) which was the result of a US
Presidential Decision Directive (PDD-63) assigned to the
Department of Transportation (DOT), have recommended
that methods should be developed to monitor, report and
locate interference sources for applications where loss of
GPS is not tolerable. With GPS becoming an integral
utility for developed society, the significance of research
projects that enhance and expand the capabilities of GPS
RFI localisation is highly important.
In response to this requirement for GPS interference
localisation, a novel technique called “Inverse Diffraction
Parabolic Equation Localisation System” (IDPELS) has
been developed. This technique exploits detailed
knowledge of the local terrain and an inverse diffraction
propagation model based on the Parabolic Equation
method (PEM). In wave-propagation theory, an inverse
problem may involve the determination of characteristics
concerning the source, from field values measured at a
certain point or certain regions in space. PEM is an
electromagnetic propagation modelling tool that has been
extensively used for many applications. This paper will
present simulation and field trial results of IDPELS.
Simulation results show that this technique has good
promise to be useful in locating GPS jamming sources in
highly-complex environments, based on networks of GPS
sensing antennas. Results also show that the method is
capable of locating multiple interference sources. Trials
concerning the practical application of IDPELS are also
provided. With measured lateral field profiles recorded
with a single moving sensor platform in a van, results
indicate IDPELS to be a pragmatic localisation technique.
Key words: Parabolic, Inverse Diffraction, Propagation,
Localisation
1 Introduction
An area that has received considerable research and
development in recent times is the mechanism that
discovers the spatial relationship between objects. This
process is referred to as localisation and has been
extensively applied. Areas where localisation can applied
include autonomous mobile robot navigation (Adams,
1999), local neural networks (Weaver et al., 1996), E-911
(Biacs et al., 2002) and airborne electronic warfare (EW)
systems (Stimson, 1998).
After World War II, there was extensive research and
development of radar-directed weapon systems and
secure communication systems. This saw EW-based
receiving systems, particularly Electronic Support
Measures (ESM) evolve to provide the location of an
enemies signal’s source (Sherman, 2000). The
development of such EW intelligence functions occurred
for several reasons. One reason for ESM localisation is
because the correlation of source location with the
electronic order of battle (EOB) can aid in identifying the
signal being analysed. Another reason for ESM
localisation concerns the ability to assist in real-time
threat assessment. Real-time threat assessment provides
an increase in situation awareness (SA) for both people
and various on-board electronic systems (Vaccaro, 1993).
With real-time situational awareness, effective prompt
responses can be performed to avoid or minimise the
impact of an opponents attack. By having localisation
and real-time information, both of these factors will assist

246 Journal of Global Positioning Systems
the mitigation of hostile electromagnetic aggression
against GPS.
GPS which is used as a supplemental means of
navigation by avionics systems also has a wide range of
other important uses (Spencer et al., 2003). These
diverse uses range from network time synchronisation,
criminal investigations or even for archaeological
discoveries. With the unabated penetration of GPS into
civil infrastructure, the possible loss of GPS service could
have damaging consequence to users (Baker, 2001).
Since the inception of GPS as a supplemental means of
navigation, the FAA became an organisation with a
primary interest in ensuring the integrity and availability
of GPS signals. While early FAA programs focussed on
RFI prevention, it latter became clear the GPS would
require a significantly greater real-time RFI source
localisation capability (Geyer et al., 1999). Other RFI
localisation research has shown that a network of sensors
can provide an instantaneous estimate in relation to the
direction-of-arrival (DOA) of RFI signals (Jan et al.,
2001). The continuous real-time estimation ability of a
network is a significant benefit compared to a single
moving sensor platform. This capability is a substantial
factor that should be considered in the design of RFI
localisation systems. Consequently a network-centric
framework should be chosen for the implementation of
this novel localisation technique. For a network to
provide highly accurate and real-time position estimation,
the configuration of the network will be a significant
factor to consider. Investigations concerning the
orientation of networks that can be self-configurable or
adaptive have also been undertaken (Bulusu et al., 2004).
