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BeBeC-2024-S10
A COMPARISON OF SOURCE LOCALIZATION METHODS
WITH VARYING SIZES OF THE PHASED MICROPHONE
ARRAY
Anandini Sravya Jayanthi1, Mirjam Snellen1, A.R Amiri-Simkooei1
Pieter Sijtsma 1and Nico van Oosten2
1Section Aircraft Noise and Climate Effects, Faculty of Aerospace Engineering, Delft University of Technology
Kluyverweg 1, 2629 HS, Delft, The Netherlands
2Anotec Engineering SL
Motril, Spain
Abstract
Since 2020, all commercial aircraft have been mandated to be equipped with ADS-B Out
transponders. Despite the many advantages of locating an aircraft with openly available and
accessible data, it also has some limitations. Firstly, not all aircraft, such as general avia-
tion, are required to transmit their locations; secondly, due to obstacles such as buildings,
a location is not always transmitted at lower altitudes (75-130 m); thirdly, it is vulnera-
ble to cyberattacks. Therefore, while it is convenient to have ADS-B Out data, creating a
computationally efficient alternative methodology for determining the aircraft location is
advisable. This paper investigates the accuracy, efficiency, and computational cost of two
methods of source localization using data taken by an array of microphones: a global op-
timization (GO) method called the differential evolution (DE) and the conventional beam-
forming approach (CBF). The real-world data required as input for both methods is obtained
with a 64-microphone phased array placed at a distance of 1.14 km from Rotterdam The
Hague Airport (RTHA). The 2-dimensional flight trajectories, i.e., azimuth, and elevation
relative to the array, obtained from the GO and CBF methods, are compared with the ADS-
B Out data for approaching and departing flyovers. Furthermore, the smallest size of an
array required for satisfactory localization accuracy is investigated.
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1 Introduction
With the aviation industry predicted to grow further in the next two decades, it is essential
to develop novel methods to reduce the noise footprint of an aircraft [1]. The current best-
practice method for predicting the noise footprint is known as ECAC’s Doc.29 [2]. It requires
the thrust of the engine (power) and distance between the source and receiver as input and then
predicts the noise using the Noise-Power-Distance (NPD) tables. The methodology is subject
to several simplifications, for example on physical phenomena such as sound propagation and
source decomposition. Hence, it is important to assess and improve, if needed, the model
assumptions to ensure the prediction of the noise footprint is accurate. For this, input retrieval
methods from the most accurate and openly available sources must be established.
This paper investigates methods of improving the accuracy and availability of the distance
input. Recognizing the necessity for having the positional data of an aircraft for improved air
traffic management, it is nowadays required for most aircraft to be equipped with an Automatic
Dependent Surveillance Broadcasting system Out (ADS-B Out) [3]. ADS-B Out is a surveil-
lance technique that broadcasts the identity of the aircraft and its position, determined by the
Global Navigation Satellite System (GNSS), to ADS-B signal receivers set up on other aircraft
and on the ground within a given range. The ground stations then transmit the signals to a
surveillance processing unit managed by the OpenSky network [4], [5]. The system gives easy
access to the positional data for individual aircraft, which is of importance for single-event noise
prediction studies such as the work done by [6].
Despite its numerous advantages, there are a few limitations, such as inaccurate information,
corrupted position data, altitude data, or the lack of signal transponders [5]. Hence, it is advis-
able to create a quick and efficient alternative framework for localizing an aircraft, and one such
method is studied in this paper. As with most source localization techniques that use the time-
of-arrival of the sound wave between different microphones in a phased microphone array, the
traditional technique of conventional beamforming in the frequency domain (CBF) is applied
in this contribution. It is a robust method that computes the acoustic strength of sources in a
predefined grid [7], as such applying an exhaustive search for identifying the location that pro-
vides an optimal agreement between measured and modelled differences in time of arrival. In
addition to CBF, the global optimization (GO) technique is applied, where an exhaustive search
is no longer carried out, but instead, a directed search through the search space is followed.
This paper compares the trends and the individual values of source locations obtained from
the various described approaches and verifies the applicability and accuracy of the source lo-
cations obtained by the GO method. Furthermore, the convergence behavior, computational
time, and accuracy of the GO method, computed by progressively reducing the number of mi-
crophones in the phased array, are also investigated. Finally, this paper aims to propose the
smallest size of the phased array required for a given accuracy. This method could also be
applied to other sources, such as UAVs.
