Acoustic Detection and Tracking of a Class I UAS with a 

Small Tetrahedral Microphone Array

by Minas Benyamin and Geoffrey H Goldman

ARL-TR-7086 September 2014

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Army Research Laboratory

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ARL-TR-7086 September 2014

Acoustic Detection and Tracking of a Class I UAS with a 

Small Tetrahedral Microphone Array

Minas Benyamin and Geoffrey H Goldman

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Acoustic Detection and Tracking of a Class I UAS with a Small Tetrahedral 

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Minas Benyamin and Geoffrey H Goldman

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14. ABSTRACT

An analysis of detection and tracking performance for a Class I unmanned aircraft system (UAS) measured with a small 

tetrahedral microphone array was performed. Detection and tracking algorithms were implemented using beamforming and 

adaptive Kalman filters. The performance of a coherent energy-based detection algorithm implemented with a delay and sum 

beamforming algorithm was assessed using receiver operation characteristics (ROC) curves. Angle tracking was implemented 

using an adaptive Kalman filter with input from a filter and sum beamforming algorithm. For good signal-to-interference-plusnoise ratios (SINR), the estimated azimuth angles had good agreement with ground truth data, but the estimated elevation 

angles were underestimated inaccurately by a scale factor.

15. SUBJECT TERMS

acoustic UAV UAS analysis detection tracking

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Geoffrey H Goldman

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iii

Contents

List of Figures iv

Acknowledgments v

1. Introduction 1

2. Measurements 1

3. Signal Processing 4

4. Detection Performance 6

5. Angle Tracking 14

6. Conclusion 22

7. References 24

Distribution List 25
iv

List of Figures

Fig. 1 Tetrahedral microphone array configuration.......................................................................2

Fig. 2 Spectrum of typical ambient noise ......................................................................................2

Fig. 3 Spectrum of the UAS...........................................................................................................3

Fig. 4 Linear fit of the acoustic power as a function of range .......................................................4

Fig. 5 Average power spectrum of the ambient noise ...................................................................6

Fig. 6 Noise histogram for band-pass filter between 80 to 2000 Hz .............................................7

Fig. 7 Signal plus noise histogram for band-pass filter between 80 to 2000 Hz ...........................7

Fig. 8 Roc curves for band-pass filter 80 to 2000 Hz ....................................................................8

Fig. 9 Noise histogram for band-pass filter 250 to 2000 Hz..........................................................9

Fig. 10 Signal plus noise histogram for band-pass filter 250 to 2000 Hz......................................9

Fig. 11 Roc curves for band-pass filter 250 to 2000 Hz ..............................................................10

Fig. 12 Noise histogram for band-pass filter 400 to 2000 Hz......................................................11

Fig. 13 Signal plus noise histogram for band-pass filter 400 to 2000 Hz....................................11

Fig. 14 Roc curves for band-pass filter 400 to 2000 Hz ..............................................................12

Fig. 15 Noise histogram for band-pass filter 800 to 1700 Hz......................................................13

Fig. 16 Signal plus noise histogram for band-pass filter 800 to 1700 Hz....................................13

Fig. 17 Roc curves for band-pass filter 800 to 1700 Hz ..............................................................14

Fig. 18 Azimuth angle tracking flight I .......................................................................................15

Fig. 19 Azimuth angle tracking for flight II ................................................................................16

Fig. 20 Azimuth angle tracking flight III.....................................................................................17

Fig. 21 Azimuth angle tracking flight IV.....................................................................................18

Fig. 22 Elevation angle tracking results for flight I.....................................................................19

Fig. 23 Elevation angle tracking results for flight II....................................................................20

Fig. 24 Elevation angle tracking flight III ...................................................................................21

Fig. 25 Elevation angle tracking results for flight IV ..................................................................22
v

Acknowledgments

We would like to thank Isabel Llerena and Suzy Goldberg for supporting ARL’s College 

Qualified Leaders (CQL) student internship program. We would also like to thank Dr Kirk 

Alberts and Dr Tung Duong Tran-Luu for helpful discussions regarding acoustic wave 

propagation, beamforming, and Fourier analysis.
vi

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1

1. Introduction

Small commercially available unmanned aircraft systems (UAS) can provide enemy forces with 

a low-cost reconnaissance and surveillance capability against US Soldiers in combat outposts 

(COPS) and forward operating bases (FOBS), potentially compromising their missions. Soldiers 

would like to negate this threat. If this is not feasible, Soldiers would like to know when they are 

being observed by a UAS and what information is being compromised. To address this need, the 

US Army is promoting the development of systems to detect, track, and classify small UAS with 

low size, weight, power, and cost (SWaP-C). Traditionally, radar and electro-optical systems 

have been used to track manned and unmanned aircraft, but many of these systems have high 

SWaP-C. An alternative approach is to use acoustic sensors that have low SWaP-C, but have 

smaller detection ranges compared to other high SWaP-C sensors. For many scenarios, this is a 

good trade-off. Additional detection range can potentially be achieved by placing acoustic 

sensors down range.

