A model of echolocation of multiple targets in 3D space from a single emission

Simulation of Pulse-Echo Radar for Vehicle Control and SLAM

Pulse-echo sensing is the driving principle behind biological echolocation as well as biologically-inspired sonar and radar sensors. In biological echolocation, a single emitter sends a self-generated pulse into the environment which reflects off objects. A fraction of these reflections are captured by two receivers as echoes, from which information about the objects, such as their position in 3D space, can be deduced by means of timing, intensity and spectral analysis. This is opposed to frequency-modulated continuous-wave radar, which analyses the shift in frequency of the returning signal to determine distance, and requires an array of antenna to obtain directional information. In this work, we present a novel simulator which can generate synthetic pulse-echo measurements for a simulated sensor in a virtual environment. The simulation is implemented by replicating the relevant physical processes underlying the pulse-echo sensing modality, while achieving high performance at update rates above 50 Hz. The system is built to perform design space exploration of sensor hardware and software, with the goals of rapid prototyping and preliminary safety testing in mind. We demonstrate the validity of the simulator by replicating real-world experiments from previous work. In the first case, a subsumption architecture vehicle controller is set to navigate an unknown environment using the virtual sensor. We see the same trajectory pattern emerge in the simulated environment rebuilt from the real experiment, as well as similar activation times for the high-priority behaviors (±1.9%), and low-priority behaviors (±0.2%). In a second experiment, the simulated signals are used as input to a biologically-inspired direct simultaneous mapping and localization (SLAM) algorithm. Using only path integration, 83% of the positional errors are larger than 10 m, while for the SLAM algorithm 95% of the errors are smaller than 3.2m. Additionally, we perform design space exploration using the simulator. By creating a synthetic radiation pattern with increased spatiospectral variance, we are able to reduce the average localization error of the system by 11%. From these results, we conclude that the simulation is sufficiently accurate to be of use in developing vehicle controllers and SLAM algorithms for pulse-echo radar sensors.

Echolocation of insects using intermittent frequency-modulated sounds

Using echolocation influenced by Doppler shift, bats can capture flying insects in real three-dimensional space. On the basis of this principle, a model that estimates object locations using frequency modulated (FM) sound was proposed. However, no investigation was conducted to verify whether the model can localize flying insects from their echoes. This study applied the model to estimate the range and direction of flying insects by extracting temporal changes from the time-frequency pattern and interaural range difference, respectively. The results obtained confirm that a living insect's position can be estimated using this model with echoes measured while emitting intermittent FM sounds.

An investigation of acoustic beam patterns for the sonar localization problem using a beam based method

Target localization can be accomplished through an ultrasonic sonar system equipped with an emitter and two receivers. Time of flight of the sonar echoes allows the calculation of the distance of the target. The orientation can be estimated from knowledge of the beam pattern of the receivers and the ratio, in the frequency domain, between the emitted and the received signals after compensation for distance effects and air absorption. The localization method is described and, as its performance strongly depends on the beam pattern, the search of the most appropriate sonar receiver in order to ensure the highest accuracy of target orientation estimations is developed in this paper. The structure designs considered are inspired by the ear shapes of some bat species. Parameters like flare rate, truncation angle, and tragus are considered in the design of the receiver structures. Simulations of the localization method allow us to state which combination of those parameters could provide the best real world implementation. Simulation results show the estimates of target orientations are, in the worst case, 2° with SNR = 50 dB using the receiver structure chosen for a potential practical implementation of a sonar system.

A beam based method for target localization: inspiration from bats' directivity and binaural reception for ultrasonic sonar

The process of echolocation is accomplished by bats partly using the beam profiles associated with their ear shapes that allow for discrimination between different echo directions. Indeed, knowledge of the emitted signal characteristic and measurement of the echo travel time from a target make it possible to compensate for attenuation due to distance, and to focus on filtering through the receivers' beam profiles by comparing received echoes to the original signal at all frequencies in the spectrum of interest. From this basis, a beam profile method to localize a target in three-dimensional space for an ultrasonic sensor system equipped with an emitter and two receivers is presented. Simulations were conducted with different noise levels, and only the contribution of the receivers' beam profiles was considered to estimate the orientation of the target with respect to the receivers. The beam pattern of the Phyllostomus discolor's ear was adopted as that of a receiver. Analyses of beam resolution and frequency ranges were conducted to enhance the accuracy of orientation estimates. The choice of appropriate resolution and frequency ranges guarantee that error mean values for most of the orientations are within [0.5°, 1.5°], even in noisy situations: Signal-to-noise ratio values considered in this work are 35 and 50 dB.

