3rd International Conference on Sensing Technology, Nov. 30 – Dec. 3, 2008, Tainan, Taiwan

Beacon-Aided Adaptive Azimuth-Elevation Localization of Sound-Sources aboard a Pass-By Rail-Car Using a Track-Side Acoustic Microphone Planar Array Yue Ivan WU, Kainam Thomas WONG ([email protected]), and Siu-kit LAU The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Abstract— A new adaptive “beamforming” signal-processing algorithm is developed to locate noise-sources aboard a passby rail-car, using an immobile track-side microphone-array. The microphone-array’s beamforming is aided by two narrowband acoustic beacons abroad the rail-car aid to track the rail-car’s spatial movement and thus to locate the noise-sources with respect to the rail-car. No other auxiliary hardware (e.g., no radar nor video-camera) is needed.

I. I NTRODUCTION Railway noise-pollution degrades the public health of neighborhoods near the rail-tracks. These noise-sources’ exact locations on the rail-car, their relative strengths, and their signals’ time-frequency structures depend on the train speed, the roughness of the wheel/rail, and the aerodynamic contours of the rail-car’s carriage. Cost-effective reduction of such annoying and health-hazardous noise-pollution could be facilitated by an accurate estimation of the individual offending noise-sources’ locations on the rail-car and their power levels. However, this estimation needs to be achieved in the presence of the rail-car’s variable and a priori unknown movements. The use of an array of multiple microphones, instead of a single microphone, allows azimuth (or azimuth-elevation) directional beam-forming.1 A common beamforming approach is the “delay-and-sum” (DAS) beamformer, which forms a spatial filter matched towards a pre-set direction-of-arrival. This pre-set direction-of-arrival focus would vary over time with the pass-by train’s movement. That is, the microphonearray’s “delay-and-sum” beamformer would “sweep” its focus to track the mobile train [6], [7]. Wayside emissions (from acoustic sources aboard a pass-by train) have been measured by an immobile microphone-array placed along the trackside, since at least the late 1970s in [4], [6], [7], [11], [14], [15], [13] , [16], [19], [22], [23], [26], [28], [29], [30]. However, [4], [11], [14], [15], [13], [16], [22], [26], [28], [29] explain little or nothing of the beamforming 0 The authors were supported by the Internal Competitive Research Grant number G-YF22 from the Hong Kong Polytechnic University. 1 Such rail-car noise-sources would lie in the microphone-array’s near-field, with the radial distance between the microphone-array and the track (which may be curved and has varying elevation) approximately known, from off-line field measurements.

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algorithm used. Nonetheless, they appear to be using the sumand-delay algorithm or the sweeping-focus algorithm in [6], [7]. To address this rail-car tracking problem, this paper proposes a new but simple measurement-system consisting of: (I) one microphone-array placed at a calibrated location besides a railway track, to collect data of a pass-by train’s airborne wayside acoustic pressure as a function of space, time and frequency. (II) two narrowband acoustic beacons (placed near the railcar’s two ends on the exterior of the rail-car carriage) to help track the rail-car’s a priori unknown movements and to facilitate the subsequent beamformer sweeping over the carriage’s entire length. The proposed microphone-array receiver will track the train’s on-board beacons via recursive-least-squares (RLS) “reference-signal distortionless-response minimum-variance beam-forming”, by exploiting the beacon’s time-frequency structure (which is a priori known to the microphone-array receiver). These beacons will transmit at an intensity inaudible to humans, on or off the train. Theses beacons will be placed away from the likely locations of the dominant noise-sources2 , but near the rail-car carriage’s two ends to facilitate interpolative scanning of the carriage’s middle sections. Each beacon’s acoustic emittance will be narrowband, so that each beaconsignal may be isolated using narrowband bandpass filtering, resulting in minimal “contamination” from the noise-sources. This means that much of the noise-sources’ power (which lies outside this narrow passband) would be rejected. The two beacon-signals will occupy distinct bands to minimize interference with each other. These bands will reside at the high end of the microphone-array’s operational spectrum, to maximize the array’s effective spatial aperture (in terms of wavelengths) for better spatial localization of the beacons. These beacon-signals will serve as reference-signals, a priori known to the microphone-array’s receiver, to track the railcar’s movement (which may vary over time and will be a priori 2 Prior train-noise studies show that the rail-car’s dominant wayside noises come from the rail wheels.

