Introduction This invention relates to a method and apparatus suitable for use in identifying the locations of animals using sounds emitted therefrom. The animal locations are identified with a high degree of accuracy. By way of example, the techniques described herein may be used to identify the locations of animals such as bats in flight. However, its use is not limited in this regard, and the invention is also applicable to identifying the locations of ground based animals, either whilst stationary or during movement thereof. The location information derived may be used for a range of purposes, for example to investigate behaviour patterns or to allow the derivation of population information. Methods for use in monitoring animal movements are available at a wide range of spatial scales. Argos (Fancy et al. 1988) can track species migrations between continents. Radar has been used at a low resolution to monitor the movements of bats at the landscape scale (Williams et al. 1973). GPS tracking (Weimerskirch et al. 2002) is able to record autonomously the location of a tagged animal with an accuracy of a few meters, and VHF radio tracking can be used to locate a tagged animal by following the source of the radio transmissions.

At the fine scale (less than a meter), non-invasive methods have been used. One method is to simply observe the behaviour of and movements of the species of interest. Infra-red cameras can help with species that are active at night, such as bats, and they can also be used to record the activity for later analysis. Monitoring the movements of animals from the calls they emit by triangulating the arrival times is common practice, and there are new developments in this area of technology. These techniques are described herein as time difference of arrival (TDOA) techniques. Mennill et al. (2012) describe a microphone array for triangulation that is built entirely from off-the-shelf acoustic recorders, using GPS to synchronise the arrival times. Another system, Bat3Data, also appears to triangulate positions of bats using an array of four microphones mounted at ground level. The method is unpublished, is from a commercial company, but does not seem to be available for purchase. These methods are non-invasive. Unlike Argos, GPS tracking and VHF tagging, there is no requirement to trap or handle the animals or attach equipment. This is particularly beneficial with protected species such as British bats, where a licence is required for any invasive study. Fine scale tracking is needed in order to understand how species interact with objects in their environment, particularly man-made features. For example, several species of bat in the UK are in decline or rare. The expanding road network (Berthinussen & Altringham, 2012b), widespread artificial lighting (Stone, Harris, & Jones, 2015) and wind turbines (Rydell et al. , 2010) are thought to be amongst the threats faced by bat populations. How a given species interacts with these structures will determine whether, in what way and to what extent they pose a threat to local populations. If a species shows avoidance behaviour, such structures have the potential to fragment the landscape and to restrict access to suitable habitat whereas the very same structures may pose a direct threat to species that do not show avoidance behaviour.

In order to mitigate the potential threats posed by roads, artificial lighting or wind turbines it is important to understand how closely bats interact with these structures, whether they utilise their environs, how local ecology might influence these interactions and whether the response to these structures varies between species. Fine scale non- invasive monitoring of the movements of bats is essential if we are to understand these interactions. Bat detectors can provide a proxy measure of bat activity and enable the identification of species assemblages but do not provide any directional information and can have a detection range of tens of metres. As such, they are best suited to questions of bat ecology at the landscape scale such as whether activity and species diversity decline with proximity to a road along a transect of kilometres (Berthinussen & Altringham, 2012b; Kitzes & Merenlender, 2014), or differ between lit and unlit locations (Mathews et al., 2015).

To observe how bats interact with structures at a much finer scale requires more precise information about the movements of bats. Infra-red cameras have been used to study the use of over-road gantries and under-road passages by bats (Berthinussen & Altringham, 2012a). Radio tags have been used to compare habitat use and road crossing behaviour (Kerth & Melber, 2009) but radio tagging can only count the number of individuals that cross a fine scale barrier, not track their movements around it. Presented here is a method and associated apparatus that, like the TDOA techniques, records the position of individual animals from their calls or other emitted sounds. Rather than triangulating the location from call related signal arrival times, in accordance with the invention an interferometer detects differences in phase between signals detected by two or more microphones. By using microphones located orthogonally with respect to a reference microphone, additional information regarding animal location can be derived as the arrangement allows both azimuth and elevation information to be derived, but useful information can be derived using fewer microphones. Compared to TDOA arrangements using the same number of microphones, the arrangement of the invention may be used to provide more useful position information than is possible using TDOA techniques. Like the method of Mennill et al., the system conveniently uses off-the-shelf components, which are low- cost and widely available. However, it has a number of advantages over the TDOA triangulation method, particularly with respect to flying species. Described herein are a method and the associated algorithms with which information regarding the location of an animal can be extracted from the interferometric recordings.