Localization and tracking of moving objects in two-dimensional space by echolocation

Bats use frequency-modulated echolocation to identify and capture moving objects in real three-dimensional space. Experimental evidence indicates that bats are capable of locating static objects with a range accuracy of less than 1 μs. A previously introduced model estimates ranges of multiple, static objects using linear frequency modulation (LFM) sound and Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates. The delay time for a single object was estimated with an accuracy of about 1.3 μs by measuring the echo at a low signal-to-noise ratio (SNR). The range accuracy was dependent not only on the SNR but also the Doppler shift, which was dependent on the movements. However, it was unclear whether this model could estimate the moving object range at each timepoint. In this study, echoes were measured from the rotating pole at two receiving points by intermittently emitting LFM sounds. The model was shown to localize moving objects in two-dimensional space by accurately estimating the object's range at each timepoint.

A deterministic compressive sensing model for bat biosonar

The big brown bat (Eptesicus fuscus) uses frequency modulated (FM) echolocation calls to accurately estimate range and resolve closely spaced objects in clutter and noise. They resolve glints spaced down to 2 μs in time delay which surpasses what traditional signal processing techniques can achieve using the same echolocation call. The Matched Filter (MF) attains 10-12 μs resolution while the Inverse Filter (IF) achieves higher resolution at the cost of significantly degraded detection performance. Recent work by Fontaine and Peremans [J. Acoustic. Soc. Am. 125, 3052-3059 (2009)] demonstrated that a sparse representation of bat echolocation calls coupled with a decimating sensing method facilitates distinguishing closely spaced objects over realistic SNRs. Their work raises the intriguing question of whether sensing approaches structured more like a mammalian auditory system contains the necessary information for the hyper-resolution observed in behavioral tests. This research estimates sparse echo signatures using a gammatone filterbank decimation sensing method which loosely models the processing of the bat's auditory system. The decimated filterbank outputs are processed with [script-l](1) minimization. Simulations demonstrate that this model maintains higher resolution than the MF and significantly better detection performance than the IF for SNRs of 5-45 dB while undersampling the return signal by a factor of six.

Evaluation of the echolocation model for range estimation of multiple closely spaced objects

Experimental evidence indicates that bats can use frequency-modulated echolocation to identify objects with an accuracy of less than 1 μs. However, when modeling this process, it is difficult to estimate the delay times of multiple closely spaced objects by analyzing the echo spectrum, because the sequence of delay separations cannot be determined without information on the temporal changes in the interference patterns of the echoes. To extract the temporal changes, Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates are introduced. The delay time for object 1 (T(1)) is estimated from the echo spectrum around the onset time. The T(2) is obtained by adding the T(1) to the delay separation between objects 1 and 2. Further objects are located in sequence by this procedure. Here echoes were measured from single and multiple objects at a low signal-to-noise ratio. It was confirmed that the delay time for a single object could be estimated with an accuracy of about 1.3 μs. The range accuracy was less than 6 μs when the frequency bandwidth was less than 10 kHz. The delay time for multiple closely spaced objects could be estimated with a high range resolution by extracting the interference pattern.

Pattern-matching analysis of fine echo delays by the spectrogram correlation and transformation receiver

Among a few previous attempts to model the outstanding echolocation capability of bats, the work by Saillant et al. [J. Acoust. Soc. Am. 94, 2691-2712 (1993)] is, arguably, one of the most frequently referenced studies in which the predictions of spectrogram correlation and transformation (SCAT) model were compared to the results of relevant behavioral experiments. The SCAT model consists of cochlear, spectrogram correlation and spectrogram transformation blocks, where the latter two processes estimate the overall and the fine time delays between the animal's call and the echoes, given the neural representation of the acoustic signals generated by the cochlear block. This paper first provides a rigorous account of the spectrogram transformation (ST) block. By approximating the neural signals in analytic forms, many aspects of the ST block are explained and discussed in relation to the predictive scope of the model. Furthermore, based on these analytical arguments, the ST block is investigated from a different point of view, interpreted as a pattern-matching process which may operate at the high level of the animal's auditory pathway.

