Evolutionary TDOA-Based Direction Finding Methods ... - IEEE Xplore

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Evolutionary TDOA-Based Direction Finding Methods With 3-D Acoustic Array Xunxue Cui, Kegen Yu, Senior Member, IEEE, and Songsheng Lu

Abstract— This paper focuses on direction finding of a signal source using time-difference-of-arrival (TDOA) measurements at a 3-D acoustic sensor array. Two evolutionary computation methods are proposed to solve the direction finding problem, which are the genetic algorithm and the particle swarm optimization algorithm. Sound speed is used in the development of the algorithms, which is estimated based on observed weather parameters and initial direction estimation results from the least square (LS) estimator which is presently the key method in TDOA-based direction finding. All reference-free TDOA measurements are adopted in defining cost function to improve performance. To guarantee fast convergence, an LS estimator is also utilized to provide initial direction estimates for the two swarm intelligent algorithms. Simulation results demonstrate that the proposed methods with a full TDOA set are superior to the Cramer–Rao lower bound with a limited set of referencebased TDOA measurement, significantly outperforming the LS estimator. Extensive field experiments were conducted and there is good agreement between the experimental results and simulation results. Index Terms— Acoustic arrays, array signal processing, artificial intelligence, direction of arrival (DOA) estimation, time-delay arrays.

I. I NTRODUCTION

S

OURCE localization and direction of arrival (DOA) estimation using sensor arrays have drawn significant attention from both academia and industry in the array signal processing field for decades. DOA estimation is usually called direction finding. If the source is in the far field of array, the wavefront arriving at the array is assumed to be plane. Then the DOA can be accurately estimated, while the range estimation error would be large especially for the high range-to-baseline ratio (RBR) case. When two or more subarrays simultaneously detect the same source, the crossing of bearing lines can be used to estimate the source location. Many high-resolution algorithms such as multiple signal classification and maximum likelihood (ML) have been considered as popular beamforming techniques for DOA estimation [1]. In contrast to the beamforming approach where the data are processed in the frequency domain, the time difference of arrival (TDOA)-based DOA estimator performs the data

Manuscript received September 7, 2014; revised January 18, 2015; accepted January 21, 2015. This work was supported by the National Natural Science Foundation of China under Grant 61170252. The Associate Editor coordinating the review process was Dr. Yong Yan. X. Cui and S. Lu are with the New Star Institute of Applied Technology, Hefei 230031, China (e-mail: [email protected]; [email protected]). K. Yu is with the School of Geodesy and Geomatics, Wuhan University, Wuhan 430072, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TIM.2015.2415051

Fig. 1.

Illustration of acoustic array-based explosion source detection.

processing in the time domain. The TDOA technique is considerably more efficient in terms of computational load [2]. The azimuth and elevation are directly calculated from the estimated time delays so that it does not need a time-consuming 2-D search over the array manifold as the beamformer does. The TDOA technique has been successfully used to localize mobile users in wireless cellular networks in the form of a long baseline system where the mobile is surrounded by base stations. Some indoor localization systems can use a pair of ultrasonic transmitter and receiver to deliver the localization solution with high accuracy based on the TDOA technique [3]. In application scenarios where a long baseline system is not available or it is impractical to establish such a system, a short baseline system is attractive to locate a far-field signal source. There are a number of advantages associated with a short baseline system, including convenient deployment and maintenance, easy time synchronization, and reduced impact from terrain and wind. In the case where the signal is very transient such as those from gunshot and cannon and bomb explosion, the arrival difference of pulse time is directly measured by the localization system hardware [4], [5]. In these scenarios, beamforming is not applicable in general since the signal characteristics are unknown and probably time varying; only the relative time delays can be measured. Thus, TDOA-based direction finding with a sensor array would be the primary option for locating the transient signal source. However, there are very limited reports related to this technique in the literature. Detection and localization of an explosion sound source is very useful in military operations and services such as for military training and reconnaissance of ground tactical operation. Fig. 1 illustrates the scenario where an acoustic array is employed to detect the signal of

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a single explosion source and to locate the source. The sound source generates a far-field signal traveling as an approximate plane wave. In the past, the long baseline scheme has been used dominantly to localize the transient explosion source, because the precision of the data acquisition system was not high enough to distinguish the tiny TDOA measurements associated with small distance differences. However, the hardware performance of the present system has been improved significantly to be able to measure small TDOA values such that it is practicable to estimate DOA of a far-field source with a number of TDOA measurements. A number of gunshot location systems have been developed recently and the TDOA-based localization has become an important issue in public security [6], [7]. The primary goal of a gunshot location system is to promptly estimate the source bearing in 3-D space with the TDOA technique. However, to the best of the authors’ knowledge, there is only one time delay direction finding (TDDF) algorithm proposed in [8]. In the case of 3-D array with an arbitrary structure, the DOA estimator provides a closed-form suboptimal solution based on least square (LS) minimization. Unfortunately, there is a significant gap between the performance of this suboptimal scheme and the Cramer–Rao lower bound (CRLB) if the array is asymmetric. The case of an asymmetrical array often occurs when an array needs to be deployed quickly, especially for a battlefield application. Rapidly arranging sensors into the optimum ring structure is desirable [9], [10], but it is not easy to accurately adjust the sensor location in a short period of time. As a consequence, the array of sensors has a random distribution and the array structure is asymmetric. The aim of this paper is to develop new TDOA-based direction finding methods suited for arbitrary 3-D array to remove or significantly reduce the performance gap. The remainder of this paper is organized as follows. Section II introduces the related work. Section III describes the TDOA direction finding model when using a 3-D array. Section IV presents our design ideas and the detailed DOA estimation procedure of the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm. Section V examines the DOA estimation performance of the proposed methods through numerical simulations. Section VI evaluates the performance by field experiments. Section VII provides some discussions and Section VIII concludes this paper. II. R ELATED W ORK Previous related work mainly focused on the cases of fixed sensor structure of a special shape and the data processing is performed in the frequency domain. A 3-D maneuvering target can be tracked using the extended Kalman filter algorithm with TDOA detection data in the multisensor passive location [11]. Ho and Vicente [9] suggest that the optimal TDOA direction finding performance would be obtained when the array elements are deployed along a ring, that is, the array is circular. Gazzah [12] and Gazzah and Abed-Meraim [13] argue that a V-shape array would be better than the ring shape under some specific conditions. However, in some scenarios, the sensor network and/or array must be rapidly deployed such as in the

