ultrasonic spatial target localization using artificial ...mar 02, 2020 · no sound insulation was...

Submitted to IEEE Trans. Ultrason., Ferroelectr., Freq. Control, 2019. 1

Ultrasonic Spatial Target Localization UsingArtificial Pinnae of Brown Long-eared Bat

Sen Zhang, Xin Ma, Zheng Dong, Weidong Zhou

Abstract—Echolocating bats locate a target by echolocationand their performance is related to the shape of the binauralconformation in bats. In this study, we developed an artificialsonar system based on the vertical sound localization character-istics of the brown long-eared bat (Plecotus auritus).First, usingthe finite element method, we found that the beam of the firstside lobe formed by a pinna constructed according to that inthe brown long-eared bat shifted in an almost linear mannerin the vertical direction as the frequency changed from 30 kHzto 60 kHz. We established a model of the relationship betweenthe time-frequency features of the echo emitted by brown long-eared bats and the spatial direction by using the pre-trainedneural network. We also developed a majority vote-based methodcalled sliding window cumulative peak estimation (SWCPE) tooptimize the outputs from the neural network. In addition, an L-shaped pinna structure was designed to simultaneously estimatethe azimuth and elevation. Our field experiments indicated thatthe binaural conformation and relative binaural orientation bothplayed vital roles in spatial target localization by these bats.Accurate echolocation can be achieved using a simple binauralsonar device even without binaural time difference information.

Index Terms—Echolocation, bionic, spatial target localization.

I. INTRODUCTION

The disruptive development of mobile and flying robotssuch as automatic guided vehicles and unmanned aerial ve-hicles demands new sensory approaches for target search andobstacle avoidance. Machine vision-based methods can satisfythe basic requirements in favorable lighting environments butvariables such as darkness, fog, and smoke hinder their widerapplication. Sonar sensing can effectively complement thecommonly used vision sensing techniques in robot applica-tions. In traditional sonar systems, transmitter and receiverarrays are used widely for navigation and localization, but theexcessive number of sensors included in these systems oftencauses difficulties during installation and layout. In contrast,the bat echolocation system is an extremely compact sonarsystem with only two sound receivers and one speaker, whichwould obviously be preferable for robot applications becauseof its simplicity, low cost, and high performance [1] [2].

The excellent navigation and target localization capabilitiesof bat sonar have attracted much attention from researcherswho have focused on various aspects. In particular, the rela-tionships between echolocation and the auditory neurons or

Sen Zhang, Xin Ma, and Zheng Dong are with the School of InformationScience and Engineering, Shandong University, Qingdao 266237, China;Xin Ma is also with Shenzhen Research Institute, Shandong University,Shenzhen 518000, China; Weidong Zhou is with the School of Microelec-tronics, Shandong University, Jinan 250022, China. Emails:{max, zhengdong,wdzhou}@sdu.edu.cn. Corresponding author: Xin Ma.

auditory cortex [3] [4] [5], have been investigated in orderto identify a suitable echo processing method for navigationand localization by observing the activities of the auditorynerve and auditory cortex during echolocation by bats. Inaddition, studies of the behavior of bats [6] [7] [8] [9] [10],have provided great insights into the intrinsic mechanismresponsible for navigation and localization by bats. Moreover,investigations have considered the acoustic roles of the physi-ological structures of bats, including the sound field character-istics related to the facial physiological structure [11], auriclestructure [12], and vocal tract [13]. All of these studies haveabove provided important insights to facilitate the artificialreproduction of echolocation by bats.