Determining biosonar images using sparse representations

Echolocating bats are thought to be able to create an image of their environment by emitting pulses and analyzing the reflected echoes. In this paper, the theory of sparse representations and its more recent further development into compressed sensing are applied to this biosonar image formation task. Considering the target image representation as sparse allows formulation of this inverse problem as a convex optimization problem for which well defined and efficient solution methods have been established. The resulting technique, referred to as L1-minimization, is applied to simulated data to analyze its performance relative to delay accuracy and delay resolution experiments. This method performs comparably to the coherent receiver for the delay accuracy experiments, is quite robust to noise, and can reconstruct complex target impulse responses as generated by many closely spaced reflectors with different reflection strengths. This same technique, in addition to reconstructing biosonar target images, can be used to simultaneously localize these complex targets by interpreting location cues induced by the bat's head related transfer function. Finally, a tentative explanation is proposed for specific bat behavioral experiments in terms of the properties of target images as reconstructed by the L1-minimization method.

A modeling approach to explain pulse design in bats

In this modeling study we wanted to find out why bats of the family Vespertilionidae (and probably also members of other families of bats) use pulses with a certain bandwidth and duration. Previous studies have only speculated on the function of bandwidth and pulse duration in bat echolocation or addressed this problem by assuming that bats optimize echolocation parameters to achieve very fine acuities in receiving single echoes. Here, we take a different approach by assuming that bats in nature rarely receive single echoes from each pulse emission, but rather many highly overlapping echoes. Some echolocation tasks require individual echoes to be separated to reconstruct reflection points in space. We used an established hearing model to investigate how the parameters bandwidth and pulse duration influence the separation of overlapping echoes. Our findings corroborate the following previously unknown or unsubstantiated facts: 1. Broadening the bandwidth improves the bat's lower resolution limit. 2. Increasing the sweep rate (defined by bandwidth and pulse duration) improves acuity of each extracted echo. 3. Decreasing the sweep rate improves the probability of frequency channels being activated. Since facts 2 and 3 affect sweep rate in an opposing fashion, an optimum sweep rate will exist, depending on the quality of the returning echoes and the requirements of the bat to improve acuity. The existence of an optimal sweep rate explains why bats are likely to use certain combinations of bandwidth and pulse duration to obtain such sweep rates.

'Binaural echo disparity' as a potential indicator of object orientation and cue for object recognition in echolocating nectar-feeding bats

Echolocating bats emit ultrasonic calls through their mouth or their nostrils and receive echoes from objects with both their ears. Information conveyed in the echoes is the basis for their three-dimensional acoustic perception of the surroundings. The direction of an object is encoded in binaural echo differences, i.e. on the one hand in the different arrival times of its echo at the two ears, and on the other hand in spectral differences through direction-dependent frequency filtering of head and pinnae. Insufficient attention has been paid, however, to the fact that three-dimensional objects produce structured spatial echo fields, and that the position of the ear in this field determines the echo it receives. We were interested to determine whether the two ears, in addition to direction-specific echo differences, receive object-specific echo disparities that might be useful for the bat. Our measurements with an artificial bat head, which consisted of two microphones and a small ultrasound loudspeaker arranged to resemble a bat's ears and mouth, revealed that echoes at the two ears differed largely depending on the shape and orientation of the echo-giving object. Binaural echo disparities of a bat-pollinated flower did indeed carry information about the orientation and, to a lesser extent, the shape of the flower. During flower approach such object-specific binaural echo disparities even exceed the binaural differences encoding direction of echo incidence, because the echo from the flower in front undergoes the same directional filtering by the two symmetrical ears. Nectar-feeding bats could use these object-specific binaural echo disparities not only to determine the object's orientation relative to the approaching bat, facilitating flight planning, but also to improve object recognition through spatial reconstruction of details of the object creating the echo. Our results suggest that the evaluation of binaural echo disparity has a greater importance for these tasks than has previously been assumed.

