## 1 Vehicle Speed Estimation using Acoustic Wave Patterns

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Citations: | 16 - 1 self |

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@MISC{Cevher_1vehicle,

author = {Volkan Cevher and James H. Mcclellan},

title = {1 Vehicle Speed Estimation using Acoustic Wave Patterns},

year = {}

}

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### Abstract

Abstract — We estimate a vehicle’s speed, its wheelbase length, and tire track length by jointly estimating its acoustic wave pattern with a single passive acoustic sensor that records the vehicle’s drive-by noise. The acoustic wave pattern is determined using the vehicle’s speed, the Doppler shift factor, the sensor’s distance to the vehicle’s closest-point-of-approach, and three envelope shape (ES) components, which approximate the shape variations of the received signal’s power envelope. We incorporate the parameters of the ES components along with estimates of the vehicle engine RPM, the number of cylinders, and the vehicle’s initial bearing, loudness and speed to form a vehicle profile vector. This vector provides a fingerprint that can be used for vehicle identification and classification. We also provide possible reasons why some of the existing methods are unable to provide unbiased vehicle speed estimates using the same framework. The approach is illustrated using vehicle speed estimation and classification results obtained with field data. I.

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Citation Context ...ti) σ i=1 2 y/2 + y2 imag (ti) σ2 ) = y/2 σy √ ν, 2K (24) where ν has a Chi distribution pν(ν) with 2K degrees-of-freedom [39]. It is well-known that Chi distribution reaches normality rather quickly =-=[40]-=-–[42]. In [42], we provide normal approximations of the Chi distribution based on the Laplacian method [43] and moment matching. These approximations are highly accurate even for small sample sizes. A... |

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Citation Context ... a reference distance to the target is needed to resolve the ambiguity. This issue is similar to the world scaling issue commonly encountered in structure from motion algorithms using a single camera =-=[29]-=-. IV. INTERFERENCE PHENOMENA When the source signal has a spatial extent, it is crucial to consider the interference effects while estimating the speed. To demonstrate the interference effects, consid... |

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Citation Context ...gnal with respect to the source position. However, in this section, we use the reciprocity theorem and change the reference frame from the moving vehicle to the microphone to derive the ES components =-=[31]-=-. For simplicity, we model the ES components using three piecewise constant functions in dB scale with respect to the microphone bearing ϕ as illustrated in Fig. 4. More components may be used but are... |

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Citation Context ...er envelope as follows: E = √ 1 K∑ |y(ti)| K i=1 2 = σy √ √ 2K K ( ∑ y2 real (ti) σ i=1 2 y/2 + y2 imag (ti) σ2 ) = y/2 σy √ ν, 2K (24) where ν has a Chi distribution pν(ν) with 2K degrees-of-freedom =-=[39]-=-. It is well-known that Chi distribution reaches normality rather quickly [40]–[42]. In [42], we provide normal approximations of the Chi distribution based on the Laplacian method [43] and moment mat... |

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Citation Context ...recordings), we would like to determine, with high confidence, the label of the vehicle when it drives by another control microphone. This problem has applications in distributed sensor networks [8], =-=[9]-=-. The problem becomes complicated when 1) the control microphone has a different distance to the closest point of approach (CPA) of the vehicle, 2) the vehicle is moving with a different speed or movi... |

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Citation Context ...S power of a signal segment that is τ/K in length. Then, we have the following narrow-band observation model, which has been extensively used in the literature (e.g., for bearing estimation [6], [35]–=-=[38]-=-): y(t) =ε(t)e −j 2πf0R βc + u(t), (22) where f0 is the dominant instantaneous source frequency at time t, u(t) is an i.i.d., zero mean, complex circularly symmetric Gaussian random variable CN ( 0,σ ... |

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Citation Context ...tion recordings), we would like to determine, with high confidence, the label of the vehicle when it drives by another control microphone. This problem has applications in distributed sensor networks =-=[8]-=-, [9]. The problem becomes complicated when 1) the control microphone has a different distance to the closest point of approach (CPA) of the vehicle, 2) the vehicle is moving with a different speed or... |

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Citation Context ...of a vehicle. Unlike the engine block noise, the exhaust system noise increases significantly with the engine load. The exhaust noise is also affected by engine turbo/super chargers and after-coolers =-=[20]-=-, [21]. Manufacturers use a combination of reactive and absorptive silencers to keep the exhaust noise level down. The exhaust noise has broadband characteristics with most of its power concentrated a... |

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Citation Context ...: because of the reference frame change, any angle defined in the vehicle reference frame, denoted as φ, is related to the angles in the microphone frame, denoted as ϕ, through an aberration relation =-=[33]-=-: tan ϕ 2 = √ 1+v/c 1 − v/c φ tan , (15) 2 where the sign of the speed terms flip after the CPA. Hence, by assuming a symmetric interference pattern for the front and rear tires of the car based on co... |