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battlefield scenario. As a consequence, it would be impractical to finely adjust the sensor locations to form a specific shape within the sensor deployment region, so that the array structure may be arbitrary. It is worth noting that although the ML method has been investigated in the localization field, it is used for long baseline positioning, beamforming, and high-resolution spectrum estimation [14]. To the best of the authors’ knowledge, there is no report about adopting the ML method to infer the source azimuth and elevation angles directly from the TDOA measurements and this is a motivation for the work reported in this paper. CRLB can be used for both theoretical analysis and performance comparison, which provides a performance reference for all unbiased estimators. The CRLB for a 3-D TDOA localization system is derived for the large-scale industrial environment about indoor applications [15]. The first explicit CRLB formula was derived in [16] to benchmark the DOA estimation covariance matrix, which was valid for the narrowband DOA estimation case. In [17], CRLB for a single-source case was derived for both wideband source localization and DOA estimation. Nielsen [18] derived the analytic CRLB expressions for the azimuth and elevation estimation with a random 3-D array to take the first sensor as TDOA’s reference node. If all the available TDOA measurements could be used to estimate DOA, the direction finding performance would be improved. A similar idea has been proposed for localizing a source in a reference-free (RF) manner using a sensor network and an array [19], [20], but not for TDOA-based direction finding. Berdugo et al. [8] present a method for 1-D, 2-D, and 3-D array structures referred to as the TDDF algorithm to use reference nodes. In the 3-D array case, if the sensors are symmetrically distributed on the three coordinate axes, TDDF would achieve CRLB; however, if they are not symmetric, the estimation would not. In [21] and [22], analysis is usually performed for developing a symmetric uniform array for TDOA-based direction finding. Here a random array shape is considered, and we propose a direction finding approach based on evolutionary computation in artificial intelligence. The intelligent optimization process is adopted to search for the optimal source azimuth and elevation estimation solutions. Evolutionary algorithms are swarm-based intelligent optimization methods, some of which have been investigated for direction finding and localization. Zaman et al. [23], [24] proposed a GA hybridized with pattern search for the joint amplitude and DOA estimation using a special array of L-type shape. Lui et al. [25] employed PSO for positioning a source with TDOA measurements. We have not found any reports related to TDOA-based direction finding based on evolutionary computation and this is another motivation for the work presented in this paper. III. TDOA-BASED D IRECTION F INDING M ODEL Table I provides the main symbols used and related to direction finding nomenclature in this paper. The cap ∧ upon a symbol represents an evaluated or measurement value.

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TABLE I M AIN S YMBOLS AND T HEIR D EFINITIONS

the point P is the perpendicular projection of source P onto the horizontal plane. Usually, the first sensor is taken as the reference node located at the coordinate origin. The DOA vector K is given as follows: ⎤ ⎡ ⎤ ⎡ sin θ cos φ k(x) (1) K = ⎣ k(y) ⎦ = ⎣ sin θ sin φ ⎦. cos θ k(z)

Fig. 2.

Illustration of direction finding with a 3-D array.

All vectors and matrices are boldfaced. For convenience, the main symbols of GA and PSO to be discussed in Section IV are also included in Table I. Source direction finding with a 3-D array is illustrated in Fig. 2, where φ is azimuth and θ is elevation. In the figure there are seven symmetric sensors (s1 , s2 , . . . , s7 ), and

ˆ The purpose is to estimate the direction vector K using the TDOA measurements. The delay between any two sensors equals their distance difference divided by wave speed. The TDOA vector (τ ) equals the location vector (S) projection onto the K vector divided by propagation speed, i.e., τ = SK/c. Let εˆ τ denote the TDOA measurement error as the difference between the measured TDOA (τˆ ) and its true value (τ ). This error is the dominant factor affecting the direction finding performance and is expressed by εˆ τ = τˆ −

SK . c

(2)

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CRLB is a lower bound on the variance of any unbiased estimator. Nielsen [18] has derived CRLB expressions for azimuth and elevation estimation error when using an arbitrary 3-D array of identical omnidirectional sensors, but he formulated the expressions based on the frequency array so Fourier transform is required to transform the received signal data. To conveniently analyze TDOA direction finding in the time domain, we derive the CRLB expressions in time domain in Appendix A. Currently, the LS method is the most important method for TDOA-based DOA estimation with details of the method provided in Appendix B [26]. Note that only if the array is geometrically symmetric, i.e., sensors are distributed by a fully balanced configuration, the LS method can reach CRLB. However, when a random 3-D array is used for direction finding, the LS estimator is not efficient and the estimation performance cannot approach the CRLB. Motivated by this observation, two direction finding methods based on evolutionary computation are proposed in the following section. IV. E VOLUTIONARY DOA E STIMATORS A. Design Ideas The main design idea is fourfold. 1) The error square sum of 3-D array direction finding is defined as the cost function. 2) All TDOA measurements are fully used to improve DOA estimation performance and avoid choosing a reference sensor. 3) The azimuth and elevation estimates from LS estimator are taken as benchmark, i.e., the azimuth and elevation parameters of each individual/particle in the initial generation are randomly selected around the benchmark. 4) Through real-time measured temperature, wind speed, and wind direction, sound speed is estimated by means of DOA estimation results of the LS estimator. 1) Sound Speed Estimation: During the search process of GA and PSO, an estimated sound speed is required to compute the cost function. In the outdoor scenario, the significant factors to influence sound speed include air temperature, wind speed, and wind direction. Assume that the available real-time in situ weather parameter measurements are air temperature (Tˆ0 ), wind speed (VˆW ), and wind direction (φˆ W ). The azimuth of sound wave can be estimated by the LS method (φˆ LS ); thus the intersection angle between the estimated DOA and the measured wind direction is φˆ W − φˆ LS . The sound speed estimate is then computed by  cˆ = 20.06 273.15 + Tˆ0 + VˆW cos(φˆ W − φˆLS ). (3) 2) Variable Bound: Usually, the initial DOA estimation by the LS estimator would not deviate from the actual direction too much. To speed up the convergence of the evolutionary process and avoid the possible local minima, the initial direction is set to be the estimates from the LS estimator, i.e., φˆLS and θˆLS . The two DOA parameters are also constrained by  φˆ LS + Bφ ≥ φ ≥ φˆ LS − Bφ (4) θˆLS + Bθ ≥ φ ≥ θˆLS − Bθ

