ULA DELAY-AND-SUM BEAMFORMING FOR PLUME SOURCE LOCALIZATI ON

Gail L. Rosen

Department of Electrical and Computer EngineeringDrexel University, Philadelphia, PA 19104

gailr@ece.drexel.edu

ABSTRACT

Estimating the direction of a diffusive source is a difficultproblem, and littlehas been tried to estimate a chemical source subject to turbulence. Turbu-lence must be addressed if chemical localizer systems are tobe effectivefor real-world implementation. Previously, we show that a cross-correlationmethod is a simple and effective way to determine the direction-of-arrivalof a single chemical source subject to turbulence. Now, we examine theperformance of a uniform linear array (ULA) delay-and-sum beamformer tofind and track the direction-of-arrival of a chemical. Due tothe time-varyinggain from the beamformer, we are better able to examine the modulated (vonKarman vortex street) plume. We show that the delay-and-sum beamformerhas the best results if it is parallel to the direction of propagation and thatlocalization begins to degrade when the array is at a wide angle to the plume,due to non-rectilinear flows and dissipation outside the streamline. Yet, weshow that a ULA beamformer gives dynamic information about the plumethat can be used for direction-of-arrival (DOA) tracking, in addition to esti-mation.

Index Terms— multisensor systems, array signal processing, chemicalanalysis, turbulent media

1. INTRODUCTION

Recently, engineers have begun addressing the hard task ofdiffusive source localization ([1], [2], [3]), but diffusive fieldsare rarely found in natural atmospheric conditions. Usually,turbulence is also a factor which further compounds the diffi-culty of the chemical localization problem. This is due to thefact that turbulent advection disperses a chemical and causesdiscontinuities in the flow, not the usual rectilinear propaga-tion as in most source localization problems. To attack thisproblem, most approaches use mobile sensing robots whichcan survey and sample a large plume. In [4], an intelligentplume mapping scheme based on HMM’s for an autonomousvehicle is devised. In [5], a transient-response-based algo-rithm is used to in several modes, one being to track the plumeupwind and another to switch into a local search. Only mobileand multifaceted algorithms have been implemented becausethey are able to perform well for tracking sources in nonlinear,dynamical plumes. However, these solutions are complex anddifficult to implement. Recently, we have shown stationarysensor arrangements using cross-correlation method producea simple, viable solution [6]. We continue along these linesbut show that beamforming can provide us with DOA local-ization as well as dynamic information about the plume. Thedynamic information can be used to track the DOA, and give

an insight into the plume dynamics by comparing the delayfluctuations in the beamformer output.

2. THE MODULATED FLOW

Fig. 1. An ideal von Karman vortex street with Reynold’s number,R = 73.[7]

Fig. 2. Our modulated plume (von Karman vortex street) data with theReynolds number above 1000. The modulated turbulence dissipates due tothe effects of natural turbulence and diffusion.

In this paper, we examine the performance of a ULA beam-former in an unstable fluid flow. This flow can be modeledwith diffusion, quasi-turbulence, and a modulation effect. With-out the modulation, the plume is subject to diffusion and quasi-turbulence, where the tip is mostly non-turbulent and the tur-bulence gradually increases as the chemical spreads through-out the other medium. (e.g. the swirl of cigarette smoke).With modulation, we have a von Karman vortex street, ormodulated turbulence, from a 5 cm/s chemical flowing overa 0.8 cm diameter cylinder (Fig. 2). This modulation com-pounds the normal turbulence to create a periodic instabilityin the flow. Our data was collected with planar laser-inducedfluorescence (PLIF) technology which is a non-intrusive, op-tical measurement technique to obtain a sequence of instan-taneous, high-resolution spatial concentration fields. The 600seconds of plume data is sampled at a 10 Hz framerate, eachpixel represents approximately 1mm× 1mm in space, and theconcentration values are normalized and quantized to valuesbetween 0 and 255.

Fig. 3. Example of a vertical uniform linear array withN sensor inputs,xi(t), and gainy(t). d is the distance between each sensor.

When a chemical flow passes around a cylinder, a vonKarman vortex street results, and an ideal one is seen in Fig.1. Figures 2 is a single frame captured from the turbulentplume data. In Fig. 2, there is slight von Karman vortex shed-ding in the modulated plume, but it is subject to many diffu-sive and additional unknown turbulent forces. The image isa cropped version of the full401 × 940 pixel (y-dimension× x-dimension) images. The centerline of the plume is205pixels (20.5cm) down on the image.

