A Novel Bio-Inspired Acoustic Ranging Approach for a Better Resolution Achievement

Bat and dolphin use sound to survive and have greatly superior capabilities to current 
technology with regard to resolution, object identification and material characterisation. 
Some bats can resolve some acoustic pulses thousands of times more efficiently than 
current technology (Thomas & Moss, 2004 ). Dolphins are capable of discriminating 
different materials based on acoustic energy, again significantly out-performing current 
detection systems. Not only are these animals supreme in their detection and discrimination 
capabilities, they also demonstrate excellent acoustic focusing characteristics - both in 
transmission and reception. If it could approach the efficiencies of bat and cetacean systems, 
the enormous potential for acoustic engineering, has been widely recognised. Whilst some 
elements of animal systems have been applied successfully in engineered systems, the 
latter have come nowhere near the capabilities of the natural world. Recognizing that 
engineered acoustic systems that emulate bat and cetacean systems have enormous potential, 
we present in this chapter a breakthrough in high-resolution acoustic imaging and physical 
characterization based on bio-inspired time delay estimation approach.


Introduction
Bat and dolphin use sound to survive and have greatly superior capabilities to current technology with regard to resolution, object identification and material characterisation. Some bats can resolve some acoustic pulses thousands of times more efficiently than current technology (Thomas & Moss, 2004 ). Dolphins are capable of discriminating different materials based on acoustic energy, again significantly out-performing current detection systems. Not only are these animals supreme in their detection and discrimination capabilities, they also demonstrate excellent acoustic focusing characteristics -both in transmission and reception. If it could approach the efficiencies of bat and cetacean systems, the enormous potential for acoustic engineering, has been widely recognised. Whilst some elements of animal systems have been applied successfully in engineered systems, the latter have come nowhere near the capabilities of the natural world. Recognizing that engineered acoustic systems that emulate bat and cetacean systems have enormous potential, we present in this chapter a breakthrough in high-resolution acoustic imaging and physical characterization based on bio-inspired time delay estimation approach. A critical limitation that is inherent to all current acoustic technologies, namely that detail, or resolution, is compromised by the total energy of the system. Instead of using higher energy signals, resulting in poorer sound quality, random noise and distortion, they intend to use specifically designed adaptable lower energy 'intelligent' signals. There are around 1000 species of bats alive in the world today. These are broken down into the megabats, which include the large fruit bats, and the microbats, which cover a range of species, both small and large, which eat insects, fruit, nectar, fish, and occasionally other bats. With the exception of one genus, none of the megabats use echolocation, while all of the microbats do. Echolocation is the process by which the bat sends out a brief ultrasonic sound pulse and then waits to hear if there is an echo. By knowing the time of flight of the sound pulse, the bat can work out the distance to the target; either prey or an obstacle. That much is easy, and this type of technology has long been adopted by engineers to sense objects at a distance using sound, and to work out how far away they are. However, bats can do much more than this, but the extent of their abilities to sense the world around them is largely unknown, and the research often contradictory. Some experiments have shown that bats can time pulses, and hence work out the distance to objects 1 with far greater accuracy than is currently possible, even to engineers. Sonar is a relatively recent invention by man for locating objects under water using sound waves. However, locating objects in water and air has evolved in the biological world to a much higher level of sophistication. Echolocation, often called biosonar, is used by bats and cetaceans (whales, manatees, dolphins etc.) using sound waves at ultrasonic frequencies (above 20 kHz). Based on the frequencies in the emitted pulses, some bats can resolve targets many times smaller than should be possible. They are clearly processing the sound differently to current sonar technology. Dolphins are capable of discriminating different materials based on acoustic energy, again significantly out-performing current detection systems. A complete review of this capabilities can be found in (Whitlow, 1993). Not only are these animals supreme in their detection and discrimination capabilities, they also demonstrate excellent acoustic focusing characteristics -both in transmission and reception. What we can gain from these animals is how to learn to see using sound. This approach may not lead us down the traditional route of signal processing in acoustic, but it may let us explore different ways of analyzing information, in a sense, to ask the right question rather than look for the right answer.
This chapter presents a bio-inspired approach for ranging based on the use of phase measurement to estimate distance (or time delay). We will introduce the technique with examples done for sound in air than some experiments for validation are done in tank water. The motivation for this comes from the fact that bats have been shown to have very good resolution with regard to target detection when searching during flight. Jim Simmons (Whitlow & Simmons, 2007) has estimated for bats using a pulse signal with a centre frequency of about 80 kHz (bandwidth 40 kHz) can have a pulse/echo resolution of distance in air approaching a few microns. For this frequency, the wavelength (λ) of sound in air is about 4 mm, and so using the half wavelength (λ/2) as the guide for resolution we see that this is about 200 times less than that achieved by the bat. We demonstrate in this chapter how we have been inspired from bat and its used signal (chirp) to infer a better resolution for distance measurement by looking to the phase difference of two frequency components.