where Bφ and Bθ are constants to constrain the two DOA parameters to a rectangular area of length 2Bφ and width 2Bθ and centered at (φˆ LS , θˆLS ). The two bound parameters are defined as follows: 

Bφ = kφ cστ Bθ = kθ cστ

(5)

where the units of Bφ and Bθ are both degree, kφ and kθ are scaling factors which are selected as 100 in the simulation to be discussed later, and στ is the standard deviation of TDOA measurement error whose unit is second. In the case where {τˆi j } have different standard deviations, their average value may be used. As usual, the DOA estimation error of a practical localization system would be several up to a dozen of degrees. The initial DOA estimation by the LS method would not deviate much from the real direction. Empirically, (Bφ , Bθ ) can be set to be about 30°, which would be suitable for most DOA estimation algorithms. Too small a bounded space would not enable a normal evolutionary search, while too large a bounded space would result in a slow convergence for the optimization process. Typically GA and PSO estimators would be constrained to search in a small degree bound, e.g., several degrees, after some evolutionary generations. For convenience of algorithm implementation, PSO uses real number (decimal) coding, while GA uses binary coding. However, the binary system can be transformed into the decimal system or vice versa. Also, the azimuth and elevation values adopt the degree instead of the radian unit during the evolutionary process. In fact, the two units would be easily converted into each other as required. 3) Cost Function: If the first sensor is chosen as the reference node, we define the cost function as follows: f (φ, θ ) =

N 

[x j sin θ cos φ + y j sin θ sin φ

j =2

+ z j cos θ − cˆ · τˆ1 j ]2 .

(6)

The aim of the proposed evolutionary DOA estimators is to minimize f (φ, θ ) with respect to the azimuth and elevation, and find its global optimal solution. In the sensor location matrix (S), the first sensor is taken as the reference node and set at the coordinate origin. The LS method and CRLB given in Appendixes A and B are based on the assumption, so they are denoted by LS-R#1 and CRLB-R#1, respectively. The corresponding GA-based and PSO-based direction finding methods which use (6) as cost function are denoted by GA-R#1 and PSO-R#1, respectively. 4) Reference Free: Assuming an array with N sensors, N − 1 TDOA measurements are obtained when giving a reference sensor. However, the maximum number of distinct TDOA measurements is N(N − 1)/2. Using the full set of measurements, estimation performance would be improved significantly. Herein we propose a reference-free TDOA-based cost function to achieve the performance gain. The idea is to minimize the evolutionary fitness function using all the

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available TDOAs as follows: f (φ, θ ) N−1 N   = [(x j − x i ) sin θ cos φ + (y j − yi ) sin θ sin φ i=1 j =i+1

+ (z j − z i ) cos θ − cˆ · τˆ j i ]2 .

(7)

The corresponding GA-based and PSO-based methods are denoted by GA-RF and PSO-RF, respectively. 5) Evolutionary Convergence: Since the proposed GA direction finding method adopts the best individual preservation strategy of the evolutionary computation theory, i.e., the individual solution with the optimal fitness would not be replaced in the next generation, the global convergence of the evolutionary process can be reached theoretically. In practice, the population size and evolutionary generation can be tuned by simulation manner, so that the global convergence can still be ensured in general. Comparatively, the proposed PSO direction finding method cannot always guarantee a global convergence theoretically, although actually it can for almost all cases in this paper. Since the DOA estimation of the LS estimator is exploited as the initial direction guess and constraints in (4) are applied to the two parameters, the divergence problems related to the traditional PSO can be avoided. The PSO estimator has a very good convergence performance as evidenced by the fact that we have conducted many simulations using simulated data and field experimental data and the PSO estimator always has a global convergence. On the other hand, the GA occasionally has the convergence problem as observed from extensive simulations. In case the GA or the PSO algorithm does not converge in practice, the problem can be notified so that the estimation results such as by the LS algorithm can be used, providing useful information about the direction of the sound source. B. DOA Estimation Procedure of GA GA procedure in the pseudocode form is given as follows. Step 1: Determine an appropriate population size, maximum genetic generation, float-point precision of azimuth and elevation as a real number variable, crossover probability (Pc ), and mutation probability (Pm ). Step 2: Input the total number of sensors, 3-D coordinates of each sensor, TDOA measurement between each pair of sensors, measured air temperature, wind speed, and wind direction. Step 3: Determine the variable bounds of initial individual. 1) If the standard deviation of TDOA (στ ) is known, it is decided by (5) after the scaling factor is set. 2) If the knowledge about στ cannot be acquired in advance, the bounds are selected by user experience. Step 4: Estimate DOA with LS estimator. Step 5: Initialize population. 1) The two real number DOA variables of initial individual are randomly selected from the bound given by (4).