An array of microphones can be used to detect and estimate the direction of arrival (DOA) of 

sounds from sources such as UASs using beamforming algorithms. By triangulating with 2 or 

more microphone arrays, the location of the target can be estimated and tracked. By measuring 

the spectrum of the target, information about the type of UAS can be obtained. For this report, 

data from a single, small tetrahedral microphone array was analyzed. The array does not provide 

for optimal detection and tracking performance, but it can easily be folded up and carried in a 

Soldier’s backpack, then placed at a FOB or COP.

A detection algorithm was implemented by comparing the coherent output of a conventional 

delay and sum beamforming algorithm to a threshold. This approach is not optimal, but it is a 

standard approach that will provide a baseline for performance against a Class I UAS.3

2. Measurements

Test data for a Class I UAS was gathered using the tetrahedral microphone array shown in Fig. 1. 

Four data runs were measured during a single day over a 5-h period. The acoustic data was 

sampled at 10 kHz. Global position system (GPS) data sampled at a rate of 1 Hz on the UAS. 
2

Fig. 1 Tetrahedral microphone array configuration

Microphone calibrations were taken at the test site, but due to an unspecified error, were lost and 

replaced by calibrations made at a different time, but using the same array. The data was 

multiplied by a scaling factor calculated using a 94 dB, 1024 Hz calibration tone. Figures 2 and 3 

show typical spectrums of ambient noise and the UAS.

Fig. 2 Spectrum of typical ambient noise

18.6 cm.

20.5 cm.

20.5 cm. 20.5 cm.
3

Fig. 3 Spectrum of the UAS

The received signal at each microphone can be modeled using

(1)

where y(t) is the received signal at a microphone, s(t) is the signal from the source, is 

independent and zero mean noise, r(t) is the range to the target, and M is a constant that is equal 

to 1 for spherical attenuation. The average power of the received signal can be modeled by 

squaring Eq. 1 to obtain 

(2)

where E denotes expected value. Now, M can be estimated by taking the log of Eq. 3 and 

performing a linear regression. The results are shown for all 4 runs in Fig. 4.
4

Fig. 4 Linear fit of the acoustic power as a function of range

The slope of the line is –2.12, which corresponds to M=1.056. These results indicate that the 

attenuation of the signal is primarily due to spherical spreading.

3. Signal Processing

Beamforming algorithms have been successfully implemented in numerous applications to detect 

and track targets using a coherent array of sensors. A standard approach is the delay and sum 

beamformer algorithm, which estimates the direction of arrival (DOA) by maximizes the 

coherent power calculated using

∫

T

y t dt 2 ( )

, (3)

where

i

I

i i y(t) = ∑x (t −τ )ω

, (4)
5

c

a pi

i

′ = −



τ , (5)

xi(t) is the signal measured on the i

th sensor, T is the integration time, i τ is a fixed time delay, ωi

is a weight, a

 is the direction of arrival of a signal in the far-field traveling towards the sensor 

array, pi is the sensor location, ′ denotes transpose, and c is the propagation speed.1 

The beamformer can be further improved by compensating for channel effects on each signal 

using

( ) ∫ ∑ ∫ 



 



 = − −

T

i

I

y T xi t τ i r hi r dr ω dt

2

( ) ( ) ( )

, (6)

where hi(r) is a weighting function. A standard weighting function is based upon a Wiener filter.