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3rd International Conference on Sensing Technology, Nov. 30 – Dec. 3, 2008, Tainan, Taiwan measurement, x(t)

= b1 (t)a(φb1 (t)) + b2 (t)a(φb2 (t)) I  pi (t)a(φi (t)) + n(t) +

(1)

i=1

where φb1 (t), φb2 (t) and φi (t) symbolize the azimuth angles respectively of the beacons and the interference pi (t), b1 (t) and b2 (t) denote the two beacon’s transmitted signal waveform, a(φ(t)) represents the microphone-array’s steeringvector due to a point-source located at the azimuth-angle φ(t) ∈ [−π/2, π/2], and n(t) denotes an L × 1 vector of thermal noises. B. Beacon-Aided Rail-Car Tracking Fig. 1. 3D illustration of the geometry between the sources and the microphones

unknown to the microphone-array receiver). No other trackside auxiliary hardware (such as radar, photo cells, or video cameras needed in many existing systems) will be required in the proposed scheme to track the moving train’s motion. This hardware simplification will enhance system affordability, operational simplicity, and measurement accuracy. This work is the first in the open literature, to the best of the authors’ knowledge, to propose the use of on-board acoustic beacon signals to track the rail-car. Beacon sources are graphically indicated in a Bruel & Kjaer Powerpoint file, entitled “Pass-By Beamforming”, which, however, does not explicitly specify each reference-signal’s waveform, how the reference-sources are used, nor for what purpose. II. T HE N EW A LGORITHM A. The Data Model Suppose the train-track is straight and lies only the positive y-axis. Hence, the onboard sources would lie only on the first quadrant of the y-z Cartesian plane. Suppose a vertical planar array of L identical and omni-directional microphones is used to facilitate the azimuth-elevation localization of the onboard sources. Let microphone numbered  = 1 to lie on the x-axis, without loss of generality. Let this vertical planar array make an horizontal angle (on the x-y Cartesian plane) of α ∈ [0, π/2) with the train-track. Traveling down this railtrack is a rail-car, equipped with two acoustic beacons, each continually emitting a pure-tone at a distinct frequency that is a priori known to the track-side microphone-array receiver. These two beacons are placed at the rail-car’s two longitudinal ends on the exterior of the carriage. In between are located I number of polluting noise-sources aboard the rail-car. Figure 1 shows the spatial geometry between the passing rail-car and this microphone-array. Marked therein is the mathematical notation to be subsequently used. At time t, the microphone-array collects an L × 1 vector-

With a priori knowledge of the pure-tone beacons’ frequencies, the microphone-array can use reference-signal beamforming [1], [9] to focus separately on each of the two beacons. For the beamformer tracking the b1 (t)-beacon, the peak of this beamformer output’s azimuth-spectrum would reveal the respective beacon’s instantaneous azimuth-angle with regard to the microphone-array. This azimuth-angle estimate φˆb1 (t), along with the a priori known spatial geometry in Figure 1, locates the concerned beacon’s instantaneous spatial location. 1) Reference-Signal Beamforming: If the L × 1 microphone-array data x(t) and the beacon’s reference signal b1 (t) were stochastically jointly stationary over time, the L × 1 reference-signal beamforming weight vector would equal: wopt

arg min

w E{|wH x(t) − b1 (t)|2 } = = R−1 x,x rx,b1

(2) (3)

where the superscript H denotes the Hermitian operator, Rx,x = E{x(t)xH (t)}, and rx,b = E{x(t)b(t)}. In the present application, {pi (t), ∀i} and {x(t), ∀t} are actually stochastically non-stationary. Moreover, Rx,x and rx,b1 are a priori unknown. Hence, for any t = nTs (where Ts represents the time-sampling period), replace (3) by: −1  (n) (n) ˆ (n) ˆrx,b1 (4) wopt = R x,x where ˆ (n) R x,x