While we have a model for the diffusion, we do not knowthe exact models for the turbulence or the Reynold’s numberof the vortex shedding. This makes attacking the problemchallenging because we are blind to the turbulence involved.Therefore, we desire to localize the source of the plume usingonly the following knowledge:

• Intermittent “events” occurring in the plume due to tur-bulence which makes time information available on asmall scale

• Constant flow rate (50 mm/s or 5 pixels/sample)

3. UNIFORM LINEAR ARRAY BEAMFORMINGFOR DIRECTION-OF-ARRIVAL DETERMINATION

Suppose we haveN sensors and a source signal,s(t) prop-agating through air. Using Fick’s second law solution for acontinuous release in a 2-D, infinite boundary medium, an un-known nonlinear turbulence function,f( ), and sensor noise,the signal received by theith sensor can modeled as:

xi(t) = f(s(t)

ri

) + ni(t)

whereri is the distance from the source to theith sensor andni(t) is additive white Gaussian noise.

In [6], pairwise linear correlations of a square sensor arrayare taken, and the delays that yield the highest correlations are

multiplied by the 2-D array coordinates to give the direction-of-arrival(DOA). The drawback to this approach is that thedelays must be continually averaged to get a good estimate,and thus if the DOA changes over time, this approach willnot reflect this and just give a single averaged estimate of allDOAs. We now investigate another approach, a delay-and-sum beamformer, to exploit the propagation delay betweenthe sensors, and with this approach, it is possible to see howthe DOA varies over time.

A classical delay-and-sum beamformer with no weightingcan be seen in Fig. 3, wherex = [x1(t), x2(t), ...., xN (t)] arethe sensor inputs, and the output gain,y(t), is:

y(t) =

N−1∑

n=0

xn+1(t − [N − n]T ). (1)

WhenT is equal toτ , the propagation delay between eachsensor, the signals line up in time and add constructively, andy(t), the gain, is high. For Fig. 3,τ is related to the angleof incidence,θ, of the propagation field byτ = d

v0

sin(θ)whered is the distance between each sensor andv0 is thepropagation speed of the medium. The basic idea behind thedelay-and-sum beamformer is to delay each input by a mul-tiple of the constant propagation delay,τ , thereby positivelyreinforcing the signal strength by time-aligning them, andthebeamformer will give high output gains for theτ andθ val-ues that reflect theτ (delay) andθ (angle) of the propagatingmedium.

In our case,v0 is 50 mm/s or 5 pixels/sample. Also, forour measurements, we use a horizontal array so theτ rela-tionship is:

τ =d

v0

cos(θ) (2)

whered is the distance between each sensor,v0 is the prop-agation speed of the medium, andθ is the angle of incidenceof the medium onto the horizontal sensors.

Using the delay-and-sum beamformer, we can determinethe DOA by testing over all values ofθ for each time step.We can also determine the delay which lines up the signals intime by just testing over many values ofT = τ .

4. EXAMPLE OF DELAY-AND-SUMBEAMFORMING IN THE PLUME

In [6], we show that there is a 15 cm pairwise correlationlaterally (0◦) in the modulated plume until the diffusion dis-sipates the signal so there is no correlation left between sen-sors. Also, the paper illustrates that for an array with 2 cmsensor separation placed on the centerline in the plume, thereare approximately 4-5 correlation lags (translating to 0.4/0.5seconds between each sensor) in the plume, which can onlybe obtained after averaging the correlations over time. In thispaper, we illustrate the same concept with a ULA delay-and-

Fig. 4. A plot of the Gain,y(t), vs. Delay,τ , in seconds vs. Time inseconds with an interpolation of the time data by 10 for a horizontal, 2 cmseparation sensor arrangement on the centerline beginningat (20.5, 20) cm.1/10 secondτ are tested.

0.2 0.4 0.6 0.8 1.0

600

800

1000

1200

1400

1600

1800

τ

Max

(Gai

n(t)

)

Fig. 5. The maximum gain values of eachτ over time of the Gain vs. Delayvs. Time graph (Fig. 4) of the sensor array on the centerline of the modulatedplume.

sum beamformer but now, we have the ability to track thedelay variation.

In this example, our sensor array consists of 10 sensorswith 2 cm sensor separation parallel to the plume located at(20.5,20)cm. Sweepingτ from 0 to 1 second at 1/10 sec-ond intervals, the Gain vs. Delay vs. Time plot is shownin Figure 4. For the case of sensors separated by2 cm, theideal delay between sensors is 0.4 seconds (20 mm distancedivided by50 mm/s flow rate). Figure 4 shows that there is a0.4− 0.5 second delay between the sensors; the fluctuation isrelated to the fluctuation in the modulated plume. By pickingmax

t(y(τ, t)), the maximum gain value along the time axis

for eachτ , Fig. 5 shows that the gain at the 0.5 second delayhas a higher maximum gain than the 0.4 second one.