Some interesting results in bat research have been physicallyreproduced and even implemented in practical applications.Most two-dimensional target localization methods based onbinaural systems have been implemented based on the inter-aural time difference (ITD) [14] [15] or interaural intensitydifference (IID) [16], whereas the majority of the three-dimensional (3D) target localization systems have employedmulti-receiver designs [17] [18]. However, these types ofapplications are not fundamentally different from the conven-tional sensor array methods. Some reproduction techniquesexploit the unique sound field characteristics determined bythe physiological structure of bat ears, which more strictlyimitate the localization effect of bat sonar. For example,Chiu et al. conducted experiments based on the behaviorof big brown bats (Eptesicus fuscus) and found that thetragus is related to vertical sound localization [19]; Kucdesigned an experimental model based on acoustic mirrorformed by rotating a lancet, which exhibited an elevationversus notch frequency sensitivity [20];and Schillebeeckx etal. [21] used two microphones and one ultrasonic emitter,conducted the experiments of echolocation for a spatial targetin the laboratory. In our previous study [22],using a finiteelement method (FEM) [23], We found in a specific widerange, the time-frequency characteristics of sonar in long-earedbats had a strong relationship with the vertical direction (i.e.,elevation angle). In the present study, we estimated the angleof the echo using another approach inspired by the soundfield characteristics of the pinnae in brown long-eared batsbased on FEM simulations. The novelty of this work withrespect to previous realizations lies in the utilization of thedistinguishing ability of the brown long-eared bats in verticalspace and its simplicity in real-world application. This studyobtained the following three main conclusions. The rest ofthe paper is structured as follows. Section II describes themethods used in our work. Section III describes the results

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of our experiments, including the results of simulation andfield experiments. Section IV discusses the method in ourexperiments for target echolocation, and Section V draws aconclusion on the system and its potentiality of application.

MATERIALS AND METHODS

A. Numerical analyses of Plecotus auritus

In order to obtain more evidence to inspire the designof an accurate artificial bat-like sonar system, we conductednumerical simulations of the pinnae in Plecotus auritus byusing a FEM and Kirchhoff integral [24] to analyze the spatialfrequency characteristics. In particular, 3D digital modelsof Plecotus auritus pinnae were obtained by digital imageprocessing [25] using computed tomography scans of pinnae(Fig 1B). We placed a sound source in the inner ear canal in thenumerical model and performed numerical calculations basedon the FEM. First, we used FEM and Kirchhoff integral toobtain the beam pattern for the digital ear in the simulation.The acoustic near field inside a cuboid-shaped volume sur-rounding the ear was then calculated using a FEM comprisinglinear cubic elements derived directly from the voxel shaperepresentation. Finally, the far-field directivity pattern wascalculated by projecting the complex wave field amplitudesoutward onto the surface of the computational domain of theFEM using a Kirchhoff integral formulation.

Fig. 1. Pinna of brown long-eared bat. (A) Photo of the pinna of brownlong-eared bat. (B) Three-dimensional model of brown long-eared bat pinna.

B. Artificial bat-like Device

The artificial bat-like ears were produced using a 3D printeraccording to a 3D digital model obtained based on pinnaesamples taken from the carcass of a brown long-eared bat. Toavoid damage during assembly and to allow the fixation ofa microphone, the size of each printed artificial bat-like earwas three times larger than the original ear. The frequencyrange of Plecotus auritus ears is 2060 kHz, so the frequencyrange used in the experiments was adjusted to 5kHz to 20kHz according to the scale model principle [26]. A pair ofultrasonic microphones (SPU0410LR5H-QB, Knowles Elec-tronics, Itasca, Illinois, USA) were placed inside the pair ofartificial ears and insulating glue was smeared in the gaps

between the microphones and the pinnae to prevent outsidesound waves entering the microphones from the bottom ofthe model. The artificial ears were then fixed to a rotatingplatform and tilted forward 40◦(Fig 2E). A stepping motorwas mounted under the rotating platform to facilitate rotationof the ears and to measure positioning information at theazimuth. An ultrasonic loudspeaker (UltraSound Gate PlayerBL Light; Avisoft Bioacoustics e.K., Glienicke, Germany) wasfixed under the stepping motor (Fig 2A,B).The target was fixedon the green spots and the device was located in the eightdifferent locations in turn to obtain the training data. Yellowspots A, B, and C were used for locating the device to collectthe testing data. The layouts of the target and device in thetraining and testing processes are illustrated in Fig 2F.

Fig. 2. Bat-like sonar and layout used in the single target localizationexperiments. (A, B) Target, parallel erect pinnae device, and the environment.(C) Top view of platform. (D) Spherical coordinate. (E) Side view of theartificial pinnae.(F) Top view of the target and device during training andtesting.