The importance of GPS availability and it susceptibility
to intentional interference has provided the motivation for
this interference localisation research. The IDPELS
research program has been developed with the objective
of ensuring the integrity and availability of GPS signals
required by aviation navigation systems and users.
2 Localisation
In performing localisation, there are various approaches
that can be undertaken, each of which uses various
parameters. Trilateration and Triangulation are two basic
geolocation approaches that can be performed with
networks. The respective parameters that are required for
each of these geolocation approaches are range and
direction-of-arrival (DOA). The estimation of these
parameters is found to be a classical process with radar,
sonar and geophysical exploration (Vanderveen, 1997).
With trilateration, possible techniques for estimating
range can be based on signal strength or the transit time
of the signal. Prevalently range based on transit time has
been employed due to the greater accuracy that is
available. By finding the intersection of three range
measurements, the location of the source is able to be
unambiguously estimated. Localisation being performed
with trilateration and triangulation is graphically
presented in Figure 1.
Figure.1 Geolocation using Range and DOA
In a hostile environment, localisation should be
performed passively. This is to ensure the enemy can’t
apply retrospective electronic counter measures (ECM).
This means there would only be one-way transmission,
i.e. from the interference source. While the signals time
of arrival (TOA) is simple to measure, there is no way of
knowing when the signal was transmitted. This makes
finding the transmission time infeasible. Only cooperative
systems such as GPS are able to perform trilateration with
one-way transmission.
Triangulation requires the DOA parameter to be used. A
network consisting of two sensors is able to estimate the
location of the source. Localisation based on DOA has
been extensively applied in EW. This is because a hostile
emitter can not easily alter the DOA parameter. As a
result of the reduced susceptibility to ECM, DOA has
become an invariant sorting parameter in the
deinterleaving of radar signals for ESM (NAWCWD,
2003). This provides a strong foundation for IDPELS,
which can determine the DOA parameters.
The inability of trilateration to resolve the transmission
time in a hostile scene can be overcome by using Time
Difference of Arrival (TDOA) localisation. The TDOA
method requires the difference in a signals arrival time
between baseline sensors to be measured. With this
measurement, a line-of-positions (LOP) indicating where
the source can be found is provided. This LOP is known
as an Isochrone. The isochrone is an infinite hyperbolic
line containing all possible locations where the emitter
may be found (Boetcher et al, 2002). Various isochrones,
corresponding to different TDOA are displayed in Figure
2. For localisation to be performed with TDOA, multiple
baselines are required. The sources location will be at the
intersection of the isochrones.

Spencer et al.: Inverse Diffraction Parabolic Wave Equation Localisation Systems (IDPELS) 247
Figure.2 Hyperbolic Isochrone LOP
Another precise localisation techniques based on LOP
intersection is the Frequency Difference of Arrival
(FDOA) technique (Adamy, 2003). A desirable property
of FDOA concerns the dynamics of network sensors.
Here a similar difference with TDOA between baseline
sensors is found, but with frequency and not time. The
result of FDOA is a three dimensional surface defining all
possible transmitter locations. By taking a planar cross-
section, the curve is called an Isofreq. A set of isofreq
curves for various frequency differences is shown in
Figure 3, where the baseline sensors are moving in the
same direction. As with TDOA, multiple baselines are
required for the emitter location to be determined with
FDOA.
Figure.3 FDOA Isofreq LOP
While FDOA can be based on moving localisation
sensors, the computational load associated with moving
interference sources will most often be too large. FDOA
is therefore generally used only on stationary or slowly
moving targets. In practise, localisation systems will
typically use multiple platforms. This allows multiple
solutions to be considered. A system that combines
TDOA and FDOA measurements can determine the
precise localisation of an emitter location with a single
baseline, which is displayed Figure 4. The multiplicity of
combined TDOA and FDOA solutions produces more
accurate results over a wider range of operational
conditions. IDPELS could enhance current localisation
systems by providing multiple solutions.