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2) The DOA variables are changed into two segment chromosomes of binary coding with variable float-point precision. Step 6: Compute the fitness function of each individual with (6) or (7) for GA-R#1 or GA-RF. Step 7: Use the roulette wheel selection strategy to select the male and female individuals by individual fitness. Step 8: Randomly and respectively select two crossover points on the male and female chromosomes with two segments, and then execute crossover and mutation operations for each segment of two chromosomes by crossover probability and mutation probability. Crossover probability is the probability that a pair of chromosomes will be crossed. Mutation probability is the probability that a gene on a chromosome will be mutated randomly. Usually, Pc and Pm can be set as 0.75 and 0.05, respectively. It should be pointed out that the generated new DOA individual still is a feasible solution after crossover and mutation, as the decoding result of the binary individual is limited within the DOA parameter bound. Step 9: Preserve the elitist of current generation, and then repeat Steps 6–8 to replace other individuals in the old population till the new population has been generated. Step 10: Stop the evolutionary procedure by two termination criteria: if the maximum genetic generation has been reached, or else if the elite solution has not changed for a certain number of generations, then output two variables of the elite as DOA estimate. C. DOA Estimation Procedure of PSO PSO in the pseudocode form is given as follows. Step 1: Determine an appropriate number of total particles, maximum number of iterations, learning factors c1 and c2 , particle inertia weight ω, and velocity update maximum (vMax). Step 2: Input the total number of sensors, 3-D coordinates of each sensor, TDOA measurement between any two sensors, measured air temperature, wind speed, and wind direction. Step 3: Determine the variable bounds and set the initial particle in the same manner as used in Step 3 of the GA procedure. Step 4: Estimate DOA with the LS estimator. Step 5: Initialize particle swarm. 1) The first- and the second-dimension fly positions of each particle are randomly selected from the DOA parameter bound, respectively. 2) The initial fly velocities of two dimensions are set to be zero according to the accustomed rule. It should be explained that when using PSO, a possible solution is represented by the particle fly position vector. Here the vector consists of 2-D parameters, i.e., azimuth and elevation. Additionally, each particle has a current fly velocity vector for the associated dimensional fly positions, which represents a magnitude and direction toward a new solution. Step 6: Compute the cost function of each particle with (6) or (7) for PSO-R#1 or PSO-RF.

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Step 7: Determine the optimal solution of current generation (G best ) and the global optimal solution (T best ) with all particle fitnesses. Step 8: Assume that we know the velocity vi, j (t) and position pi, j (t) of the i th particle in the tth generation; herein j denotes the space dimensions ( j = 1, 2). If r1 and r2 are random numbers uniformly distributed within [0, 1], iteratively compute the following: vi, j (t + 1) = ωvi, j (t) + c1r1 [G best (t) − pi, j (t)] + c2r2 [T best (t) − pi, j (t)] pi, j (t + 1) = pi, j (t) + vi, j (t).

(8) (9)

Step 9: If the updated absolute value of particle velocity is larger than vMax, renew the velocity by vi, j (t + 1) = sign(vi, j (t + 1)) · vMax

(10)

where sign(u) = 1 for u > 0, otherwise sign(u) = −1. Step 10: Stop the evolutionary procedure by two termination criteria: if the maximum iteration generation has been reached, or else if the global optimal solution has not changed for a certain number of generations, then output the first and the second particle fly position parameters of global optimal solution as DOA estimate. V. S IMULATION R ESULTS A. Simulation Setup 1) Sound Speed: Assume that the current weather parameter measurements are fixed as follows: air temperature is 20°; horizontal wind speed is 10 m/s, which equals 5–6 level gales according to the Beaufort scale; horizontal wind direction is π/3. Usually, the wind velocity near the ground means the horizontal wind speed, not considering the vertical airstream by atmosphere knowledge. Under the ideal steady weather conditions, air temperature, wind speed, and wind direction are assumed to remain the same during the period from acoustic incident to the completion of measurement data sampling, and thus, the estimated sound speed is constant. In an outdoor environment, weather parameters are usually not constant, resulting in a time-varying sound speed. According to meteorology theory [27], their rational variation ranges are given by ⎧ ⎪ Tˆ + 5 ≥ T0 ≥ Tˆ0 − 5 ⎪ ⎨0 (11) VˆW + 6 ≥ VW ≥ VˆW − 6 ⎪ ⎪ ⎩ˆ φW + 22.5 ≥ φW ≥ φˆ W − 22.5 where T0 , VW , and φW are the time-varying temperature, wind speed and direction, respectively, while Tˆ0 , VˆW , and φˆ W are, respectively, their means. In simulations these real weather parameters are set to take the measured data as the means, which vary around these means within the above ranges under the nonsteady weather conditions. In simulations in which the array and source locations are known in advance, the real azimuth of sound wave (φ) can be obtained from these locations. Actually, the simulated real sound speed is determined by

(12) c = 20.06 273.15 + T0 + VW cos(φW − φ).

2) Geometry Structure: Assume that the sound source location is (500, 300, 100) m. If the array is symmetric, each sensor is in turn located at (0, 0, 0), (−30, 0, 0), (30, 0, 0), (0, −30, 0), (0, 30, 0), (0, 0, −30), and (0, 0, 30) m when the sensor population is set as seven. The reason for taking array dimensions as about 30 m is that the distance can provide adequate TDOA measurement accuracy, and moreover, time synchronization precision can be guaranteed when connecting sensors by a wired cable of this length. If the sensor array is not symmetric, the x-axis and y-axis positions are randomly selected in a ring of 30-m radius. As the actual altitude difference among employed sensors would not be large for convenient installation, herein the z-axis positions are randomly selected in the small range [−10, 10] m. Except that the array installation becomes easier, the elevation estimation performance degradation can be observed under the relatively small difference among sensor altitudes. The asymmetrical array size (i.e., number of elements/ sensors) is set as eight in simulations, which is in accordance with the experimental hardware setup to be discussed in the next section. The position coordinates of the eight array sensors are selected as: (4.00, 29.73, 0.38), (26.21, −14.58, −9.35), (−29.86, −2.83, 0.65), (−25.84, −15.23, −0.18), (−1.86, 29.94, 9.11), (−6.32, −29.32, 0.81), (17.43, −24.41, −2.94), and (−29.62, −4.72, 4.20) m. The first sensor can be set as the coordinate origin through coordinate translation. The ratio of array aperture to the distance between the array and the source is denoted by ρi ρi = si − s1 /p − s1 .