C. Data acquisition

All of the data acquisition experiments were conducted inan experimental chamber (8 m (length) 6 m (width) 3.6m(height)) (Fig 2A). No sound insulation was present in thechamber. The acquisition parameters are listed in Table I. Thetarget for measurement was a small ball made of rubber witha diameter of 11cm and it was suspended by a string. Thefrequency response of the ear model in different directionscould be measured by controlling the height of the targetand the rotation angle of the motor (Fig 2A,2C,2D). Theultrasonic signal acquisition and processing device was asignal acquisition card (PXIe-6358 and PXIe-1082; NationalInstruments, Austin, Texas, USA; sampling at 100 KS/s),which allowed multi-channel synchronous signal acquisition.The signal emitted by the brown long-eared bat is a type of



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linear frequency-modulated pulse signal, which has similarfrequency characteristics to a chirp [27], so we set the ul-trasonic loudspeaker to emit a chirp pulse signal (see Fig 3A)in our active target echolocation experiments in order toimitate the pulse emitted by the brown long-eared bat, andits time-frequency intensity is shown in Fig 3D. We set thesignal acquisition card in the work mode for two-channelsynchronous signal acquisition in order to collect the binauralsignals in a synchronous manner. Details of the signals emittedin the active echolocation experiment are also listed in Table I.

Fig. 3. Example of a signal emitted by the loudspeaker and echoesreceived by the two ears. (A,B,C) Emitted signal and echoes received byleft and right microphones. (C)Top view of the platform. (D,E,F) Spectrogramsfor the emitted signal and echoes received by the left and right microphones.

D. Feature extraction

The signals received by the left and right microphonesare shown in Fig 3B and 3C. Zero crossing rate endpointdetection with center clipping was conducted to detect thebeginning position of the echo. The effective signals were thentransferred into time-frequency representations as:

Xn(ejω) =

∞∑m=−∞

x(m)W (n−m)e−jωm, (1)

where x(n) is the signal received after the endpoint detectionprocess and W (n) is the window function, which shifts thesound signal by a step length on the time axis. We usedHamming windows with a length of 1 ms (100 samples) asthe window function and the shift step was half of the windowlength. The time frequencies at 0.5 kHz frequency resolutionfor the pulse signals received by the left and right microphonesare shown in Fig 3E and 3F.

The spectrogram energy in the emitted pulse signal wasmainly concentrated near the diagonal line, so the spectrogramenergy for the echo was also concentrated near the diagonalline. Thus, we set a threshold to suppress the effects of inter-ference components while maintaining the value constant onor near the diagonal line in the spectrogram. The spectrogramwas then restricted to one vector by summing the values alongthe frequency channels. After the treatment, a time-frequencyrepresentation with length T was transformed into a vectorwith n elements, as described in Equation 2. In our experiment,we selected n = 30 and connected the vectors from the leftand right echo signals to obtain one vector with 60 elementsas the input for the classifier.

X =

x11 x12 · · · x1T...

.... . .

...xn1 xn2 · · · xnT

set threshold−−−−−−−−→

0 · · · x1 i x1 i+1 · · · x1 i+d · · · 0...

......

. . . . . . . . . . . ....

0 · · · · · · · · · xn i+n−1 xn i+n · · · xn i+n−1+d

truncate−−−−−−→

x1 i x1 i+1 · · · x1 i+d · · · 0...

. . . . . . . . . . . ....

0 · · · xn i+n−1 xn i+n · · · xn i+n−1+d

∑−→

X1

...Xn

(2)