Figure.4 Single Baseline Localisation
There are also localisation techniques that are intended
for an urban environment. Intended for picocell and
microcell multipath scenarios, the database correlation
method (Wolfe et al., 2002) compares a signals path-loss
with a look-up table. Depending on the urban layout, the
workload for adequate resolution in the look-up tables
could be considerable. While any technique that
contributes to interference signal localisation in an urban
environment should be considered valuable, this database
correlation method is not functional in hostile scenarios.
In urban EW, there is no method to determine the hostile
interference transmission power level. As a result, no
path-loss calculations can be made. This renders the
database method unsuitable for RFI localisation in an
urban EW scene.
With IDPELS localisation being based on the DOA
parameter, several common DF techniques will be briefly
reviewed. The simplest DF method uses amplitude
comparison and a mechanically rotated narrow-beam
antenna. While highly accurate DF can be yielded, the
probability of signal interception is relatively low (Tsui,
1986). To overcome this low probability of interception
(LPI), an array can be configured to provide 360°
coverage. This coverage is displayed with a four-
quadrant amplitude DF system in Figure 5.

248 Journal of Global Positioning Systems
Figure.5 Monopulse DF System
By identifying the greatest (P1) and second greatest (P2)
received power levels, the DOA can be determined.
While amplitude comparison systems are frequency
independent and able to cover wide bandwidths, the DOA
estimation has a high probability of being contaminated
by multiple signals simultaneously received. These
systems also require calibration with signals that have
known DOA information. Another common DF
technique employed in EW is Phase interferometry
shown in Figure 6.
Figure.6 Phase Interferometry
Application of interferometry is however restricted to
narrow-band signals. By measuring the phase difference
between baseline sensors, the DOA can be determined via
trigonometry. In most interferometric systems, the
baseline is between 0.1 and 0.5 λ. A baseline less than
0.1 λ does not provide enough accuracy and if over 0.5 λ
ambiguous results are provided. There are many other
DF finding techniques that could have been analysed,
however a tutorial of many existing DOA estimation
methods is provided by Godara (1996). A special class of
these DF techniques that has high-resolution capabilities
will conclude this discussion on localisation techniques.
The high-resolution DF methods are the subspace class of
spectral estimation techniques that determine a signals
DOA by computing the spatial spectrum and finding the
local maximas of the spectrum. Subspace techniques
require the noise and signal subspace to be extracted from
the covariance matrix of signal observations. Eigen-
analysis can be used on symmetrical matrices, or Singular
value decomposition (SVD) can be applied with
asymmetric matrices. Both of these techniques will
elliptically fit the observed covariance matrix (Therrien,
1992). Subspace based DF methods have the ability to
surpass the limiting behaviour of classical Fourier-based
DF methods. They are also referred to as super-
resolution algorithms. The first subspace method was
developed by Pisarenko (1973), which is referred to as
Pisarenko Harmonic Decomposition (PHD). It should be
noted that PHD does not directly estimate DOA, instead
it determines frequency and power of real sinusoids in
additive white noise. PHD is based on Caratheodory`s
theorem which is an indication of the required data-set
size for dynamics of desired parameters to be captured
(Sidiropouls, 2001). The extension of PHD to DOA
estimation was made by Schmidt (1982) with Multiple
Signal Classification (MUSIC). One of the limitations
associated with MUSIC is that the number of sensors
must be greater than the number of signals present. The
Joint Angle and Delay Estimation (JADE) method
developed by Vanderveen (1997) can overcome this
limitation, provided that signal fading is constant. JADE
is based on multiple channel estimates and is best suited
for TDMA systems where training signals are available.
While blind estimation is possible with JADE, it is
considered to have an undesirable intensive
computational load. The simplicity of IDPELS in
comparison with JADE in performing localisation is
significant.
3 Researc h O b j e ct ives
From the localisation methods previously discussed, there
are different limitations associated with each. These
limitations range from the jammer/sensor dynamics to
intensive computational loads. As noted with the
combined TDOA/ FDOA method, multiple solutions and
simplicity is the ultimate goal of localisation methods.
The primary objectives of the IDPELS development were
twofold;
• To investigate if an inverse EM propagation
model can be used to provide an accurate
localisation solution.
• To determine if an improved localisation can be
made if detailed knowledge of the local terrain
is known.