2

For beamforming algorithms that are implemented in the frequency domain, the Fourier 

transform of the weighting can be calculated using 

( ) ( )

( ) ( )

ω ω

ω

ω

P P

P

ss nn

ss H

+ =

, (7)

where P (ω) ss is the power spectral density of the signal and P (ω) nn is the power spectral density 

on the noise. For independent signals and noise measured with matched microphones, H(ω) can 

be estimated using

∑

∑ −

≈

I

i

I

i nn

Y I

Y I

H

P

( ) /

( ) / ( )

( ) 2

2

ω

ω ω

ω

, (8)

when 

( ) / ( ), 2

∑ >

I

i Pnn Y ω I ω

otherwise H(ω) = 0 ,

where (ω) Yi is the Fourier transform of yi(t).

The weighting function was estimated using the noise power spectrum calculated over 4-s 

intervals using all the noise data. Figure 5 shows the average power spectrum of the noise.
6

Fig. 5 Average power spectrum of the ambient noise

4. Detection Performance 

Receiver operating characteristics (ROC) curves are used to describe the performance of a binary 

detection algorithm. They show the probability of false positive rate versus the probability of 

detection. The detection algorithm is based upon the coherent energy from a delay and sum 

beamforming algorithm exceeding a threshold. The data are processed over non-overlapping 4-s 

intervals. 

The data used to generate the ROC curves can be visualized by comparing histograms of the 

signal against histograms of the signal plus noise. The histograms of the noise were calculated 

from the power of the delay and sum beamformer signal when there was no target present for 

several frequency bands of interest and at several angles. The results were calculated at an 

elevation angle of π/2 and azimuth angles of 0, π/2, π, and 3π/2 radians for each frequency band 

of interest. The histograms of the signal plus noise were only calculated when the azimuth 

tracking algorithm had locked onto the UAS. This requirement reduced the probability of signals 

from other targets in the vicinity artificially increasing the energy estimates for the UAS plus 

noise. Results from the tracking algorithm are presented in the tracking algorithm section.
7

ROC curves were generated using data measured with the tetrahedral microphone array over 4

different runs on the same UAS at 4 different range intervals. Acoustics data were preprocessed 

with 4 different band-pass filters implemented with a rectangular window in the frequency 

domain. The first bandpass filter was between 80 to 2000 Hz. The output of the beamforming 

algorithm was used to generate histograms of the noise and signal plus noise, as shown in Figs. 6 

and 7. These data were used to generating ROC curves in Fig. 8.

Fig. 6 Noise histogram for band-pass filter between 80 to 2000 Hz

Fig. 7 Signal plus noise histogram for band-pass filter between 80 to 2000 Hz
8

Fig. 8 Roc curves for band-pass filter 80 to 2000 Hz

Next, a bandpass filter between 250 and 2000 Hz was used to preprocess the data. The resulting 

histograms of the noise and signal plus noise are shown in Figs. 9 and 10, and the resulting ROC 

curves are shown in Fig. 11.
9

Fig. 9 Noise histogram for band-pass filter 250 to 2000 Hz

Fig. 10 Signal plus noise histogram for band-pass filter 250 to 2000 Hz
10

Fig. 11 Roc curves for band-pass filter 250 to 2000 Hz

Next, a bandpass filter between 400 and 2000 Hz was used to preprocess the data. The resulting 

histograms of the noise and signal plus noise are shown in Figs. 12 and 13, and the resulting 

ROC curves are shown in Fig. 14.
11

Fig. 12 Noise histogram for band-pass filter 400 to 2000 Hz

Fig. 13 Signal plus noise histogram for band-pass filter 400 to 2000 Hz
12

Fig. 14 Roc curves for band-pass filter 400 to 2000 Hz

Next, a bandpass filter between 800 and 2000 Hz was used to preprocess the data. The resulting 

histograms of the noise and signal plus noise are shown in Figs. 15 and 16, and the resulting 

ROC curves are shown in Fig. 17. The narrowest frequency interval had the best results.
13

Fig. 15 Noise histogram for band-pass filter 800 to 1700 Hz

Fig. 16 Signal plus noise histogram for band-pass filter 800 to 1700 Hz
14

Fig. 17 Roc curves for band-pass filter 800 to 1700 Hz

The detection algorithm with data filtered from 800–1700 Hz had a 99.5% probability of 

detection for ranges less than 450 m, with a 0.3% false alarm rate compared to a 95% probability 

of detection with a 10% false alarm rate (Fig. 14). The detection performance increased at the 

farthest ranges, as well giving a 99% probability of detection for the UAS ranging from 450–

600 m with a 3% false alarm rate. The previous performance shown in Fig. 14 was a 95% 

probability of detection with a 25% false alarm rate. 