E. Neural network for estimating the angle of the spatial target

Artificial neural networks are used widely in pattern recog-nition tasks as efficient methods. At present, deep learning isvery popular because of its good classification performance,but we selected the traditional back-propagation (BP) feed-forward neural network as an estimation tool because of itssimplicity and practicality, but also because of its convenientregression function. We applied the BP feed-forward neuralnetwork to three tasks comprising elevation estimation inthe case of parallel erect pinnae, elevation in the case oforthogonal pinnae, and azimuth estimation. The BP feed-forward neural networks used in the three tasks had the samestructure (Fig 4A), which comprised an input layer with 60neurons (30 + 30, i.e., the features extracted from the echosignals for the left and right artificial ears where fed directlyinto the network), a hidden layer with nine neurons, and anoutput layer with one output neuron. The three layers werefully connected in the BP neural network. Tan-sigmoid andpure linear were selected as the activation functions in thehidden layer and output layer, respectively. In the trainingphase, the neural network learned the characteristics of thetime-frequency patterns reflected by the target at differentangles (elevations or azimuths). The network was trainedusing the LevenbergMarquardt optimization algorithm. Aftertraining, the time-frequency patterns generated from untrainedultrasonic echoes were fed into the network. The structureof the neural networks used in the three tasks was thesame but the normalization functions were different becausethe output angles differed. The three types of outputs werelinearly transformed into activities between 0.05 and 0.95, andthey are shown in Fig 4B, 4C, and 4D, respectively. In theestimation process, the output neuron activities were linearlyre-transformed according to the activity functions and theywere used as the angle estimates for the respective inputs ineach task.



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Fig. 4. Back-propagation feed-forward neural network used in oursystem. (A) Structure of the neural network. (B), (C) and (D) Transformationfunctions between the angle value and output neuron activity for training andtesting in different tasks.

F. Sliding window cumulative peak estimation (SWCPE) undermulti-pulse input

The activities of the output neurons indicated the valuesof the azimuth or elevation during the analysis of one pulse.If multiple pulses were analyzed for one target by the sameclassifier, multiple estimated values were exported. In general,further optimization could be conducted based on the multipleestimated values and the optimized values obtained by themethod had a higher level of confidence. This principle mayexplain why bats locate targets based on a pulse train. In orderto imitate the actual signals that are generally emitted by batsin the form of a pulse train, we developed a novel directionangle estimation enhancement method called SWCPE forobtaining near-optimal estimates based on multiple relativelyrough estimation values. For n initial estimate values, the P-levels SWCPE process is explained as follows.(1) For n estimated values (each value represented one sample)obtained by a certain method, such as a BP neural network, thefirst level moving window with length L moved over the rangeof all n samples with a step length l. The starting positionof the window (left edge) was aligned with the point withthe minimum value and the end position (right edge) was thesample point with the maximum value. Each point in the rangewas set with an initial token value y of 0.(2) When the window moved one step, the y value for eachpoint in the window increased by the number of samples inthe current window. After the window reached the end, wecalculated the point with the maximum y value as the optimalvalue of the first-order moving window. If more than one pointhad the maximum value, we selected the intermediate pointbetween the left and right points with the maximum value asthe optimum solution.(3) In general, the first-order moving window was used toobtain an optimized scope that could include the optimumsolution with the maximum probability. Next, L/2 length

second-level window and L/4 length third-level window es-timation were performed up to a p-level window estimationto obtain a narrower search scope. The number of levelsdetermined the accuracy of the estimate. In principle, theaccuracy of the estimate was less than the half of the windowswidth.

RESULTS

Numerical analysis results: Spatial acoustic characteristics ofdigital brown long-eared bat pinnae

Frequencies spanning the entire frequency range (from 20kHz to 60 kHz with a step size of 1 kHz) known to becovered by the first harmonic [28] of the biosonar pulseswere analyzed using the numerical method (Method A). Thefirst side lobe in the beam pattern (Fig 5A, 6B) exhibiteda frequency-driven scanning characteristic and its power wasrelatively strong when the frequency exceeded 32 kHz. Whenthe frequency was less than 30 kHz (Fig 5C), the half-powerbeam width curve was relatively large whereas the power ofthe side beam was low and the orientability of the lobe was notconcentrated, which resulted in low directional resolution. Thebeam direction of the first side lobe shifted along the elevationin an almost linear manner as the frequency changed from 30kHz to 60 kHz, whereas the azimuth of the side lobe remainedalmost stable (Fig 5D). The peak of the beam for differentfrequencies appeared to alternate along the elevation, therebysuggesting that in this frequency band, the combination modeof the frequency intensities changed greatly in the directionof elevation, and this implied that the vertical resolutionwas strong under this frequency combination with a potentialfunctional relationship.