Time delay and distance measurement using conventional approaches
Considering a constant speed of sound in a medium, any improvement in distance measurement based on acoustic techniques will rely on the accuracy of the time delay or the time-of-flight measurement. The time delay estimation is also a fundamental step in source localization or beamforming applications. It has attracted considerable research attention over the past few decades in different technologies including radar, sonar, seismology, geophysics, ultrasonics, communication and medical ultrasound imaging. Various techniques are reported in the literature (Knapp & Carter, 1976;Carter, 1979;1987;Boucher & Hassab, 1981;Chen et al., 2004) and a complete review can be found in (Chen et al., 2006). Chen et.al in their review consider critical techniques, limitations and recent advances that have significantly improved the performance of time-delay estimation in adverse environments. They classify these techniques into two broad categories: correlator-based approaches and system-identification-based techniques. Both categories can be implemented using two or more sensors; in general, more sensors lead to increase robustness due to greater redundancy. When the time delay is not an integral multiple of the sampling rate, however, it is necessary to either increase the sampling rate or use interpolation both having significant limitations. Interpolating by using a parabolic fit to the peak usually yields to a biased estimate of the time delay, with both the bias and variance of the estimate dependent on the location of the delay between samples, SNR, signal and noise bandwidths, and the prefilter or window used in the generalized correlator. Increasing the sampling rate is not desirable for practical implementation, since sampling at lower rates is suitable for analog-to-digital converters (ADCs) that are more precise and have a lower power consumption. In addition, keeping the sampling rate low can reduce the load on both hardware and further digital processing units.
In this chapter, we present a new phase-based approach to estimate the time-of-flight, using only the received signal phase information without need to a reference signal as it is the case for other alternative phase-based approaches often relying on a reference signal provided by a coherent local oscillator (Belostotski et al., 2001) to count for the number of cycles taking the signal to travel a distance. Ambiguities in such phase measurement due to the inability to count integer number of cycles (wavelengths) are resolved using the Chinese Remainder Theorem (CRT) taken from number theory, where wavelength selection is based on pair-wise relatively prime wavelengths (Belostotski et al., 2001;Towers et al., 2004). However, the CRT is not robust enough in the sense that a small errors in its remainders may induce a large error in the determined integer by the CRT. CRT with remainder errors has been investigated in the literature (Xiang et al., 2005;Goldreich et al., 2000). Another phase-based measurement approach adopted to ensure accurate positioning of commercial robots, uses two or more frequencies in a decade scale in the transmitted signal. In this, the phase shift of the received signal with respect to the transmitted signal is exploited for ranging (Lee et al., 1989;Yang et al., 1994). However, this approach is valid only when the maximum path-length/displacement is less than one wavelength, otherwise a phase ambiguity will appear. The time delay estimation approach proposed here, is based on the use of local phase differences between specific frequency components of the received signal. Using this approach overcomes the need to cross-correlate the received signal with either a reference signal or the transmitted signal.The developed novel approach for time delay estimation, hence for distance and speed of sound measurement outperform the conventional correlation-based techniques and overcomes the 2π-phase ambiguity in the phase-based approaches and most practical situations can be accommodated (Assous et al., 2008;2010).  Consider the time-frequency plot of a single bat pulse shown in Fig.1, we note that at any particular time within the pulse there are essentially two frequencies present. The pulse length is about 2 ms and the frequency bandwidth is about 40 kHz. Let describe in the following how using two or more frequencies we may infer a distance.