2 Experimental setup
The measurements were taken near Rotterdam The Hague Airport (RTHA), which houses one
runway and is located in a densely populated area. The maximum wind speed on the day of
5th September 2023 was 4.63 m/s, and the temperatures ranged from 15 ◦C to 29 ◦C, with
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relative humidity reaching a maximum of 49%. A total of 9 flyovers were recorded, where the
average altitude from the center of the array to the nearest point of take-off flyovers was 360
m, and for the one approaching flyover was 230 m. Every flyover was recorded by each of
the microphones in the phased array shown in Figure 1. Furthermore, a progressively smaller
number of mics described as subsets are given in Table 1. The table indicates the boundaries of
the squares that contain the microphone subsets. Subset 4 uses all available microphones. The
aircraft location is determined in spherical coordinates θ(◦) and φ(◦) to the center of the array,
which are the elevation and azimuthal angles, respectively, while taking an arbitrary value for
the range, assuming a plane wave at the array.
Figure 1: 2-dimensional phased array with 64 microphones.
Array subset Axis coordinate limits (m)
4 -2:2
3 -1.5:1.5
2 -1:1
1 -0.5:0.5
Table 1: Selection of array subsets depending on the axis limits of the two-dimensional config-
uration.
3 Source localization techniques
3.1 Conventional beamforming (CBF)
The Conventional frequency domain beamforming is one of the most popular methods for ob-
taining source localization and source strength. This algorithm is fast and robust and makes
use of the phased microphone array by taking the Fourier transforms of the pressure responses
recorded by each of the Nindividual microphones as
p(f) =
p1(f)
.
.
pN(f)
(1)
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where p(f)is the N-dimensional Fourier-transformed pressure vector at frequency f[7, 8]. The
beamformer output Bjis computed as
Bj(f) = g∗Cg
||g||4.(2)
where Cis the covariance matrix or the cross-spectral matrix (CSM), which is obtained as
C=⟨pp∗⟩.(3)
This matrix takes the ensemble average (⟨⟩) of the product of the pressure response vector p(f)
and its complex conjugate transpose, denoted by ∗. Due to the movement of the acoustic source,
i.e., the aircraft, no averaging is done for the current contribution. With the speed of sound,
c=340 m/s, the steering vector g(f)used to find the maximum response within a defined
two-dimensional scan grid (grid points denoted by j) is computed as follows:
g(f) = gn,j(f) = e−2πi f rn,j
c(4)
where rn,jis the distance between the nth microphone and the grid point j. The two-dimensional
scan grid is defined in spherical coordinates θand φ. The scanning occurs at an interval of 2.86◦
in the range of θ=0 : 90◦and φ=0 : 360◦.
CBF is known as a robust but exhaustive process as its algorithm models the beamformer
output in each of the locations in the defined scan grid and identifies the location at which there
is a maximum agreement between the modelled and measured values as the location of the noise
source.
3.2 Global Optimization (GO)
Unlike the computationally heavy and exhaustive search process of conventional beamforming,
global optimization methods find the best match between the measured and the modeled values
without requiring a predefined scanning grid. Among numerous GO methods analyzed for
source localization purposes, the genetic algorithm known as the differential evolution (DE) has
shown to be one of the most appropriate and accurate choices [9]. Differential evolution is an
approach that imitates evolution, keeping only the fittest solution members per generation from
generation to generation [10]. Several independent DE runs are typically carried out to avoid
identifying a local optimum as the global optimum. For this contribution, only two independent
runs have been considered. Each of the two independent runs begins with a population of 8
members, which mutate over 100 generations. The multiplication factor is 0.6, and the cross-
over probability is 0.6 (Table 2). In this paper, the global minima of the energy function are
determined for localization purposes. The energy function is the summation of the square of the
difference of the measured phase delay of the signal to the modeled phase delay over frequencies
in the range of 400 - 800 Hz [11].
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Search parameters θ,φ
Population 8
Number of independent runs 2
Cross-over probability 0.6
Number of generations 100
Multiplication factor 0.6
Table 2: Settings applied for GO of θand φwith DE algorithm.
4 Results
In this section, the estimation of the two-dimensional location of the aircraft as a monopole
source from ADS-B Out data, the GO method, and the CBF method is exhibited. For each of
the flyovers recorded, the localization is also carried out for subsets of the microphone array.
4.1 Qualitative comparison
Figure 2: Comparison of estimates of θobtained from ADSB-Out, CBF, and GO method
using various subsets for a single flyover.
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Figure 3: Comparison of estimates of φobtained from ADSB-Out, CBF, and GO method
using various subsets for a single flyover.