Target representation of naturalistic echolocation sequences in single unit responses from the inferior colliculus of big brown bats

Echolocating big brown bats (Eptesicus fuscus) emit trains of frequency-modulated (FM) biosonar signals whose duration, repetition rate, and sweep structure change systematically during interception of prey. When stimulated with a 2.5-s sequence of 54 FM pulse-echo pairs that mimic sounds received during search, approach, and terminal stages of pursuit, single neurons (N = 116) in the bat's inferior colliculus (IC) register the occurrence of a pulse or echo with an average of < 1 spike/sound. Individual IC neurons typically respond to only a segment of the search or approach stage of pursuit, with fewer neurons persisting to respond in the terminal stage. Composite peristimulus-time-histogram plots of responses assembled across the whole recorded population of IC neurons depict the delay of echoes and, hence, the existence and distance of the simulated biosonar target, entirely as on-response latencies distributed across time. Correlated changes in pulse duration, repetition rate, and pulse or echo amplitude do modulate the strength of responses (probability of the single spike actually occurring for each sound), but registration of the target itself remains confined exclusively to the latencies of single spikes across cells. Modeling of echo processing in FM biosonar should emphasize spike-time algorithms to explain the content of biosonar images.

An echolocation model for the restoration of an acoustic image from a single-emission echo

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. It is therefore necessary to restore the acoustic image from limited information. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, a method is proposed for restoring an acoustic image from the echo. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the amplitude spectra, which vary with its location. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The location is estimated from the temporal changes of the amplitude spectra.

Delay accuracy in bat sonar is related to the reciprocal of normalized echo bandwidth, or Q

Big brown bats (Eptesicus fuscus) emit wideband, frequency-modulated biosonar sounds and perceive the distance to objects from the delay of echoes. Bats remember delays and patterns of delay from one broadcast to the next, and they may rely on delays to perceive target scenes. While emitting a series of broadcasts, they can detect very small changes in delay based on their estimates of delay for successive echoes, which are derived from an auditory time/frequency representation of frequency-modulated sounds. To understand how bats perceive objects, we need to know how information distributed across the time/frequency surface is brought together to estimate delay. To assess this transformation, we measured how alteration of the frequency content of echoes affects the sharpness of the bat's delay estimates from the distribution of errors in a psychophysical task for detecting changes in delay. For unrestricted echo frequency content and high echo signal-to-noise ratio, bats can detect extremely small changes in delay of about 10 ns. When echo bandwidth is restricted by filtering out low or high frequencies, the bat's delay acuity declines in relation to the reciprocal of relative echo bandwidth, expressed as Q, which also is the relative width of the target impulse response in cycles rather than time. This normalized-time dimension may be efficient for target classification if it leads to target shape being displayed independent of size. This relation may originate from cochlear transduction by parallel frequency channels with active amplification, which creates the auditory time/frequency representation itself.

An echolocation model for range discrimination of multiple closely spaced objects: transformation of spectrogram into the reflected intensity distribution

Using frequency-modulated echolocation, bats can discriminate the range of objects with an accuracy of less than a millimeter. However, bats' echolocation mechanism is not well understood. The delay separation of three or more closely spaced objects can be determined through analysis of the echo spectrum. However, delay times cannot be properly correlated with objects using only the echo spectrum because the sequence of delay separations cannot be determined without information on temporal changes in the interference pattern of the echoes. To illustrate this, Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The delay time for object 1, T1, can be estimated from the echo spectrum around the onset time. The delay time for object 2 is obtained by adding T1 to the delay separation between objects 1 and 2 (extracted from the first appearance of interference effects). Further objects can be located in sequence by this same procedure. This model can determine delay times for three or more closely spaced objects with an accuracy of about 1 micros, when all the objects are located within 30 micros of delay separation. This model is applicable for the range discrimination of objects having different reflected intensities and in a noisy environment (0-dB signal-to-noise ratio) while the cross-correlation method is hard to apply to these problems.

Evaluation of an auditory model for echo delay accuracy in wideband biosonar

In a psychophysical task with echoes that jitter in delay, big brown bats can detect changes as small as 10-20 ns at an echo signal-to-noise ratio of approximately 49 dB and 40 ns at approximately 36 dB. This performance is possible to achieve with ideal coherent processing of the wideband echoes, but it is widely assumed that the bat's peripheral auditory system is incapable of encoding signal waveforms to represent delay with the requisite precision or phase at ultrasonic frequencies. This assumption was examined by modeling inner-ear transduction with a bank of parallel bandpass filters followed by low-pass smoothing. Several versions of the filterbank model were tested to learn how the smoothing filters, which are the most critical parameter for controlling the coherence of the representation, affect replication of the bat's performance. When tested at a signal-to-noise ratio of 36 dB, the model achieved a delay acuity of 83 ns using a second-order smoothing filter with a cutoff frequency of 8 kHz. The same model achieved a delay acuity of 17 ns when tested with a signal-to-noise ratio of 50 dB. Jitter detection thresholds were an order of magnitude worse than the bat for fifth-order smoothing or for lower cutoff frequencies. Most surprising is that effectively coherent reception is possible with filter cutoff frequencies well below any of the ultrasonic frequencies contained in the bat's sonar sounds. The results suggest that only a modest rise in the frequency response of smoothing in the bat's inner ear can confer full phase sensitivity on subsequent processing and account for the bat's fine acuity or delay.