(13)

For far-field sources (ρi  1), the signal is treated as a plane wave. We can take any location of array as the benchmark point of DOA estimation, as the plane wave has the same direction for any point on the array. However, as ρi is not much less than one, the statistical performance of DOA estimation would be affected a little by different benchmark locations. Based on the above discussions, in the following simulations and experiments, DOA benchmark location is selected as follows: LS-R#1, GA-R#1, PSO-R#1, and CRLB-R#1 adopt the first sensor as the benchmark point, while GA-RF and PSO-RF use the array center as the benchmark point. If the array is not in a regular shape, the array center calculated with the sensor (x c , yc , z c ) is   Nlocations as follows: N x c = (1/N) i=1 x i , yc = (1/N) i=1 yi , z c = (1/N) N z . i=1 i 3) TDOA Noise: With the given array geometry structure, the TDOA measurement error can be assumed as a Gaussian random variable with a specific standard deviation. The TDOA noise power (10 log στ2 ) ranges from −70 to −40 dB, i.e., στ ranges from 0.3 to 10 ms. This TDOA noise bound would be basically within the range of realistic measurement noise/error. The simulated TDOA measurement is the signal arrival distance difference divided by the simulated real sound speed plus Gaussian noise d j − di + ετi j . (14) τˆi j = c

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Fig. 3.

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RMSE of azimuth estimation with a symmetric array. Fig. 5. RMSE of azimuth estimation with a random array under steady weather conditions.

Fig. 4.

RMSE of elevation estimation with a symmetric array. Fig. 6. RMSE of elevation estimation with a random array under steady weather conditions.

4) Evolutionary Parameters: The simulation parameters of GA and PSO are selected as follows. GA’s float-point precisions of azimuth and elevation are set as 0.01, cross probability is 0.75, and mutation probability is 0.05. PSO’s particle inertia weight is 0.08, the learning factors c1 = 2 and c2 = 2, the maximum renewal velocity is 5◦ . The population sizes of GA and PSO are set as 100. When the global optimal solution has not changed in recent 20 generations, GA and PSO stop search according to the regular evolutionary criterion. B. DOA Estimation Results 1) Symmetric Array: In this case the weather conditions is assumed time varying, which is a hard condition compared with steady weather. The nonsteady weather would result in an unfixed speed of sound wave. In the proposed GA-based and PSO-based methods, the unfixed sound speed needs to be estimated. The root mean squared error (RMSE) criterion is used to evaluate DOA estimation performance with 2000 simulation runs, while the square root of CRLB is computed to compare them. Figs. 3 and 4 show the RMSE of azimuth and elevation estimation versus TDOA measurement noise, respectively.

It can be seen that even if the weather conditions is not steady, GA-R#1, PSO-R#1, and LS-R#1 have the same performance that obviously reaches CRLB-R#1. GA-RF and PSO-RF are noticeably superior to CRLB-R#1, as they use many more TDOA measurements. This conclusion is drawn under nonsteady weather, let alone steady condition. As expected, the DOA estimation error increases as the TDOA measurement noise increases. 2) Random Array Under Steady Weather: Now 2000 simulations are run for random array under steady weather conditions with a constant sound speed at first. Figs. 5 and 6 show the RMSE of the azimuth and elevation estimation results, respectively, for the case of a random array. As observed, the elevation estimation performance is much inferior to the azimuth estimation one. It can be seen that GA-R#1 and PSO-R#1 are a little better than LS-R#1, but there is a relatively large gap between the three estimators and CRLB-R#1. It would be useful to develop a better estimator to reduce the large gap in the future. Similar to the symmetric case, GA-RF and PSO-RF significantly outperform the widely used LS estimator.

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Fig. 9.

Number of evolutionary generations of GA-R#1.

Fig. 10.

Number of evolutionary generations of GA-RF.

Fig. 11.

Number of evolutionary generations of PSO-R#1.

Fig. 7. RMSE of azimuth estimation with a random array under nonsteady weather conditions.

Fig. 8. RMSE of elevation estimation with a random array under nonsteady weather conditions.

3) Random Array Under Nonsteady Weather: For the random array and nonsteady weather conditions, the DOA estimation results with 2000 simulation runs are given in Figs. 7 and 8. It can be seen that the results are similar to those in the steady weather case. From Appendix B it is known that the LS estimator does not need any information about the sound speed. Although knowledge of sound speed is required for the GA-based and PSO-based methods, these two methods are insensitive to the sound speed variation in outdoor nonsteady weather conditions. The performances of the GA-based and PSO-based estimators are improved significantly when using the full set of TDOA measurements since more measurements include more information, producing a diversity gain. C. Evolutionary Generation When the cost functions of GA and PSO do not change, or the change is very small in the recent 20 generations, it is considered that the evolutionary process has approached the global optimum solution from a statistical probability perspective. Two thousand simulation runs are conducted for

each TDOA noise power. Evolutionary generations are counted until the algorithm approaches the steady state, and the results are plotted by boxplot. The required generations of GA-R#1, GA-RF, PSO-R#1, and PSO-RF are shown in Figs. 9–12, respectively. On every box the central stripe is the generation median,

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Fig. 12.

Fig. 13.

Geometry locations of deployed sensors and sound source.

Fig. 14.

Picture of the field experiment system.