=

ˆ rx,b1

(n)

=

 H Γ ⊗ 1L,1  X(n) X(n)  H (n) Γ ⊗ 1L,1  X(n) b1

X(n)

=

[x(n), x(n − 1), . . . , x(n − Ns + 1)],

(n) b1

=

[b1 (n), b1 (n − 1), . . . , b1 (n − Ns + 1)].,

(5) (6)

and  denotes an element-by-element matrix-product, ⊗ refers to the Kronecker product, 1L,1 symbolizes an L × 1 vector of all ones, and Γ = [γ Ns −1 , γ Ns −2 , . . . , γ 0 ] is related to the “forgetting factor” 0 < γ ≤ 1 to emphasize the more recent data. A computationally efficient method to update (5) and (6) for (4) is the “recursive least squares” (RLS) algorithm [10] and is summarized in Table I.

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3rd International Conference on Sensing Technology, Nov. 30 – Dec. 3, 2008, Tainan, Taiwan TABLE I RLS A LGORITHM S UMMARY

estimated as: φˆb(n) 1

For each discrete-time index n, initialize the algorithm by setting w(n) (0) = 0 and P(0) = δ −1 I, where δ is a small positive constant. For the iteration-index m = 1, 2, ...M , do: π(m)

=

κ(m)

=

k(m)

=

α(m)

=

(n)

w (m) P (m − 1)

= =

P(m)

=

xH (n − M + m)P(m − 1) γ + π(m)x(n − M + m) P(m − 1)x(n − M + m) κ(m)  H b(n − M + m) − w(n) (m − 1) x(n − M + m) w(n) (m − 1) + k(m)α∗ (m) k(m)π(m)  1 P(m − 1) − P (m − 1) γ (n)

After the above iteration, set wopt = w(n) (M ).

2) Adaptive Localization of Beacons Aboard the Moving Rail-Car in the Microphone-Array’s Near Field: As the railcar may pass in front of the microphone-array as close as only a few meters,3 near-field considerations hold in the subsequent analysis. That is, the microphone array manifold depends implicitly on the azimuth angle, elevation angle and the radial distance between any onboard noise-source and any microphone. However, the radial distance geometrically depends on the other two independent parameters, azimuth and elevation angles, given the (a priori known) spatial relationships between the rail-track and the microphone array in Figures 1. Denoting as Si,j the separation between the ith onboard noise-source and the jth microphone, application of the Cosine Law to Figure 1 gives: of the ith source be   Let the Cartesian coordinates 0, −D tan φi , − cos φiDtan θi ; and let the jth microphone be located at [xj , yj , zj ]. Then, the distance between this ith source and the jth microphone in (8) equals 2

D 2 x2j + (yj + D tan φi ) + zj + (7). Si,j = cos φi tan θi

=

 (n) H φ, θ wopt anear (φ, θ) ,  

arg max

(n)

=B1

(9)

(φ,θ)

C. Localization of Noise-Sources w.r.t. the Moving Rail-Car’s Carriage The two beacons’ above-estimated locations defines a straight line segment on which all onboard noise-sources must lie. Any position on this line segment corresponds to a unique n azimuth-angle with respect to the microphone array. Hence, spatial match-filtering (i.e., delay-and-sum beamforming) may next be employed to scan along the rail-car’s entire length to locate acoustic noise-sources. The resulting azimuth powerspectrum equals: (10) P (φˆb(n) + φ, θˆb(n) + θ) 1 1 n    1 ˆ ˆ |aH γ n−m x(m) |2 = near φb(n) + φ, θb(n) + θ 1 1