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Citation Context ...odel (20). Finally, other reasons for the possible bias are the ignorance of inherent estimator biases, multipath propagation, vertical dimension of the vehicles, and atmospheric turbulence [5], [7], =-=[49]-=-. C. Vehicle Classification Results The vehicle profile vector provides a natural feature vector for classifying vehicles. Figures 14(a) and (b) show that the vehicles can be separated into two classe... |

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Citation Context ...interaction with the road surface. The tire noise is the main source of a vehicle’s total noise at speeds higher than 50km/h [14]. It consists of two components: vibrational noise and air noise [15], =-=[16]-=-. The vibrational component is caused by the contact between the tire threads and the pavement texture. Its spectrum is most dominant between 100 − 1000Hz. The air noise is generated by the air being ... |

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Citation Context ...he RMS power of a signal segment that is τ/K in length. Then, we have the following narrow-band observation model, which has been extensively used in the literature (e.g., for bearing estimation [6], =-=[35]-=-–[38]): y(t) =ε(t)e −j 2πf0R βc + u(t), (22) where f0 is the dominant instantaneous source frequency at time t, u(t) is an i.i.d., zero mean, complex circularly symmetric Gaussian random variable CN (... |

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Citation Context ...pplied to field data. When an array of passive acoustic sensors is used, existing approaches in the literature concentrate on the correlation among the multiple microphone signals. Forren and Jaarsma =-=[4]-=- aim to classify vehicles based on their axle detections by exploiting the tire noise generated by vehicles. They use signal correlations among three known microphones under assumption B. However, the... |

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Citation Context ...λ σse { mτ + √ βr } N (0,1) √ 4K ∏ i=γ,θ,ψ 10 ρ i(ϕ)/20 . (28) Aside from the ES components, the approximation (28) is somewhat different than the commonly used additive noise model in the literature =-=[44]-=- (denoted as E∼p2(E)): E ∼ σs √ βr + σwN (0, 1) , (29) where σw is assumed independent of σs. In this paper, we use p1(E) in (28) for estimation. We compare the range estimation performance of both mo... |

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Citation Context ...en the wind speed is much less than the vehicle speed. For this case, perturbation analysis methods can yield analytical expressions for the mean and the variance of the turbulent velocity components =-=[24]-=-. These expressions may be used to further improve the results presented in this paper. III. SPEED ESTIMATION AS A SPATIO-TEMPORAL SAMPLING PROBLEM To understand the speed estimation problem, it is in... |

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Citation Context ...are no multipath effects. When there are multipath effects, a parametric form of the source signal must be known. Without these assumptions, range estimation using a single microphone is not possible =-=[34]-=-. The power envelope function E is calculated using τ-discrete samples of the microphone output z[n] as follows: ∣ E[nτ] =E(t) = √ Pz[nτ ]= √ 1 τ−1 ∑ z τ 2 [nτ τ + k], (20) ∣ t= nτ τ Fs k=0 where subs... |

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Citation Context ...]–[6]. When a single passive acoustic sensor is used, wave propagation effects are used to determine the source movements based on the following assumptions that the vehicle A) is a point source [1], =-=[2]-=-, B) has stationary signal characteristics that admit a model such as an autoregressive moving average (ARMA) model [2], and C) produces a pure tone [1]. These assumptions are only partially satisfied... |

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Citation Context ...A can be approximately determined by windowing the short-time power estimates and finding the time of the maximum received power. This threshold can then be used to segment the desired vehicle signal =-=[3]-=-, [9], [46]. B. Approximate Cost Function and Its Solution In our detector, if we threshold the amplitude measurements E by a positive constant ϖσu, then the false alarm probability is given by PF = P... |

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Citation Context ...ization can be done 4 , which is applicable to the vehicles of interest, the number of cylinders can also be estimated robustly. Estimation of χ can be done accurately using harmonic analysis methods =-=[45]-=-. In our estimation, we use the power spectral density of the acoustic signal to determine λf . Further details can be found in [45]. VI. PRACTICAL ASPECTS OF ESTIMATION A. Detector With a gross simpl... |

6 |
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Citation Context ...d speed estimates as in [2]. They also explain the bias of their estimates using a delay error term that models the movement of the vehicle during the acoustic signal propagation [7]. Lo and Ferguson =-=[5]-=- develop a nonlinear least squares method for speed estimation using multiple microphones with a quasi-Newton method for computational efficiency. The estimated speed is based on time-delay-of-arrival... |

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Highway modeling Part I: Prediction of velocity and turbulence fields in the wake of vehicles
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Citation Context ...mediately after the vehicle passes by the sensor (as a distinctive whoosh sound). The turbulence noise depends on the aerodynamics of the vehicle as well as the ambient wind speed and its orientation =-=[22]-=-, [23]. In our problem, we only consider the case when the wind speed is much less than the vehicle speed. For this case, perturbation analysis methods can yield analytical expressions for the mean an... |