9

Number of evolutionary generations of PSO-RF.

and the top and bottom edges of the box are the 25th and the 75th percentile, respectively. The top and bottom whiskers of the box extending to the most extreme data points respectively represent the maximum and minimum statistical generation not considered outliers. From the boxplots we can see the approximate generation bound and their probability distribution. It is shown that the GA-based and PSO-based methods converge after about 30 and 90 generations, respectively. Notably, their maximum generation does not exceed 150 and 400, respectively. Additionally, the required generation numbers of GA-RF and GA-R#1 are indistinguishable; so is the case with PSO-RF and PSO-R#1. It is concluded that the GA-based and PSO-based DOA estimation methods can complete the evolutionary search process rapidly, and the convergence is guaranteed from a statistical viewpoint. VI. E XPERIMENTAL R ESULTS To verify the feasibility of the proposed methods, we conducted extensive experiments in the fields. The acoustic signal sources are bomb explosions. A total station was used to precisely measure the locations of sensors and sound source, which can achieve centimeter accuracy. The total station is an electronic/optical instrument used in modern surveying and building construction, which actually is an electronic theodolite integrated with an electronic distance meter to read slope distances from the instrument to a particular point. The eight sensor locations are given as follows (meter as unit): (6.06, −26.44, −0.48), (−5.36, −25.13, 1.70), (−20.92, −9.99, 5.33), (−24.35, −3.50, 5.45), (−3.67, 29.42, −1.50), (8.86, 28.13, −3.21), (25.86, 20.88, −5.43), and (13.54, −13.36, −1.85). The sound source location is (251.18, −361.50, 21.20) m. The longest and the shortest distances between sound source and sensors are 467 and 415 m, respectively; while the largest distance between a pair of sensors is 57 m. The 3-D view plot of their locations is provided in Fig. 13, where the digit near sensor location indicates the sequential number of the related sensor.

A picture of the field experiment system is shown in Fig. 14. The data acquisition instrument was located at the center of the array, while the eight sensors were deployed around it. Each acoustic sensor with a windshield was fixed on a tripod. The sampling frequency of data acquisition is 51 200 Hz. The detailed parameters of the acoustic sensor used for the experiments are as follows. The sensitivity is 50 mV/Pa, responding frequency is 6.3 Hz–20 KHz, output impedance is 110 , and maximum output voltage is 4.5 Vrms. The data acquisition board CompactRIO-9234 of National Instruments (NI) Company was used to synchronously collect the acoustic signal from eight channels. At the same source location, ten sound sources of bomb blast were tested on April 21, 2014. The experimental process lasted 2 h. The explosions occurred when the temperature was 19 °C, the average wind speed was 6 m/s, and the wind direction was approximately along the direction from sensor#4 to sensor#1. Since sensor#1 has the shortest distance to the explosion point, the sound wave first arrives at this sensor. The peak time point (i.e., the time instant of the maximum amplitude of the received sound waveform) at sensor#1 is taken as the reference time point and set as zero. Table II shows the measured peak time points of all the eight sensors for the ten experiments/explosions. In this table the peak time point is a decimal fraction and not an integer, as these data are outputted

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TABLE II P EAK T IME P OINTS (N UMBER OF S AMPLES ) OF R ECEIVED S OUND WAVEFORMS AT E IGHT S ENSORS

TABLE III DOA E STIMATION R ESULTS OF T RUE D ATA

Fig. 15.

Set of eight received sound waveforms.

by the NI LabVIEW software with a higher data resolution precision. The TDOA (expressed in seconds) between any two sensors is simply calculated as the difference between the two peak time points (expressed as the number of samples), divided by the sampling frequency. A set of eight received sound waveforms is illustrated in Fig. 15, which contains the noise and the starting part of the waveform of the field TDOA measurements. The peak time points are indicated in the figure, which can be easily observed. In our field experiment, the acoustic signal sources are bomb explosions, which produce a strong sound pressure. As mentioned earlier, the longest and the shortest distances between the sound source and the sensors are 467 and 415 m, respectively. As the largest distance difference in arrival is only 52 m, about one tenth of the distance, such a small distance difference would produce a rather minor difference

in the sound pressure received at the sensors. Under the same propagation condition and using exactly the same sensor, the received sound pressure would decrease as the distance increases. However, as shown in Fig. 15, the third sound pressure waveform has the highest amplitude, while the fifth and the seventh have relatively small amplitudes. This abnormality would mainly be due to the diversity in the parameters of the sensors, although the slight difference in the propagation paths may also make some contribution. Note that the unit of the sound pressure in Fig. 15 is pascal (Pa) and the highest sound pressure received at the sensors is about 250 Pa. The sensitivity of the sensor is 50 mV/Pa, so the highest amplitude in Fig. 15 is equivalent to 12.5 V. The individual DOA estimation errors of the ten field experiments and the RMSE of the different methods are given in Table III. The RMSE of true data is calculated by RMSE = (STD2 + Mean2 )1/2 , where STD and Mean represent the standard deviation and mean error, respectively. For comparison, the RMSE values related to 10log(στ2 ) = −40 dB in Figs. 7 and 8 are also listed in Table III with RMSE1 and RMSE2 denoting the experimental results and the simulation results, respectively. There is a good match between the simulated and experimental azimuth RMSE for some algorithms; while a good match between the simulated and experimental elevation RMSE is obtained for other algorithms. On average, the results of simulated azimuth estimation are better than the experimental results, while the results of simulated elevation estimation are inferior to the experimental results. From Table III it can be seen that there