Distance measurement using the received signal phase differences between components: new concept
To explain the concept, consider a scenario where an acoustic pulse contains a single frequency component f 1 with an initial zero phase offset. This pulse is emitted through the medium, impinges on a target, is reflected and returns back. The signal is captured and its phase measured relative to the transmitted pulse. Given this situation, we cannot estimate the distance to and from an object greater than one wavelength away (hence, usually, we would estimate the time of arrival of the pulse and assume a value for the velocity of sound in the medium to estimate the distance to the target).
For simplicity, assume the pulse contains a single cycle of frequency f 1 of wavelength λ 1 .
The distance D to the target can be expressed as where λ 1 = v/ f 1 , n 1 is an integer, r 1 is a fraction of the wavelength λ 1 and v is the speed of sound in the medium.
r 1 can be expressed as follows where φ 1 is the residual phase angle in degrees. Combining equations (1) and (2) and rearranging If we transmit a second frequency component f 2 within the same pulse, then it will also have associated with it a wavelength λ 2 and a residual phase φ 2 , similarly: Equations (1) and (2) can be solved by finding (2) − (1) × ( λ 2 λ 1 ) and rearranged to give Using Knowing D = v × t we deduce the time delay t as If we impose the condition that Δn ≤ 1 then (6) can be solved. This restriction on Δn is imposed as follows: • A distance D is chosen within which we require an unambiguous range measurement.
• Select a frequency f 1 within the bandwidth of the system, and its corresponding wavelength λ 1 , n 1 = D λ 1 (from (1)). • Similarly, using (1), select frequency f 2 with its corresponding wavelength λ 2 such that the number of cycles is n 2 = n 1 + 1.
Considering (6), the maximum range is achieved by this approach when Δn=1; is Therefore, R is the maximum unambiguous range that can be achieved using two frequencies f 1 and f 2 as described above, where any distance within the range R can be determined unambiguously.
• Consider a distance to target d= 1000.1234 mm, we wish to estimate (which is unknown but is within the unambiguous range R).
• Now, v = 1.500 mm/μs, Δ f = 1 kHz, substituting into (7) gives a first estimate of the rangê d f 1 f 2 = 1000.1233 mm. The Unambiguous Range R (8) is independent of the frequencies used, depending only on the difference in frequency Δ f .
• Note that in practice such resolution may not be achievable and limitations must be considered. For example, if the uncertainty of estimating the phase is within ±0.5 • , then the phases in the example above become φ 1 =126.0 and φ 2 =6.0, giving d=1000.0 mm implying an error of 0.1234 mm.

Using multiple frequencies through a "Vernier approach"
In (6), we imposed the condition that Δn ≤ 1. The values of frequencies f 1 and f 2 were chosen to insure this condition and to obtain a first estimate of the distanced f 1 f 2 (6), and an estimate of the time delayt f 1 f 2 (7).
Using (6) with Δφ 13 and different values of Δn 13 (0 to 6) to get different distance estimated f 1 f 3 .
Thus, this example is reminiscent of the operation of a Vernier gauge as follows: • Δφ 12 , related to the frequencies f 1 and f 2 , gives the first estimate of the distanced f 1 f 2 , hencê t f 1 f 2 .
• A higher frequency f 3 is then used (decade difference) to measure the same range but with a finer resolution. So a more accurate approximation to the measured range is obtained d f 1 f 3 .
• Similarly, the measured ranged f 1 f 4 corresponding to Δφ 14 within f 1 and f 4 , will give the ultimate estimate of the measured range d.
• Consequently, the maximum distance and the minimum resolution achieved are determined by the choice of the frequencies f 1 , f 2 , f 3 and f 4 .

Phase offset measurement calibration
In the numerical example above, it is assumed the phases are faithfully transmitted and received, with no phase error on transmission or reception. It is also assumed that all frequencies have zero phase offset with respect to each other. In practice this is almost certainly not the case and such phase offsets between frequencies should be accounted for as discussed below.
Considering two frequencies f 1 = 200.0 kHz and f 2 = 201 kHz, assuming the speed of sound in water (v =1.5 mm/μs), from (8), the unambiguous range R = 1500 mm and Δn is 0 or 1. Considering the above Consider two distances d 1 , d 2 corresponding to two "times" t 1 and t 2 such that the number of cycles n is the same for both frequencies over these distances, and assume the phase measured includes a phase offset for that frequency. As an example, suppose the unknown phase offset for f 1 is 10 • , for f 2 is 30 • and assume d 1 = 100 mm.
If we had known the phase offset between the two frequencies (20 • ) then in the calculation of times we would have obtained for t 1 a new phase difference of (174 − 130 − 20) = 24 • giving a time for t 1 = 6.6666 μs.
Similarly, for t 2 we obtain a new phase difference of (318 − 250 − 20) = 48 • giving a time for t 2 = 13.3333 μs. Both t 1 and t 2 are now correct.
Note that: • If we assumed d 1 was 100 mm but it was actually say 120 mm and that d 2 was 200 mm but it was actually 220 mm, then we obtain the phase offset as 15.2 • , the slope of (10) above however, is unaffected. For example, such uncertainty may arise if the distance traveled by the wave within the transducers is not taken into consideration.
• If the temperature changes and so v changes, this changes the slope of (10) but not the time intercept or the phase offset. For example, if v=1.6 mm/μs, then equation (10) becomes t = (1/1.6) × d + 5.5555 = 0.625 × d + 5.5555.

Experiment
To demonstrate this approach, a series of measurements were performed in a water tank measuring 1530 × 1380 × 1000 mm 3 . Two broadband ultrasonic transducers were used, having a wide bandwidth with a centre frequency between 100 kHz and 130 kHz. They operate as both transmitters (Tx) and receivers (Rx) of ultrasound with a beam width of around 10 degrees at the centre frequency, where -3dB bandwidth is 99 kHz (72 kHz to 171 kHz). The transducers were mounted on a trolley, moveable in the Y-direction, which was in-turn mounted on a rail, moveable in the X-direction. The experimental set-up is illustrated in Fig.  2.