Artificial bat-like sonar device experiment: Vertical spatialresolution of the frequency combination and application totarget localization

A potential relationship between the frequency combinationand spatial direction was demonstrated by the simulations, butwe had little information about how wide this relationshipmight spread in the hemispherical space and how to applyit in the physical space. Thus, physical verification was stillrequired for the spatial resolution of the frequency combina-tion in the vertical direction and the range of the width alsohad to be clarified. Thus, a bat-like device was designed toestimate the angle of the spatial point-like target (Fig 2A) bymimicking the function of the ears of the brown long-earedbat in order to clarify whether the consistency width range ofthe frequency combination changed with the vertical direction.The detailed experimental parameters are shown in Table I.

A. Target elevation estimation using parallel erectpinnae under different width ranges.

We used the artificial bat-like sonar device to emit andreceive acoustic signals with the two artificial pinnae pointingupward and collected data using the data acquisition device(Method C), as summarized in Table I. Inspired by the highresolution of the pinna and the potential functional relationship



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Fig. 5. Acoustic characteristics of the digital pinnae. (A) Beam patternof the pinna. (B) Beam pattern of the sound field under different frequency.(C) Half-power beam width and energy ratio for the side lobe and main lobe.(D)Elevation and azimuth for the side lobe with different frequencies.

TABLE IExperimental parameters

ID Name Comment1 Sampling rate 100 kHz2 Model size of bat ear Three times the original size3 Microphone distance 5 cm4 Transmission signal Linear frequency modulation sig-

nal5 Frequency range 5-20kHz6 Active signal duration 5 ms7 Alteration mode of azimuth By altering the height of the tar-

get(small ball).8 Alteration mode of elevation By rotating the pinna.9 Scope of azimuth alternation -90◦ to 90◦(step length: 10◦)

for estimating the elevation inparallel erect pinnae experiments;-28◦ to 28◦(step length: 7◦)for the orthogonal pinnae experi-ments.

10 Scope of elevation measure-ment

20 to 55◦ (step length: 5◦) inparallel erect pinnae experiments,1268◦(step length: 7◦) for theorthogonal pinnae experiments.

implied by FEM analysis, a BP neural network was employedto estimate the continuous position in the vertical direction.The detailed structure of the BP neural network used in ourstudy is presented in Method E.

1) Single pulse target elevation estimation under differentwidth ranges

The simulation results demonstrated the differentiation ofthe frequency combination with the elevation in a linear region.To test whether the properties of this frequency combination

were related to the elevation in a wider range, we combined10 data sets of spatial feature samples according to thedifferent widths in the horizontal direction, and estimated theelevations in each data set. Single pulse and different setsof data categories under different azimuth scopes for everystatistic (Fig 6A) were used to evaluate the accuracy of theelevation estimated under different width ranges. In order toobtain reliable results, the sonar device was located at eightdifferent sites (blue circles in Fig 2F), where the small ballused as the target was located at the center, as indicated bythe green circle in Fig 2F. The horizontal distance betweenthe ball and the sonar device was 1.5m. The training data andtesting data were different but they came from the same dataset, as explained in Method G. The values of −N◦ to +N◦

represented the scope of the limited azimuth angle from theleft and right (Fig 6A). Tenfold cross validation was conductedto obtain reliable results for each −N◦ to +N◦ scope. Theamounts of data in each training and testing set were relatedto this range, i.e., (((N/10) × 2 + 1) × 8) × 0.9 for trainingand (((N/10) × 2 + 1) × 8) × 0.1 for testing. In order toensure that the distribution of the data was reasonable, thetraining data and test data were evenly sampled from eightdifferent locations. The mean results obtained by tenfold cross-validation are shown in Fig 6A. The average precision wasnearly 100% with the scope from −20◦ to +20◦ of the limitedazimuth. The average accuracy exceeded 90% when the limitangle of the azimuth was −60◦ to +60◦ and the averageaccuracy exceeded 80% even when the limit angle of theazimuth was −90◦ to +90◦. These findings illustrated thegood wide-angle effect on elevation estimation and the highaccuracy in the middle direction of the azimuth, which areessential for target detection. In contrast, the average accuracyof the azimuth estimation was only about 35 percent when thelimited angle of elevation was 20◦ to 55◦ (Fig 6B). Thus, theazimuth estimates were clearly not as good as the elevationresults, thereby indicating that the changes in the features withthe azimuth lacked regularity compared with the elevation.The experimental results confirmed the results obtained in thesimulation experiment and they clarified the effective widthrange in the vertical direction.