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is good consistency between the field experimental results and the simulation results shown in Figs. 7 and 8. In fact, for the elevation estimation performance degradation problem under the small difference among sensor altitudes, the GA-based and PSO-based methods can have an excellent performance. They even achieve better performance than the simulation for GA-R#1 and PSO-R#1. VII. D ISCUSSION The traditional direction finding technique is the LS estimator, estimating the azimuth and elevation of a signal source with TDOA measurements at a 3-D sensor array. From the above results and analysis we can see that the LS estimator has a closed-from expression and is a good choice for scenarios where the sensor array is symmetric and only one set of reference-node-based TDOA measurements is used. On the other hand, when using the TDOA measurements of all pairs of sensors as suggested in this paper, the proposed GA-based and PS-based estimators would be preferred for both symmetric and asymmetric array configuration. In the proposed algorithms, the source signal propagation speed is needed; however, only imperfect sound speed estimate can be obtained. It seems to be feasible that the propagation speed may be treated as the third unknown parameter in addition to azimuth and elevation during the evolutionary process of GA-based and PSO-based estimators. However, the introduction of the third unknown parameter would incur performance degradation since the search for the solutions is performed in 3-D instead of 2-D parameter space. The exact sound speed is dependent on several factors, mainly including air temperature, wind, as well as propagation environment. Provided that the air temperature and wind can be measured in real time, the sound propagation speed can be adjusted online by using the measured temperature, wind speed and direction, as well as the LS-based DOA estimation results. In fact the weather parameters (air temperature, wind speed, and wind direction) can be easily measured by some meteorological instruments or devices. That is, the sound propagation speed can be readily determined based on the proposed method, although it is inevitable to produce some estimation error which can be accommodated by the proposed DOA estimation methods in general. Certainly, the direction of a source can also be determined accordingly once the source position estimate is available. The method in [25] is suited for positioning and direction finding only when there is a long baseline system especially for wireless cellular networks where the source or the mobile is surrounded by a group of base stations and radio frequency signals are used. The proposed PSO algorithm is intended for determining the direction instead of location of an acoustic source using an acoustic sensor short baseline system. Although the implementation of the PSO algorithm is similar, the motivations and application scenarios are rather different. It is worth mentioning that the TDOA measurements can be used to estimate the position of the acoustic target such as using a hyperbolic positioning algorithm [28]. However, as indicated by the results presented in [29], the position estimation error is really large, between 99 and 304 m for

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six different estimation algorithms, while the propagation range is about 200 m and the array radius is about 25 m so that the RBR is about four. It is obvious that such position accuracy would be unsatisfactory. As stated previously, the propagation range in the experiments reported in this paper is between 415 and 467 m, while the array radius is still about 25 m, resulting in a RBR greater than eight. Such a large RBR would produce worse position estimation performance. Therefore, it is impractical to employ TDOA measurements to get the position of the acoustic target using a single short baseline sensor array. However, it is feasible to utilize multiple short baseline sensor arrays to determine reliably the position of a target by combining the accurate direction estimations from different arrays separated from each other with sufficient distances. Usually obstacles like buildings will influence the sound transmission. However, since an acoustic array-based short baseline system is employed, the RBR is usually rather high. Thus, the obstacle influence on time of arrival at all sensors would be very similar provided that the obstacle is not very close to some sensors. As a consequence, the impact of obstacles on the TDOA measurements would be minor in general. In practice, it is necessary to deploy an acoustic array over a suitable area to avoid nearby obstacles, so that the obstacle impact on the direction finding of the proposed two methods can be minimized. The application scenario considered is the direction finding of a source such as a bomb explosion or a gunshot which emits a transient signal. The proposed algorithms would perform reliably as long as the peak of the transient pulse which is usually sharp can be accurately located even in the presence of significant environmental noise. However, when the source location is very far away from the sensor array, the time difference between the acoustic sensors is very small and the signal’s intensity is easily influenced by environmental noise. To enable a reliable direction finding in such a challenging scenario, advanced signal processing techniques such as pattern recognition should be exploited. This is beyond the scope of this paper, but it would be a good future research direction. The proposed methods focus on the scenarios where only a single source emits the acoustic signal over a specific period of time. Direction finding of multiple sources can be realized if the signal arrival time of a source is significantly different from that of other sources, regardless of their locations. On the other hand, it would be a challenge to perform direction finding when the signal arrival times of two or more different sources are nearly the same. However, it would be still possible to realize direction finding of multiple sources if the pulse of the transient signal of a source can be distinguished from those of other sources such as based on the power and pattern of the pulse. In this case, the performance of direct finding would be degraded. It is worth conducting more investigations on this issue in the future. VIII. C ONCLUSION In this paper we have proposed two direction finding methods based on TDOA measurements, i.e., GA-based and

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PSO-based estimators. To guarantee fast convergence and avoid local minima, the LS estimator is utilized to provide initial estimates of the azimuth and elevation parameters, and the parameter bounding rule is proposed to constrain the direction parameters. To improve the direction estimation performance, all the TDOA measurements instead of a set of reference-based measurements are exploited in the definition of the cost function. We propose that the sound speed be estimated using the measured weather parameters and the LS-based direction estimation results. Simulation results demonstrated that the proposed two direction finding methods can quickly reach steady state after a small number of evolutionary generations. When GA-based and PSO-based estimators utilize the full TDOA measurement set, their performance can be better than the CRLB using reference sensor-based TDOA measurements when the noise power is relatively high. The proposed two methods also significantly outperform LS estimator when either a symmetric or a random array is used. Extensive field experiments have been conducted and results related to ten explosion sources have been reported in this paper. The experimental results are in consistent with the simulation results. In addition, the PSO-based estimator outperforms the GA-based estimator in terms of RMSE. In the future, we will investigate the LS estimator and CRLB when using the full TDOA measurements. Additionally, we will also develop the optimization procedure of ML for TDOA-based direction finding using either the reference node mode or the reference-free mode. A PPENDIX A CRLB W ITH R EFERENCE N ODE Consider sensor#1 as the reference node and define  N the array center as (x c , yc , z c ) where x c = (1/N) i=1 xi , N N yc = (1/N) i=1 yi , z c = (1/N) i=1 z i . The CRLB for the azimuth and elevation estimation can be derived as    2 CRLB(φ) = Jθθ / Jφφ Jθθ − Jθφ   (15) 2 CRLB (θ ) = Jφφ / Jφφ Jθθ − Jθφ where Jθθ = G

N 

[(x i − x c ) cos φ cos θ

i=1

+ (yi − yc ) sin φ cos θ − (z i − z c ) sin θ ]2 Jφφ = Gsin2 θ

N 

[(x i − x c ) sin φ − (yi − yc ) cos φ]2

i=1

Jθφ = G sin θ

N  [(x i − x c ) sin φ − (yi − yc ) cos φ] i=1

· [(x i − x c ) cos φ cos θ + (yi − yc ) sin φ cos θ   G = 1/ c2 στ2 .