The new solution can be combined with other methods to
provide multiple localisation solutions. Where networks
already exist, the integration of IDPELS is also intended
to be relatively simple, provided the receiving sensors are
available. All that is required for the extra solution is the
software for inverse diffraction propagation. The
application of IDPELS with a moving single sensor is

Spencer et al.: Inverse Diffraction Parabolic Wave Equation Localisation Systems (IDPELS) 249
also a possible configuration option if a network
configuration in not possible.
4 Methodol og y
The principle methodology of IDPELS is based on
applying inverse diffraction to the Parabolic wave
equation propagation model (PEM). Fundamentally
IDPELS involves measuring a received signal profile
using a large antenna array or from a moving vehicle.
This received field profile is then inverse propagated over
the terrain profile. The source location is then identified
by determining the field convergences. This classifies
IDPELS as an inverse problem. With the development of
IDPELS being based on the PEM and inverse theory,
these two areas will be briefly reviewed.
The classification of inverse problems was defined by
Keller (1976). Keller defines two problems as inverses of
one another if the formulation of each involves all or part
of the solution of the other. One of the problems has
been extensively studied (forward problem), while the
other is not so well understood (inverse problem). From
a mathematical perspective, the decision of what is direct
or inverse can be arbitrary. However in reference to
physics (i.e. astronomy, mechanics, geophysics, wave
propagation, etc) the decision of which problem is
forward or inverse is not as arbitrary. Turchin et al.
(1971) define forward problems in the physics domain as
a process that is oriented along a cause – effect sequence.
A corresponding inverse problem is associated with the
reversed, effect – cause sequence. This means that a
forward problem involves determining what observation
will be made, given various parameters of the systems.
An inverse problem will determine the unknown
parameters of the system, from the observation made with
respect to the system. Another important link that should
be considered with forward and inverse problems is the
model identification problem (Aster et al., 2004). The
combination of these three factors of Inverse Theory is
shown in Figure 7.
Figure.7 Inverse Theory
Models concerning the physical properties or processes of
the systems are generally already known. Over history
there have been many mathematicians and physicists who
discovered and identified models for many different
systems. Various examples of such people include
Gauss, Faraday, Maxwell and Einstein. The model used
for IDPELS is the numerically efficient PEM which has
been extensively researched and developed (Lee et al.,
2000). With wave-propagation theory, a possible forward
problem could be the computation of a field radiated by
the source. A corresponding inverse problem could
involve the determination of the source position from the
knowledge of the radiated field. The solution of this
inverse problem is the intended function of IDPELS,
where the applied model is PEM.
The use of inverse theory has been extensively applied in
imaging. The X-ray computer tomography (CT)
technique developed in 1971 (Hounsfield, 1973) is the
first case of medical images obtained as a process
involving inverse problems. Other topics that have
applied inverse theory include atmospheric sounding,
particle scattering or seismology. One inverse problem
that is similar to IDPELS is sonar-based and was studied
by Zhu (2001). This sonar research was concerned with
image reconstruction by back propagating the PEM
model with a focus-marching procedure.
PEM being the model employed by IDPELS, was
originally proposed by Mikhail Aleksandrovich
Leontovich (1944) for long range radio propagation. In
1946, Leontovich together with Fock (1946) were able to
provide a planar and spherical PEM solution. PEM
involves approximating the elliptic Helmholtz wave
equation with a parabolic partial differential equation to
reduce the difficulties experienced in obtaining a
Helmholtz solution. After the original development of
PEM, application of PEM remained significantly
restricted till the 1970`s when computer technology had
advanced to allow numerical solution to be developed.
With advances in computer technology, Frederick D.
Tappert and R. H Hardin (1973) introduced the parabolic
approximation to oceanic acoustic propagation with the
efficient Split-Step method that can propagate a signal
with the Fast-Fourier-Transform (FFT). Claerbout
(1976) latter developed a finite difference PEM version
for geophysical applications. Eventually PEM returned
to radio propagation where propagation over a littoral
environment (i.e. sea or flat terrain) was initially
considered. With the development of faster algorithms,
Kuttler and Dockery (1991) were able to adapt the split-
step method (developed by Tappert) for radio
propagation. Further application of PEM was made
possible with researchers such as Barrios (1994), who
tested the Tappert approach on a variety of irregular
terrain profiles. Walker (1996) extended PEM for use in
GPS propagation studies. Because radio domains are
generally large with respect to the wavelength,
approximation of Maxwell’s solution must be made.