2) Improving the echolocation accuracy using a pulse train

Many studies have shown that bats can enhancetheir echolocation ability by transmitting a pulsetrain [29] [30] [31] [32] [33]. Thus, we used a pulsetrain estimation method to imitate this behavior and theSWCPE method (Method F) was developed to obtainaccurate results. Increasing the pulse number in each traincould effectively compensate for the reduced accuracy of theelevation estimation caused by the increase in the azimuthrange. When the number of pulses in one pulse train reached20, the elevation estimation accuracy was more than 95%under an error standard of ±3◦ (middle panel in Fig 7B)within an azimuth range of ±50◦ and more than 90% underan error standard of ±5◦ within a large azimuth range upto ±90◦ (bottom panel in Fig 7B). Thus, by using the pulsetrain, the bats could obtain higher accuracy and a betterwide-angle range for target localization.



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Fig. 6. Single pulse estimation results obtained with parallel erect pinnae.(A) Average accuracy (under ±5◦ error) of the elevation estimates in 10cross-validation cycles. The 10 histograms for each cycle represent the limitedscopes of the azimuth for the training set ranging from ±0◦ to ±90◦.Thevertical axis represents the average precision ratio where the value with anerror less than 5◦ was considered to be the correct result.(B) Average accuracy(under ±5◦ error) of the azimuth estimations in 10 cross-validation cycles.Only one histogram in each cycle represents the result obtained under thelimited scope of 20◦ to 55◦ for the elevation.

3) Generalization tests

Robustness testing methods were designed to verify thegeneralizability of the system used for estimation. The trainingdata were the same as those used for single pulse targetelevation estimation. The training process was also similarto the process employed for single pulse target elevationestimation, except no data in the training set were retainedfor use as test data. Thus, for every limited scope of theazimuth, the amount of data used in each training set was(((N/10) × 2 + 1) × 8). The generalization testing sampleswere collected in the same experimental chamber but underconditions where the artificial bat-like devices were placedoutside the eight sites used in the training process (e.g., sitesA and B in Fig 2F). The neural network used for the test wastrained with the 90◦ limited scopes of the azimuth and underthe 1.5-m condition, as described above. Cross-validation wasnot conducted in the testing process. SWCPE (Method F)was also used for multiple pulse testing to obtain the finalestimated values. Fig 7C shows the performance under sixconditions. The results were similar for the steel ball used asa reflector in this experiment, although it was not used fortraining. The results were similar although the steel ball wasnot used for training. The performance was greatly influencedby the distance (the green line with a cube and blue line witha diamond). The intensity of the echo was larger at 1 m than 2m, but the performance was not better than that with 2 m. Themultiple pulse chains effectively improved the performancewith distances of 1 m and 2 m, and the improvements wereslightly greater with 2 m than 1 m.

B. Target angle estimation using orthogonal pinnae

In the elevation estimation process described above, the twopinnae of the brown long-eared bat were parallel to each other.We observed that the two pinnae of the brown long-eared bat

Fig. 7. Pulse train estimation results obtained with parallel erect pinnaeunder different conditions. (A) Spatial distribution of the elevation estimatedusing a pulse train under conditions with different numbers of pulse trains(from left to right, the number of pulses in a single pulse train range fromthree to 20) and different sliding window levels (from top to the bottom, thenumbers of levels in SWCPE are one, two, and three, and the widths of thesliding window at each level are 10, five, and two, respectively; see MethodF). The horizontal and vertical axes in each small colormap represent thelimited azimuth and estimated elevation (range from 20◦ to 55◦), respectively.(B) Average elevation estimation accuracy using pulse trains under differenterror criteria (from top to bottom: ±1◦, ±3◦, and ±5◦, respectively) andunder different limited azimuth ranges. The different colors represent variousnumbers of pulses in a single pulse train. (C) Average accuracy of elevationestimation for a steel ball with a single pulse at 1.5 m, rubber ball with asingle pulse at 1.5 m, rubber ball with 20 pulses at 2 m, rubber ball with 20pulses at 1.0 m, rubber ball with a single pulse at 2 m, and rubber ball witha single pulse at 1.0 m.

often stretch to a certain angle when hunting for prey. If theangle is 90◦, the orthogonality of the two pinnae can be usedto obtain the aspect angles in the two orthogonal directions.The orthogonal pinnae of the artificial brown long-eared batsused for target localization are shown in Fig 8. Except for thedifferences shown in Table I, the other measurement conditionswere the same as those employed in the generalization tests.