Typically, for both the CBF method and the GO method of the DE algorithm, as many micro-
phones as available are used for the localization. In this section, however, we vary the number
of microphones used to obtain the DE-derived estimates for the aircraft position. Varying sub-
sets whose sizes are described in section 2 are considered. Figure 2 and Figure 3 illustrate the
results for these four subsets of the array microphones for a take-off of a B737-700. Here, the
aircraft location estimate in spherical coordinates for the various subsets of microphones is rep-
resented by green markers. For each time snapshot, multiple estimates are obtained by varying
the reference microphone to calculate the phase variation over the array. Also shown are the
estimates obtained through CBF using all microphones, represented by the dashed black line.
Finally, the accuracy of the calculated values by both methods is determined by comparing them
to the relative aircraft locations determined by ADS-B Out data, shown in red. It is necessary to
highlight that only the GO method is carried out with different subsets, whereas the CBF curve
is only determined using all available microphones. As such, it is easier to check the behav-
ior of the GO method as a function of the microphone subset. The estimates obtained through
CBF and GO methods align with better accuracy for varying subsets than with ADS-B, and the
estimations obtained with subsets 4 & 1 exhibit very slight differences.
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Figure 4: Comparison of estimated θof two individual flyovers by subset 1.
Figure 5: Comparison of estimated φof two individual flyovers by subset 1.
Subsequently, the reliability of the locations estimated by subset 1 (smallest number of mi-
crophones) is studied by considering the obtained values for all the flyovers, two of which are
illustrated in Figure 4 and Figure 5. The trends of the estimates continue to exhibit good agree-
ment with the values estimated by CBF and obtained from ADS-B Out data.
4.2 Quantitative comparison
Generally, a flyover is described as being overhead when θ=90◦, which is also the closest point
in the flight track to the array. However, to generalize the source localization process for most
realistic cases when this condition is not met, the dataset considered in this paper does not have
any direct flyovers. Hence, it is interesting to determine the location with the shortest distance
between the aircraft and the array. The shortest distance is calculated at the maximum value
of θamong all estimates (varying reference mics and CBF and ADS-B Out). Thus obtained
values from subset 1 are compared in Figure 6. In most cases, the values obtained by ADS-B
Out, CBF, and GO align with a difference less than 2◦. However, in two cases, the difference
is more than 5◦. The corresponding values of φare determined from the time step at which
the maximum θvalues are found. These values align with a difference of less than 5◦in most
cases. However, these differences remain even when subsets 3 & 4 are used for determining
the location with the GO method. It is interesting to note that the choice of subsets does not
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affect the accuracy of determining the closest point of the track to the array with the given GO
method.
Figure 6: Comparing the locations of each measured take-off flyover at the overhead position
obtained by ADS-B, GO, and CBF methods with subset 1.
Figure 7: Convergence behavior of two runs of GO method excited by subsets 4 & 1.
In gauging the accuracy and reliability of a specific GO algorithm, computational time and
convergence behavior are often discussed. Therefore, the convergence behavior for one flyover
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is shown in Figure 7. This shows the convergence rate of the minimal value of the energy
function in the subsequent generations of the GO method for subsets 4 & 1. The dashed lines
represent subset 4, whereas the solid line represents subset 1. Additionally, red lines repre-
sent the first run, and blue lines represent the second run. The limited number of independent
runs prohibits a further assessment of the convergence behavior. For the runs shown, the re-
quired number of generations is about 30. Given a population size of 8, this corresponds to 240
function evaluations.
5 Conclusions
This paper describes the comparison of two types of source localization methods, GO and CBF,
and the verification of these results with the ADS-B Out positional data. The qualitative com-
parison shows that the final localized values from GO and CBF methods align with less than a
3% difference for all the flyovers. This implies that in cases where the noise source location is
unknown or the locations obtained from ADS-B Out need to be verified, the much quicker and
more computationally affordable option, the GO method, could be taken. Along with establish-
ing the reliability of this method for localizing sources that are mostly 350 (m) away from the
array, this paper also proposes that a 1 (m) x 1 (m) non-symmetric array that contains 10-12
mics would give satisfactory two-dimensional locations. Performing the DE algorithm with
the signal responses obtained from the mics gives good agreement and is much more computa-
tionally affordable than the beamforming method. However, there is an insufficient agreement
on identifying the closest point of the flight track to the array for some flyovers, this could be
attributed to the lack of reliable altitude parameters, especially from ADS-B Out data.
6 Acknowledgement
The authors are grateful to the EC for supporting the present work, performed within the
NEEDED project, funded by the European Union’s Horizon Europe research and innovation
programme under grant agreement no. 101095754 (NEEDED). This publication solely reflects
the authors’ view and neither the European Union, nor the funding Agency can be held respon-
sible for the information it contains.
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