− (z i − z c ) sin θ ]

A PPENDIX B L EAST S QUARE DOA E STIMATION When the number of sensors is larger than three, the system of DOA estimation based on the set of TDOA measurement equations is overdetermined. The LS method is widely adopted to solve the minimization problem in parameter estimation. According to LS criterion, the estimate of DOA K is produced as ˆ = −c(ST S)−1 ST τˆ . K

(16)

Accordingly, the azimuth estimate is calculated by ˆ ˆ φˆ LS = tan−1 (k(y)/ k(x)) and the elevation estimate is given by   ˆk(x)2 + k(y) ˆ 2 /k(z) ˆ ˆθLS = tan−1 .

(17)

(18)

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[18] R. O. Nielsen, “Estimation of azimuth and elevation angles for a plane wave sine wave with a 3-D array,” IEEE Trans. Signal Process., vol. 42, no. 11, pp. 3274–3276, Nov. 1994. [19] Y. Wang and G. Leus, “Reference-free time-based localization for an asynchronous target,” EURASIP J. Adv. Signal Process., vol. 2012, p. 19, Jan. 2012. [20] A. Amar and G. Leus, “A reference-free time difference of arrival source localization using a passive sensor array,” in Proc. IEEE SAM, Jerusalem, Israel, Oct. 2010, pp. 157–160. [21] U. D. Amin and R. Hussain, “Direction finding of a single far field acoustic source using a smart 3-D array of acoustic sensors,” in Proc. ICET, Islamabad, Pakistan, Nov. 2007, pp. 226–231. [22] D. J. Mennitt, “Multiarray passive acoustic localization and tracking,” Ph.D. dissertation, Dept. Mech. Eng., Virginia Polytechnic Inst. State Univ., Blacksburg, VA, USA, 2008. [23] F. Zaman, I. M. Qureshi, A. Naveed, J. A. Khan, and R. M. Asif Zahoor, “Amplitude and directional of arrival estimation: Comparison between different techniques,” Prog. Electromagn. Res. B, vol. 39, pp. 319–335, Mar. 2012. [24] F. Zaman, I. M. Qureshi, J. A. Khan, and Z. U. Khan, “An application of artificial intelligence for the joint estimation of amplitude and two-dimensional direction of arrival of far field sources using 2-L-shape array,” Int. J. Antennas Propag., vol. 2013, pp. 1–10, May 2013, Art. ID 593247. [25] K. W. K. Lui, J. Zheng, and H. C. So, “Particle swarm optimization for time-difference-of-arrival based localization,” in Proc. EUSIPCO, 2007, pp. 414–417. [26] J.-S. Hu, C.-Y. Chan, C.-K. Wang, M.-T. Lee, and C.-Y. Kuo, “Simultaneous localization of a mobile robot and multiple sound sources using a microphone array,” Adv. Robot., vol. 25, nos. 1–2, pp. 135–152, Apr. 2011. [27] J. R. Holton, An Introduction to Dynamic Meteorology, 4th ed. Burlington, MA, USA: Elsevier, 2004. [28] Y. T. Chan and K. C. Ho, “A simple and efficient estimator for hyperbolic location,” IEEE Trans. Signal Process., vol. 42, no. 8, pp. 1905–1915, Aug. 1994. [29] C. Xunxue, L. Songsheng, C. Yunfei, G. Haomin, and Y. Ting, “Combination TDoA localization algorithms for far-field sound source based on short base-line sensor network,” (in Chinese), J. Comput. Res. Develop., vol. 51, no. 3, pp. 465–478, Mar. 2014.

Xunxue Cui received the B.S. degree in artillery command and the M.S. degree in operation research from Hefei Artillery Academy, Hefei, China, in 1991 and 1996, respectively, and the Ph.D. degree in pattern recognition and artificial intelligence from the University of Science and Technology of China, Hefei, in 2001. He served as a Post-Doctoral Fellow with the Department of Computer Science and Technology, Tsinghua University, Beijing, China, from 2002 to 2004. He is currently a Professor with the New Star Institute of Applied Technology, Hefei. He holds five authorized patents of invention, and has authored two scientific research monographs and two textbooks. His current research interests include sensor network, target localization (in particular, for acoustic source), swarm intelligent algorithms, and multiobjective optimization. Dr. Cui is a member of the China Computer Federation Technical Committee on Sensor Network.

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Kegen Yu (SM’12) received the Ph.D. degree in electrical engineering from the University of Sydney, Sydney, NSW, Australia, in 2003. He was with Jiangxi Geological and Mineral Bureau, Nanchang, China, Nanchang University, Nanchang, China, the University of Oulu, Oulu, Finland, the CSIRO ICT Centre, Sydney, Australia, Macquarie University, Sydney, and the University of New South Wales, Sydney. Since 2011, he has been an Adjunct Professor with Macquarie University. He is currently a Professor with the School of Geodesy and Geomatics and the Collaborative Innovation Center for Geospatial Technology, Wuhan University, Wuhan, China. He has co-authored a book entitled Ground-Based Wireless Positioning (Wiley and IEEE Press) (also available in Chinese), and made contributions in positioning and remote sensing to five books. He has authored or co-authored over 80 refereed journal and conference papers. His current research interests include the global navigation satellite system (GNSS) reflectometry and ground- and satellite-based positioning. Dr. Yu is on the Editorial Boards of the EURASIP Journal on Advances in Signal Processing, the IEEE T RANSACTIONS ON A EROSPACE AND E LECTRONIC S YSTEMS , and the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY. He was a lead Guest Editor of a Special Issue of Physical Communication on Indoor Navigation and Tracking and a Special Issue of the EURASIP Journal on Advances in Signal Processing on GNSS Remote Sensing.

Songsheng Lu received the Ph.D. degree from the Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China, in 2006. He was involved in the design and manufacture of Experimental Advanced Superconducting Tokamak (EAST) for fast control power supply, and acquiring and processing data for fault diagnosis. He is currently an Associate Professor with the New Star Institute of Applied Technology, Hefei. His current research interests include computer control system theory and application, signal processing, and machine vision.