5 |
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Citation Context ...pproximately determined by windowing the short-time power estimates and finding the time of the maximum received power. This threshold can then be used to segment the desired vehicle signal [3], [9], =-=[46]-=-. B. Approximate Cost Function and Its Solution In our detector, if we threshold the amplitude measurements E by a positive constant ϖσu, then the false alarm probability is given by PF = Pr ( χ 2 τ >... |

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Citation Context ...imation and classification results obtained with field data. I. INTRODUCTION Estimation of vehicle motion parameters using signals received at passive sensors is a classical signal processing problem =-=[1]-=-–[6]. When a single passive acoustic sensor is used, wave propagation effects are used to determine the source movements based on the following assumptions that the vehicle A) is a point source [1], [... |

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Citation Context ...onents: a) Engine Noise: The noise from an internal combustion engine contains a deterministic harmonic train and a stochastic component so it can be modeled by the same methods used for human speech =-=[10]-=-, [11]. The stochastic component of the engine noise is largely due to the turbulent air flow in the air intake (or intercooler), the engine cooling systems, and the alternator fans. This stochastic c... |

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Citation Context ...ise is defined as the noise emitted from a rolling tire as a result of its interaction with the road surface. The tire noise is the main source of a vehicle’s total noise at speeds higher than 50km/h =-=[14]-=-. It consists of two components: vibrational noise and air noise [15], [16]. The vibrational component is caused by the contact between the tire threads and the pavement texture. Its spectrum is most ... |

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Citation Context ...ely after the vehicle passes by the sensor (as a distinctive whoosh sound). The turbulence noise depends on the aerodynamics of the vehicle as well as the ambient wind speed and its orientation [22], =-=[23]-=-. In our problem, we only consider the case when the wind speed is much less than the vehicle speed. For this case, perturbation analysis methods can yield analytical expressions for the mean and the ... |

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Citation Context ...(9) then one can approximate ri ≈ r and βi ≈ β as defined in the monopole source case (Fig. 2). Derivation of (9) uses the Taylor series expansion of the range terms and is the dual of the problem in =-=[30]-=- for determining the near field of an array for a point source. The condition (9) defines an approximate boundary of the near field of the dipole source, after which the individual monopole ranges and... |

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Citation Context ... i=1 2 y/2 + y2 imag (ti) σ2 ) = y/2 σy √ ν, 2K (24) where ν has a Chi distribution pν(ν) with 2K degrees-of-freedom [39]. It is well-known that Chi distribution reaches normality rather quickly [40]–=-=[42]-=-. In [42], we provide normal approximations of the Chi distribution based on the Laplacian method [43] and moment matching. These approximations are highly accurate even for small sample sizes. A norm... |

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Citation Context ...dels and obtain biased speed estimates as in [2]. They also explain the bias of their estimates using a delay error term that models the movement of the vehicle during the acoustic signal propagation =-=[7]-=-. Lo and Ferguson [5] develop a nonlinear least squares method for speed estimation using multiple microphones with a quasi-Newton method for computational efficiency. The estimated speed is based on ... |

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Citation Context ...licated by the tread geometry [17]. In the driving direction of the car, the road and the tire forms a geometrical structure that amplifies the noise generated by the tireroad interaction [16], [18], =-=[19]-=-. This effect is called the horn effect and has a directional pattern [18]. This amplification results in a strong vehicle tire noise component in the frequency range 600 − 2000Hz ( [16]: Chapter 7.1.... |

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Engine exhaust noise control,” available online at http://www.ashraeregion7.org
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Citation Context ...ehicle. Unlike the engine block noise, the exhaust system noise increases significantly with the engine load. The exhaust noise is also affected by engine turbo/super chargers and after-coolers [20], =-=[21]-=-. Manufacturers use a combination of reactive and absorptive silencers to keep the exhaust noise level down. The exhaust noise has broadband characteristics with most of its power concentrated around ... |

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Citation Context ...pole at the sidewalk. The distance of the bottom of the microphone pole to the center of the street is 7.4m. A video camera is used to establish the ground truth and identify the vehicles in the test =-=[48]-=-. A. Vehicle Profiling Table III and Figs. 9-11 show the results of the vehicle speed estimates obtained by three different methods using τ = 480 samples: M1) This method uses full vehicle profile vec... |

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Works Committee, Noise Pollution and Abatement Act of
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Citation Context ...are most sensitive to (1kHz to 4kHz) [11]. In addition, the manufacturers try to suppress the noise levels outside the car as mandated by the federal standards for highway noise (e.g., in the US, see =-=[12]-=-, [13]). They design quieter engines and also exploit the body of the vehicle to filter the engine noise. To achieve this, the interior of the engine compartment is usually treated with material for a... |

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Citation Context ...nd the use of the ES components and are not concerned with the computational issues. However, we note that the final solution is usually not sensitive to the initialization. Moreover, we note that in =-=[47]-=-, Searle explains an efficient solution of a similar computational exercise, where bank of template signals are used to determine the vehicle speed. A similar approach may be taken in our problem, sin... |