Fig. 2. Schematic diagram of the experimental setup
For this purpose, linear encoders were used to measure displacement of the rails in the x-direction. Software written in Visual Basic provided readouts of transducer positions. The temperature in the tank was measured by thermocouples which were calibrated using a quartz thermometers which are traceable to national standard. They were positioned on the four sides panels of the tank and recorded 19.84, 19.89, 19.89 and 19.88 • C during the experiment.
The transmitter was driven directly by a 20 V peak-to-peak waveform consisting of four sine waves with zero phase offset (70 kHz, 71 kHz, 80 kHz and 170 kHz) added together. A modular system comprising a 16-bit arbitrary waveform generator (Ztec ZT530PXI) and a 16-bit digital storage oscilloscope (Ztec ZT410PXI) were used to transmit and receive signals. A program written in C++ was used to control the signal transmission and acquisition. Distances between Tx and Rx of 612. 859 mm, 642.865 mm, 702.876 mm, 762.875 mm, 822.847 mm , 882.875 mm, 942.863 and 999.804 mm were chosen to be within the unambiguous range R ≈ 1500 mm (8), as set by the linear encoders. A set of 10 signals; were transmitted for each distance described above. Note that, before transmitting, each signal was multiplied by a Tukey window (cosine-tapered window with a 0.1 taper ratio) to reduce the "turn on" and "turn off" transients of the transducers.
At each distance, 3 repetitive pulses were transmitted and received for each distance. Furthermore, 6 repetitive pulses were transmitted and received while keeping the distance constant at 999.804 mm to assess the repeatability of the system (see Fig.3). Each pulse was 3 ms long containing the 4 added frequency components described above. The sampling frequency Fs was set to 10 MHz, giving a number of samples N=20000. A Discrete Fourier Transform (DFT) was then applied to the received pulses to obtain the magnitude and phase information for each of the 4 frequency components, using a window of [ N 2 + 1 : N] for each received signal. This gave a resolution Fs N/2 =1 kHz which was consistent with the smallest step between the 4 frequencies.  Note the DFT reports phase with respect to cosine, whereas sine waves were used in this experiment. Sine waves are returned with a phase of −90 • relative to cosine waves by the DFT. This was not an issue, since relative phase differences were used.

Results and discussion
Using the phase difference for each distance, the phase-based time delay approach was applied to obtain the corresponding estimated times for each phase difference Δφ 12 , Δφ 13 , Δφ 14 , Δφ 23 , Δφ 24 and Δφ 34 , for the pairs f 1 f 2 , f 1 f 3 , f 1 f 4 , f 2 f 3 , f 2 f 4 and f 3 f 4 , respectively. Note that a careful use of the Fourier transform (DFT) have to be considered to calculate the phase offset for each component. To do this, we have to take into account the fact that all the frequency components have to be integer number of cycles and have to be in the frequency bins defined by the smallest frequency difference between components. Using a simple calculation of the first estimate by t 12 = Δφ 12 /( f 2 − f 1 ) as a first estimate using (7), gave corresponding estimated timest 12 ,t 13 ,t 14 ,t 23 ,t 24 andt 34 , respectively. For each distance,t 14 should be the best estimate (i.e. the greatest Δ f ). Note that,t 14 parameter is taken as a best estimate for time delay measurement in Table.1. Fig. 3   between Tx and Rx of 582.893 for 5 repeat pulses. The repeatability is shown to be within 8 ns.

Conclusion
In this chapter, a high resolution time delay estimation approach based on phase differences between components of the received signal has been proposed. Hence no need to do a cross-correlation between the transmitted and the received signal as all the information is comprised in the received signal in the local phase between components. Within an unambiguous range defined by the smallest and the highest frequency in the signal, any distance can be estimated. This time delay technique leads also to high resolution distance and speed of sound measurement. This approach is tolerant to additive gaussian noise as it relies on local phase difference information. The technique is costly effective as it relies on software and no need for local oscillator to overcome such phase ambiguity by counting the integer number of cycles in the received signal as it is done by the conventional methods. We have mentioned that, authors in Whitlow & Simmons (2007), concluded that, bat can achieve a resolution of 20μm in air, if we can measure the phase to an accuracy of 1 degree then this would allow us to get a resolution of 4mm/360=11μm, using the same wavelength as the bat do.

Acknowledgment
This work was undertaken as part of the Biologically Inspired Acoustic Systems (BIAS) project that is funded by the RCUK via the Basic Technology Programme grant reference number EP/C523776/1. The BIAS project involves collaboration between the British Geological Survey, Leicester University, Fortkey Ltd., Southampton University, Leeds University, Edinburgh University and Strathclyde University.