With the efficiency and accuracy provided by PEM, it has
largely superseded geometric optics and mode theory in

250 Journal of Global Positioning Systems
achieving the approximations. Current PEM applications
are wide ranging.
Having provided a brief historical background to PEM,
the process of applying inverse diffraction within PEM
will now be provided. While finite difference or the
Fourier split-step technique (FSS) can be used to solve
the PEM, discussion will be restricted to FSS as this was
the method employed in the code. One of efficiencies
offered by PEM over other propagation models is that it
is an open boundary problem. The numerical solution for
an elliptical wave equation requires all boundary
condition to be specified. This situation is not required
by PEM. With FSS, the forward propagation provided by
PEM involves marching an input field profile as shown in
Figure 8.
Figure.8 Open Boundary PEM Marching
The initial field profile is transformed into the angular
spectrum via the fast Fourier transform (FFT). This
angular spectrum is also referred to as the vertical spatial
frequency spectrum as it involves the vertical component
of the wavenumber. In the angular spectrum a
propagator is multiplied with the transformed field
profile, which effectively propagates the field to the next
marching step. By inverse transforming the angular
spectrum that has been propagated, the field at x+∆x is
able to be determined. The propagator term is also
referred to as the Diffraction function, which is multiplied
with the angular spectrum. The actual equation employed
in PEM may slightly vary depending of factors that are
considered in the model. One example could be to
account for the atmospheric refractive index. A
propagator that has been employed by Hawkes (2003) is
shown in Eq. (1) and is based of the Fourier imaging
domain method suggested by Eibert (2002).
(){
}
22
D(p)expj xkp=∆ −
(1)
where,
k is the spatial frequency spectrum
p is the vertical spatial frequency spectrum
∆x is the distance covered in a propagation step
With the previously discussed forward propagation
problem, the diffraction term must be multiplied with the
angular spectrum. A high level equation representing this
forward propagation is provided by Eq. (2).
1
u(xx)T(UD)
−
+∆ =× (2)
where,
u is the envelope function of the signal
U is the angular spectrum of the signal
(i.e. FFT of u)
As IDPELS intends to apply inverse diffraction with back
propagation in order to resolve the location of the source,
it will divide the diffraction term with the angular
spectrum. A high level equation representing inverse
propagation is provided in Eq. (3).
1
u(xx)T (UD)
−
−∆ =÷ (3)
Simulation results of inverse propagation with IDPELS
are provided in the following section. The final factor
that will be discussed with respect to PEM and IDPELS
is associated with their upper boundary condition. To
ensure there is no reflection of signal from the upper
boundary, a windowing function must be applied. With
IDPELS, the propagation domain height was doubled for
application of the window. Figure 9 provides a display of
the gradual signal attenuation in the window domain.
Figure.9 Hanning Window
The chosen window for PEM and IDPELS was the
Hanning window. This note is important as it must be
considered when viewing the IDPELS display of Figure
13. Further information concerning radio propagation
with PEM, is provided by Levy (2000).
5 Simulation Results
Simulation results will be presented to demonstrate the
theoretical feasibility of IDPELS to perform geolocation.
When analysing IDPELS under simulation, the

Spencer et al.: Inverse Diffraction Parabolic Wave Equation Localisation Systems (IDPELS) 251
generation of a forward propagation field with PEM is a
prerequisite. The first example is a simple demonstration
of IDPELS where the terrain profile is a single block with
a height and width of 20m as shown in Figure 10. The
transmission source is chosen to be on the far left-hand
side of the block, and 20m above the block. A range of
100m was chosen for field analysis.
Figure.10 PEM – Block
The corresponding IDPELS result is shown in Figure 11.