The results in Fig 9 demonstrated that elevation estimationand the azimuth estimation could be performed simultaneouslywith the orthogonal pinnae, thereby indicating the effective-ness of the proposed method. In the box plots in Fig 9Aand 10B, the red horizontal lines denote the median estimated



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Fig. 8. Orthogonal pinnae active sonar device and design of theexperiment. (A, B) Images of the target, orthogonal pinnae device, andenvironment. (C, D, E, F) Process employed to form the effective targetregion. Before tilting the pinna, the effective ranges of the beam patterns forthe two pinnae corresponded to the shaded regions in panel C. The estimatedelevation regions for each pinna are shown as the shaded regions in panelD. Each pinna tilted forward 40◦ to form the overlapping region, which isshown as the shaded region in panel E. The actual statistical scope was −28◦to +28◦ in the azimuth and 12◦ to 68◦ in the elevation.

angles, and these result show that 50% of the estimated angleswere located in the blue box, and thus both the elevationand azimuth estimation method achieved good results. Thestandard deviations of both the elevation and azimuth resultsremained fairly stable at various angles. This result indicatedthat although the signal-to-noise ratio (SNR) was poor athigh elevations or in the marginal azimuth, the correlationsbetween the sweeping frequency and elevation were stronglymaintained. Similar to the case with parallel erect pinnae,the pulse train estimation method was used to correct thedeviations in the estimated angle and to enhance the accuracy.Fig 9C shows the localization results under different pulsetrains. For all of the pulse trains, the percentages increased asthe number of pulses increased. For the pulse train with 10pulses, more than 60% of all the target angles were estimatedwith an error of |θ−θ| ≤ 3◦ and |φ−φ| ≤ 3◦, more than 91%with an error of |θ − θ| ≤ 5◦ and |φ− φ| ≤ 5◦, and the errorrate was only less than 1% when the demand was |θ−θ| ≤ 7◦

and |φ − φ| ≤ 7◦. Clearly, using a pulse train improved theestimation accuracy. Fig 9D shows the performance under 2.0m using the training data obtained with 1.5 m. The differentdistance decreased the match between the training data andtest data, but the pulse chain effectively compensated for theloss of the performance in the case of orthogonal pinnae.

Fig. 9. Elevation and azimuth estimated with the active orthogonalpinnae. (A, B) Comparisons of the azimuth and elevation estimates in thesingle pulse test with the actual values. (C) Cumulative distributions for thecorresponding azimuth and elevation errors. The abscissa axis represents theerrors for both the azimuth and elevation to meet. (C) Cumulative distributionsfor the corresponding azimuth and elevation errors with 1.5 m. (D) Cumulativedistributions for the corresponding azimuth and elevation errors with 2.0 m.

DISCUSSION

In this study, we developed a strictly bat-like sonar systeminspired by the brown long-eared bat (Plecotus auritus). Thesonar system comprised one emitter and two microphonesfitted with artificial pinnae to imitate the physical conformationof the sonar system in bats, and the signals emitted weresimilar to those produced by brown long-eared bats. In contrastto other bat-like sonar systems, our strictly bat-like sonar hadalmost the same pinna construction, while the same soundwas emitted and received as the prototype. This strict bat-like method for reproducing the behavior of bats can providefurther insights into the true sonar mechanism employed bybats as well as serving as a validation method.

Schillebeeckx et al. established a set of artificial pinnamodels for 3D target location [34] as an important advancein the development of strictly bat-like sonar. They used aBayesian classification method to separately model all of thepositions in hemispheric space at a resolution of 1◦. Theirexperiments demonstrated the feasibility of a strict bat-likemodel for spatial localization. The process determined in theirexperiments suggested that the echo transfer functions in eachdirection are independent of each other, i.e., the input featuresneed to be calculated in every model. We suggest that thismethod is theoretically suitable to some degree for all typesof bionic models of pinna, including the human ear. However,in practice, the results obtained by this method for each typeof auricle will be quite different, because the differences inthe feature distributions in different directions are not alwaysconspicuous, and thus the model parameters will be too closein different directions.