Time-frequency model for echo-delay resolution in wideband biosonar

A time/frequency model of the bat's auditory system was developed to examine the basis for the fine (approximately 2 micros) echo-delay resolution of big brown bats (Eptesicus fuscus), and its performance at resolving closely spaced FM sonar echoes in the bat's 20-100-kHz band at different signal-to-noise ratios was computed. The model uses parallel bandpass filters spaced over this band to generate envelopes that individually can have much lower bandwidth than the bat's ultrasonic sonar sounds and still achieve fine delay resolution. Because fine delay separations are inside the integration time of the model's filters (approximately 250-300 micros), resolving them means using interference patterns along the frequency dimension (spectral peaks and notches). The low bandwidth content of the filter outputs is suitable for relay of information to higher auditory areas that have intrinsically poor temporal response properties. If implemented in fully parallel analog-digital hardware, the model is computationally extremely efficient and would improve resolution in military and industrial sonar receivers.

Transformation of external-ear spectral cues into perceived delays by the big brown bat, Eptesicus fuscus

The external-ear transfer function for big brown bats (Eptesicus fuscus) contains two prominent notches that vary from 30 to 55 kHz and from 70 to 100 kHz, respectively, as sound-source elevation moves from -40 to +10 degrees. These notches resemble a higher-frequency version of external-ear cues for vertical localization in humans and other mammals. However, they also resemble interference notches created in echoes when reflected sounds overlap at short time separations of 30-50 micros. Psychophysical experiments have shown that bats actually perceive small time separations from interference notches, and here we used the same technique to test whether external-ear notches are recognized as a corresponding time separation, too. The bats' performance reveals the elevation dependence of a time-separation estimate at 25-45 micros in perceived delay. Convergence of target-shape and external-ear cues onto echo spectra creates ambiguity about whether a particular notch relates to the object or to its location, which the bat could resolve by ignoring the presence of notches at external-ear frequencies. Instead, the bat registers the frequencies of notches caused by the external ear along with notches caused by the target's structure and employs spectrogram correlation and transformation (SCAT) to convert them all into a family of delay estimates that includes elevation.

Selectivity for echo spectral interference and delay in the auditory cortex of the big brown bat Eptesicus fuscus

The acoustic environment for an echolocating bat can contain multiple objects that reflect echoes so closely separated in time that they are almost completely overlapping. This results in a single echo with a spectrum characterized by deep notches due to interference. The object of this study was to document the possible selectivity, or lack thereof, of auditory neurons to the temporal separation of biosonar signals on a coarse (ms) and fine (micros) temporal scale. We recorded single-unit activity from the auditory cortex of big brown bats while presenting four protocol designs using wideband FM signals. The protocols simulated a pair of partially overlapping echoes where the separation between the first and second echo varied between 0 and 72 micros, a pulse followed by a single echo at varying delay from 0 to 30 ms, a pulse followed at a fixed delay by a pair of partially overlapping echoes that had a varying temporal separation of 0-72 micros, and a pulse followed, with a varying delay between 0 and 30 ms, by a pair of echoes that themselves had a fixed temporal separation on a microsecond time scale. About half of the cortical units showed increased spike counts to pairs of partially overlapping echoes at particular separations (6-72 micros) compared with a baseline stimulus at 0-micros separation. For many neurons tested with a pulse followed by two overlapping echoes, we observed a sensitivity to the coarse delay between the pulse and pair of overlapping echoes and to the separation between the two echoes themselves. The sensitivity to the partial overlap between the two echoes was not tuned to a single temporal separation. For bats, this means that the absolute range to the closest reflector and range between reflectors may be jointly encoded across a small population of single units. There are several possible neuronal mechanisms for encoding the separation between two nearby echoes based on the sensitivity to spectral notches.