The increased performance with the more restrictive frequency ranges can be explained by 

examining the histograms of the noise and the signal plus noise. Reducing the frequency range of 

the data slightly reduced the values of the signal plus noise, but it had a large effect on reducing 

the values of the noise.

5. Angle Tracking

The UAS was tracked in the azimuth and elevation angles using input from a filter and sum 

beamformer that was filtered using an adaptive Kalman filter.

4 The beamforming algorithm used 

estimates of the noise shown in Fig. 5 to calculate weighting functions using Eq. 7. Results are 
15

shown for each of the 4 runs. First, the azimuth angle tracking results are shown for the first 

UAS flight in Fig. 18. The range of the UAS is included on the right side of the y-axis.

Fig. 18 Azimuth angle tracking flight I

The predicted azimuth angle tracking was close to the GPS calculations for the first flight. The 

range varied between 0 and 800 m. There were no other known targets in the scene. The second 

UAS flight is shown in Fig. 19.
16

Fig. 19 Azimuth angle tracking for flight II

The tracking accuracy was poorer for flight II due to the presence of a helicopter, which 

interfered with the angle estimation for the UAS. This occurred again during the third flight, 

which degraded the tracking performance, as seen in Fig. 20.
17

Fig. 20 Azimuth angle tracking flight III

Flight III had the worst tracking performance of the 4 runs. Despite limiting the look angle of the 

beamformer, which aided it into locking onto the UAS, the previously tracked target, the strong 

signal of a helicopter interfered with the signal of the UAS. Flight IV showed the best tracking 

results, with almost complete agreement with the ground truth, as shown in Fig. 21.
18

Fig. 21 Azimuth angle tracking flight IV

Elevation angle tracking results were also processed and compared to ground truth data for the 4

flights. Figures 22–25 show the results for the 4 flights.
19

Fig. 22 Elevation angle tracking results for flight I
20

Fig. 23 Elevation angle tracking results for flight II
21

Fig. 24 Elevation angle tracking flight III
22

Fig. 25 Elevation angle tracking results for flight IV

The elevation angle tracking results appeared to have offset and scaling issues. Overall, the

elevation tracking results improved at higher elevations relative to lower ones. Poor elevation 

tracking results appear to be somewhat correlated with range, but only loosely since poor 

performance occurs everywhere. 

6. Conclusion

An acoustic systems analysis of detection and tracking performance for a Class I UAS measured 

with a small tetrahedral microphone array was performed. Detection and tracking algorithms 

were implemented using an adaptive Kalman filter with input from a beamforming algorithm. 

The performance of a coherent energy-based detection algorithm implemented with a delay and 

sum beamforming algorithm was assessed using ROC curves. The detection algorithm had the 

best performance with a passband of 800–1700 Hz with a 99.5% probability of detection at 

ranges below 600 m and a 3% false positive rate. Detection algorithm results should be improved 

by using a filter and sum beamformer rather than a delay and sum beamformer, but it would 

require a much more sophisticated simulation to estimate the performance.

The tracking angle results were mixed. Despite constraining the look angle of the beamforming 

algorithm, the tracking algorithm often lost track when other targets were present. When the 
23

tracking algorithm reacquired the track, it was often tracking a helicopter, rather than the UAS.

Overall, azimuth tracking was adequate, following the GPS over 60% of the time within a 10°

margin. 

The elevation tracking results were poor. There appeared to be an offset and scaling error 

associated with the elevation angle estimates. This may be likely the result of using a standard 

beamforming algorithm, rather than using an algorithm that incorporated a ground bounce into 

the calculation. 
24

7. References

1. Johnson DH, Dudgeon DE. Array signal processing: concepts and techniques. Prentice Hall, 

1993.

2. Nilsen CC, Holm S. Wiener beamforming and the coherence factor in ultrasound imaging. 

Ultrasonics, Ferroelectrics and Frequency Control. IEEE Transactions on 57.6. 2010;1329–

1346.

3. Kay SM. Fundamentals of statistical signal processing: estimation theory.Prentice-Hall, 

1993.

4. Goldman GH. Adaptive angle-of-arrival estimation and tracking algorithm for rotorcrafts. in 

Proceedings of MSS BAMS, Oct 2012. (FOUO)

5. Mucci FA. A comparison of efficient beamforming algorithms. IEEE Trans on Acoasr, 

Speech, Signal Processing. Jan. 1984;32(3): 548–558.
25

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