Figure.11 IDPELS – Block
The geolocation capability of IDPELS is clearly
demonstrated in this simple scenario with unobstructed
line-of-sight (LOS) paths. Where the inverse propagated
field acutely converges, this is a highly accurate
estimation of the sources locations. It should be noted
that the inverse propagation range has been extended an
extra 100m. It’s also important to recognise that Figure
11 is a reversed view of the forward propagated field.
This means the input field profile for IDPELS being on
the left-hand side of Figure 11, is the same field profile
located on the far right-hand side of Figure 10. This
reversed view is present in all other simulated IDPELS
displays. The next demonstration of IDPELS is with
respect to a wedge. In this evaluation of IDPELS, the
source was chosen to be located 20m above the floor of
the domain. A display of the forward propagated field is
provided in Figure 12.
Figure.12 PEM – Wedge
The corresponding IDPELS result is shown in Figure 13.
Figure.13 IDPELS – Wedge
This scenario was investigated to consider the feasibility
of IDPELS when a non-line-of-sight (NLOS) will exist
with inverse diffraction propagation. It should be noted
that the position of the source at 20m height still allows
LOS paths above 88m on the right-hand side of Figure
12. Measuring antenna elements will be required to be
positioned at heights greater than 88m in this scenario.
With the input IDPELS field profile corresponding to the
right-hand of Figure 12, accurate localisation is again
provided by IDPELS as indicated by the intersection of
the ground reflected beam with the downward directed
beam originating from the left-hand side of Figure 13.
Please note that visual interpretation must be currently
made to determine the location of the source.

252 Journal of Global Positioning Systems
With Figure 13 using an input field profile analogous to
principles associated with Synthetic-Aperture-Radar
(SAR), a further investigation was made with a reduced
set of antenna measurements to examine how a network
configuration will affect localisation results. A 9-element
uniform-linear-array (ULA) configuration is applied to
the measure field profile from the right-hand side of
Figure 12. The corresponding IDPELS field is shown in
Figure 14.
Figure.14 Network Configuration
With the array configuration, there is no definite
indication of the interference source location. Only a
LOP is provided by the sensor that experienced a LOS to
the source. It should also be noted that the sensors with a
NLOS to the source did converge to the apex of the
wedge that shadows the source. This indication can
provide assistance for localisation being conducted in an
urban environment.
The next evaluation of IDPELS was to consider its
effectiveness against multiple interference sources. A
display of three sources simultaneously transmitting
interference signals is provided in Figure 15.
Figure.15 PEM – Multiple Sources
With multiple sources, one source was positioned to be
completely obstructed by the wedge. The IDPELS input
has no account of this source. Figure 16 shows the
IDPELS field generated for the multiple sources in Figure
15.
Figure.16 IDPELS – Multiple Sources
All sources with a LOS where able to be localised. This
is indicated by the field convergence at their relative
positions in Figure 16. The source that did not have a
LOS was not able to be localised.
While the geolocation feasibility of a network based
IDPELS was not demonstrated in Figure 14, this was due
to the NLOS orientation of the source. A demonstration
of IDPELS functionality with an array configuration of
two antenna array elements is provided in Figure 17.

Spencer et al.: Inverse Diffraction Parabolic Wave Equation Localisation Systems (IDPELS) 253
Figure.17 Two-element array configuration
The accuracy of the estimated source location in Figure
17 is subject to a large elliptical-error of probability
(EEP) compared with Figure 11. This localisation error
can however be reduced according to the array
configuration. Factors that govern the localisation error
are,
• number of sensors used
• sensor aperture
The localisation error is reduced by increasing either of
these two factors. Figure 18 shows this affect where
there is an increase in the number of field sensors used,
all of which have a relatively larger aperture.
Figure.18 Reduced Localisation Error
6 IDPELS Field Trials
To test the practical application of IDPELS, field trials
were conducted in collaboration with the Navigation
Warfare, Electronic Warfare and Radar Division of
DSTO, Edinburgh, South Australia. The transmission
source was a 1.399GHz tone signal being transmitted
from a helix antenna as shown in Figure 19.