  M m=n−M +1 weighted data D. Simulations

Deployed is a 20 × 20 uniform rectangular array, with half-wavelength inter-sensor spacings. The distance from the reference origin to the first microphone equals D = 1000λ = 68.8 meters. The train travels at 60 meters / second. One beacon is placed on each end of a rail-car carriage of length (tan φb1 − tan φb2 )D ≈ 201.4 meters, but with different heights, where initially (φb1 = 142◦ , θb 1 = 57◦ ) and (φb2 = 233◦ , θb2 = 135◦ ). The beacons emit pure-tone sinusoids at 5 kHz and 4.8 kHz, both at a unity power. The 5 kHz beacon-signal has a wavelength of λ = 0.0688. The two beacons are placed respectively at the left end and the right end of the carriage, and with statistically independent initial temporal phases that are randomly distributed over [0, 2π). Two dominant noise-sources are aboard the rail-car carriage, located initially at (φ = 210◦ , θ = 70◦ ) and (φ = 180◦ , θ = 100◦ ), and each with power 104 . There also exist I − 2 = 5 number of weak noise-sources aboard the rail-car carriage, uniformly spaced along the line between the two beacons and each at a power level of 103 . These give a signal-toThe near-field steering-vector for the ith narrowband noise- interference-plus-noise ratio (SINR) slightly below −40 dB, for data pre-filtered by a narrow passband centered around source would then be the φb -beacon’s pure-tone frequency. Hence, the actual raw (8) data’s SINR is still much lower and much more adverse. anear (φi , θi ) =  Si,L −Si,1 T Si,2 −Si,1 Si,3 −Si,1 The noise-sources as a group emits a spatio-temporally white λ λ λ = 1, e−j2π , e−j2π , . . . , e−j2π Gaussian time-series. The time-sampling frequency is 20 kHz. Also, the microphone-array parameters of L and Δ are a priori All simulations below (unless otherwise stated) have an RLS known. This work will assume the rail-track/array separation window length of M = 10 and a forgetting-factor of γ = 1. Figure 2a shows the beamformer output’s magnitudeD to have been measured off-line. (n) response B n (φ, θ) at n = 6000 for α = 0◦ . The plots are With wopt computed from (4) via the RLS algorithm in normalized to give a unity peak amplitude. In Figure 2a, Table I, the beacon’s azimuth-angle at time t = nTs is the difference between the beacon’s estimated angles, both azimuth and elevation, and the true angles are within 0.5◦ . 3 Given 2L2 /λ as the demarcation between the far field and the near field, the onboard noise-source are in the near-field of the microphone-array. Figure 2b shows plots the delay-and-sum beamformer output

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3rd International Conference on Sensing Technology, Nov. 30 – Dec. 3, 2008, Tainan, Taiwan power profile for α = 0◦ . The dominant noise sources’ directions-of-arrival are estimated from the locations of the two highest peaks, while the weak noise sources are estimated from the locations of the five minor peaks.

Fig. 3a. Magnitude-response of beamformer steering to the beacon, α = 30◦

Fig. 2a. Magnitude-response of beamformer steering to the beacon, α = 0◦

Fig. 3b.

Fig. 2b.

Beamformer output power profile, α = 0◦

Similarly, Figure 3a and 3b show the normalized beamformer output’s magnitude-response and power profile when the track is not parallel to the array plane. The beacon azimuthelevation angle is estimated correctly to within 1◦ . The noise sources may be localized from the peak-locations in Figure 3b. R EFERENCES [1] B. Widrow, P. E. Mantey, L. J. Griffiths & B. B. Goode, “Adaptive Antenna Systems,” Proceedings of the IEEE, no. 12, vol. 55, pp. 21432159, December 1967.

Beamformer output power profile, α = 30◦

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