The main difference between our method and that employedby Schillebeeckx et al. is that we considered the characteristicsof the long-eared brown bat where the spatial sound fieldbeam clearly changed with the frequency in the verticaldirection (central axis of the auricle). This effect was clearlydemonstrated in our FEM simulations. However, the scope ofthe width of the effect and the effect on the horizon were not



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clear based on the results obtained in our FEM simulations.Experiments using our artificial bionic ear model showed thatthe changes in the echo features in the vertical direction wererelated to the combination of the frequency components andthis vertical correlation was maintained in a wide range upto ±60◦ (Fig 7B). The correlation was still present in thehorizontal direction (Fig 6B), but it was significantly weakerthan that in the vertical direction.

We also identified the intrinsic relationship between thetime-frequency features of the echoes used by the brownlong-eared bat and the spatial direction. Spatial angle infor-mation could be obtained from the echo, and thus the echomust contain angle information. Thus, the echo features weredirectly related to the angle information. According to therelationship between the features of the echolocation-relatedtransfer function (ERTF) and spatial position, if we use X todenote the ERTF features and f to express their distributionin two-dimensional space (θ, ϕ), then X can be written asfollows.

X = f(θ, ϕ) (3)

Our experiments suggested that in a certain range of azimuthangles, a function g(X) exists that is only related to ϕ:

ϕ = g(X) = g(f(θ, ϕ)) (4)

where θ and ϕ denote the azimuth and elevation of a target,respectively. Thus, it is necessary to determine the function interms of the relationship between the angle information andfeatures in the orthogonal coordinate system. This functionis usually difficult to obtain, but the relationship can beapproximated by the BP-based feed forward neural networkas:

gk(x) = f2(

nH∑j=1

Wkj · f1(d∑i=1

Wji · xi +Wj0) +Wk0) (5)

where k is the number of output variables, and f1 and f2are discrimination functions in the hidden and output layers,respectively. In the case of parallel erect pinnae, we can obtain:

gϕ(X) =9∑j=1

Wjϕ · f(60∑i=1

Wjϕi ·Xi +Wjϕ0) +W0ϕ (6)

where f is the discrimination function in the hidden layer:

f(x) =2

1 + ϕ−2x− 1 (7)

For orthogonal pinnae, we can obtain gϕ(X) and gθ(X)separately using two independent neural networks.

Feature distortion had important effects on the estimatedresults and a change in the SNR ratio was one of thefactors responsible for feature distortion, as also mentioned bySchillebeeckx et al [35]. However, for the results estimateddirectly for the targets made of different materials and at

different distances (Fig 8C), the SNR ratio was not the onlyfactor responsible for distortion. In particular, the SNR ratiofor the echo from the steel ball was much stronger than thatfor the wave reflected from the rubber ball, but there was nosignificant difference in the estimates for the steel ball andrubber ball. When we tested the targets located at 2 m usingthe network trained at 1.5 m, the results were poor even thoughthe SNR of the reflected echo at 1 m was better than that forthe target at 2 m. No other form of distance compensationwas conducted in our experiments apart from using a simpleclassification decision method for multiple outputs. However,a real bat may have the ability to compensate for distance.Effectively compensating for the loss of echo features atdifferent distance should be addressed in future research.

CONCLUSION

In contrast to other spatial angle classifier estimation meth-ods, our proposed algorithm only used a one-dimensionallabel, i.e., either the elevation or azimuth, as the output fromour classifier model. Our experiments also suggested that theproposed structure and model are suitable for accurate spatialtarget echolocation with a limited computational load in a real-time system.

ACKNOWLEDGMENTS

This work was supported by the Shenzhen Science andTechnology Research and Development Funds (Grants No.JCYJ20170818104011781) and the Key Research and De-velopment Program of Shandong Province (Grants No.2017GGX10113 and 2019GGX101063). We also thank allthe anonymous reviewers for their helpful and stimulatingcomments on earlier versions of the manuscript.

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