Figure.19 Helix Transmission Antenna
Two sets of data were collected. One data set concerns
the transmission source approximately 13km east of
Truro, SA (34°25’2.85” S, 139°14’10” E) at the base of
the Mt Lofty Ranges (Figure 20). The other data set has
the transmission source positioned at DSTO Radio
Research Station (34°43’26.2” S, 138°32’15.6” E) at St
Kilda, SA (Figure 21).
Figure.20 Mt Lofty Base Trials
Figure.21 St Kilda Trials

254 Journal of Global Positioning Systems
The input field profiles for IDPELS were recorded based
on the SAR analogy. An overview of the signal
recording process is shown in Figure 22.
Figure.22 Signal recording process
With Truro data sets, Figure 23 is a display of the
IDPELS field where the signal was recorded in a moving
van approximately 4.8kms from the transmission site on
Baldon road. Figure 24 corresponds to data recorded on
Woolshed road, approximately 5.9kms from Baldon rd.
Figure.23 Signal Recorded on Pine Creek Track
Figure .24 Signal recorded on Woolshed Road
These IDPELS results have not provided a solution as
accurate in comparison with simulation results. While
data recorded on Pine Creek Track has shown a clear
convergence region, Woolshed road data only provided a
LOP. Various causes for the solution degradation include
noise, clutter, multipath factors and a non-linear phase
shift in the recorded signal. A factor that will have
contributed to a non-linear phase shift is the road section
not being perfectly straight. While scattering and
reflection will also have had some impact on the recorded
signal, modelling of obstacles was not incorporated into
the prototype IDPELS code. This is because the selected
region was considered to approximate a littoral
environment. A photo of the general terrain profile at the
base of the Mt Lofty ranges is shown in Figure 25.
Figure.25 Littoral Mt Lofty Base Region
A photo of the McEvoy road section used to record the
test signal is shown in Figure 26. The displayed repeater
was used to account for Doppler shift generated by the
movement of the van.
Figure .26 McEoy Road

Spencer et al.: Inverse Diffraction Parabolic Wave Equation Localisation Systems (IDPELS) 255
The displayed IDPELS result concerning McEvoy road
shown in Figure 27 has similar visible field convergence
to Pine Creek Track. The range of McEvoy rd from the
St Kilda Radio Research Station is approximately
3.9kms.
Figure.27 McEvoy Road
The IDPELS field profile corresponding to data recorded
on Pt Gawler road is shown in Figure 28. The range to Pt
Gawler approximated 10.8kms.
Figure.28 Pt Gawler Road
The localisation result for Pt Gawler road has many field
convergent regions. This demonstrates Rayleigh fading
where there is no dominant wave component. The terrain
profile for this region was also considered to be semi-
urban. Van speeds were also greater compared with all
data sets. The general driving pattern was initiated with a
steady acceleration and maintain at a constant speed.
Near the end of the recording session, a steady de-
acceleration was applied to being completely stationary.
Speeds reached on Pt Gawler road varied between 80 –
100 km/hr, while all other data sets varied between 10 –
30 km/hr.
Conclusion
The simulation results of IDPELS has demonstrated that
inverse diffraction propagation is capable in providing a
geolocation estimate to multiple sources that have a direct
LOS to network sensors. While IDPELS was unable to
geolocate a source that only has a NLOS, it could indicate
the direction to objects that shadow the source. This
could be beneficial in an urban environment. A network
configured IDPELS was also shown to improve accuracy
with the number of sensors, and sensor aperture.
Field trial results demonstrating the practical feasibility of
inverse diffraction propagation were based on a SAR
analogy for generation of the input field profile. Trials
conducted in regions that approximated a littoral
environment indicated the method to be feasible. The
trials however also showed that great care must be taken
to ensure the phase-shift in the recorded signal profile is
linear. Other factors such as multipath propagation and
noise also degraded localisation accuracy. It should also
be noted that given the experimental nature of the trials,
experienced conditions and measurements conducted
were not ideal.
For localisation to be performed with novel inverse
diffraction propagation methods, further research and
development is required for an efficient localisation
method to be readily available and operational.
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