Using the relation in (2), we sweep over angles 0 to 180with 1◦ intervals to plot the Angle vs. Delay vs. Time graphin Figure 6. We can see that the angle resolution is approx-imately 0-20 degrees (the ideal angle is0◦). An advantageof the three-dimensional data is that we can see the periodichigh gain in the angle. This illustrates that a linear delay-and-sum beamformer cannot track the angle uniformly due to thenonlinearities from the Karman Vortex Street (modulation).Nonetheless, it is clear that the array picks up a consistentangle in this direction.

Fig. 6. A plot of the Gain,y(t), vs. the Angle vs. Time with an inter-polation of the time data by fifteen for 10 sensors placed 2 cm apart on thecenterline of the modulated plume. Each angle degree is tested.

5. DIAGONAL ULA CONFIGURATIONS

With a delay-and-sum beamformer, there are a few parame-ters to take into consideration with each plume:

• The distance between sensors / array size

• The sensor array angle in the plume

The data also limits us because if we pick an angle thatis too steep, some sensors will fall out of the path of theplume and not obtain significant inputs, thus skewing the re-sults. Therefore, we use narrower angles,−5◦ and−30◦, toillustrate the concept of tilting the sensor array. Due to theorientation, these arrays should localize the angle of the fluidflow to be5◦ and30◦. Examples of a 5-sensor array and a20-sensor array both diagonal at−5◦ are shown in 7 a) andb). Shown in Fig. 7 c) We also examine a 5-sensor array with2 cm sensor separation at a−30◦ tilt to verify the feasibilityof wider angles.

The Gain vs. Angle vs. Time profile for the 5-sensor−5◦ array is shown in Fig. 8. The one for the larger 20-sensor array is shown in Fig. 9. Both arrays have profileswith high gains from 0-20 degrees, but for the larger array,the gains at these angles are much higher in intensity than theother angles when compared to the small array profile. In thesmaller array, there is a noticeable high gain at an80◦ angle,and the profile is much “noisier”. As expected, a linear arraywhich has more sensors and covers more distance is able toextract a better measure of the DOA as compared to a smallerarray which has a limited distance to measure the delays.

For the 5-sensor−30◦ array, the gain profile is similar tothe 5-sensor−5◦ array but has even more spurious gains and“noise” in the profile. But by taking the measure that looksat the maximum gains over all time (taking the best gain foreach angle), it is shown in Fig. 10 that the array does find thetrue30◦ angle in the search. Other cases with a wide angledo not yield as good of results. The wider angle the uniform

(a) (b)

(c)

Fig. 7. a) Zoomed in view of the 5-sensor array with 2 cm sensor sepa-ration, starting at coordinate (20, 40)cm and b) Zoomed in view of the 20-sensor array with 3cm sensor separation, starting at coordinate (18.5,32.5)cmtilting at a−5◦ angle with respect to the x-axis. c) Zoomed out view of the5-sensor array with 2cm sensor separation with a−30◦ tilt starting at coor-dinate (18.5,50)cm

Fig. 8. A plot of the Gain,y(t), vs. Angle vs. Time with an interpolation ofthe time data by eight for the sensor configuration in 7(a) .θ is tested every2 degrees.

Fig. 9. A plot of the Gain,y(t), vs. Angle vs. Time with an interpolation ofthe time data by eight for the sensor configuration in 7(b) .θ is tested every2 degrees.

0 50 100 15030 80 130220

240

260

280

Angle

Max

(Gai

n(t)

)

Fig. 10. A plot of the max gain over time vs. angle,maxt

(y(θ, t)), for

a 5-sensor array located 50 cm down the plume and tilted at a−30◦ angle.The maximum is exactly at the true30◦ with respect to the array despite thegenerally noisy profile.

linear array is, the further out of the streamline the array isand the harder it is for it to pick up delay information.

6. CONCLUSIONS

This paper illustrates the use of a uniform linear delay-and-sum beamformer to localize the DOA of an unstable fluidflow. The closer to the centerline the array is, the better thelo-calization due to the mainstream fluid flow. Despite the con-stant fluid rate, the modulation effects of the Karman Vor-tex Street can be seen in the periodic fluctuations in the gain,and the beamformer enables us to study the plume dynamicsfrom the delay variation. Consequently, we propose investi-gations into array placement, such as nonuniform and two-dimensional arrays for turbulent and quasi-turbulent plumes.Also, DOA beamforming should be explored for mobile andmultiple chemical sources, since adaptive beamforming is well-suited for multitarget tracking.

7. ACKNOWLEDGEMENTS

We thank Jiri Janata’s laboratory at the Georgia Institute of Technology Chem-istry department for providing the turbulent plume data, and James McClellanin the Center for Signal and Image Processing at Georgia Techfor valuablediscussions.

8. REFERENCES

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[6] G.L. Rosen and P. Hasler, “Chemical source localizationin unknownturbulence using the cross-correlation method,” inIEEE InternationalConference on Acoustics, Speech, and Signal Processing (ICASSP), May2006.

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