According to one aspect of the invention, there is provided a method of locating an animal as set out in the appended claims. Further features of the method will be apparent to the skilled reader from the description set out herein. The invention further relates to an apparatus suitable for use in the method as set out in the appended claims.

The invention will further be described, by way of example, with reference to the accompanying drawings, in which:

Figures 1a and 1 b are diagrammatic illustrations showing an apparatus in accordance with an embodiment of the invention, in use; Figure 2 is a diagram illustrating the invention in use;

Figures 3a, 3b, 4a and 4b are graphs explaining the operation of the invention;

Figures 5 to 9 illustrate the use of the invention with sample data; and Figures 10a, 10b, 11 and 12a to 12 d are diagrammatic representations of alternative embodiments of the invention.

Method and materials

Ultrasonic sound recordings from two microphones 10, 12 that are positioned close together can be used to detect phase differences due to the changing path lengths to the source of the sound. The two microphones 10, 12 and an associated control unit 16 form an interferometer, the geometry of which is shown in Figure 1. The direction from which a call from an animal 14 is emitted can be derived by the control unit 16 from the phase difference from the signals detected by the microphones 10, 12. In the arrangement shown, the Fraunhoffer approximation that the source is a far field source and hence that the paths from the bat to each microphone are parallel. When a call is emitted directly between two the microphones (Figure 1 a), the path lengths to each microphone are equal and there is no phase shift. When a call is emitted from an off centre location relative to the microphones 10, 12 (Figure 1 b), the sound will arrive at the microphones at different times. Consequently the signals a _t and b _t detected at time t will be shifted in phase. The direction to the call source, Θ, can be calculated from the phase difference Φ. More specifically:

where v is the velocity of sound, f is the call frequency and d is the spacing between the two microphones 10, 12. Φ ₀₃ ι is a calibration phase offset to compensate for any cross-channel timing offset and misalignment between the microphones.

Calls with constant frequency For the simple case where frequency is constant over time, the phase recorded at each microphone can be determined from the discrete Fourier transform (DFT) of N sequential samples k _n taken from the call. The difference between the signal phases corresponds to the phase difference Φ at the interferometer. The DFT, calculated with the FFT algorithm, will produce N complex Fourier coefficients K _n . If |K _n | is the amplitude of K _n and |K _kmax | is the amplitude of the FFT bin containing the greatest magnitude, then is the corresponding phase for the dominant frequency. Note that Φ _η depends on the signal frequency, and that we choose to calculate Φ at the dominant frequency bin kmax. Calls modulated in frequency and amplitude

Animal calls usually vary in amplitude and frequency over time (they are frequency and amplitude modulated). The FFT of the signal does not, therefore, present a single dominant frequency over the duration of the call from which we can determine the signal phase. With a time variant signal, however, we can consider the instantaneous frequency and instantaneous amplitude of the signal throughout the duration of the call. By way of example, these properties can be computed from the analytic form of the signal, derived from the Hilbert transform of the recorded timeseries for each channel. It will be appreciated, however, that a number of other techniques may be used to derive the call angle without departing from the scope of the invention.

If k(t) represents the signal recorded at one of the microphones then the analytic representation of k(t) can be computed from k(t)=F ^"1 (F(k)2H) were F is the FFT and H is the Heaviside step function. The analytic form is complex. Equations 2 give the representation of the analytic signal k(t) as a complex exponential along with the instantaneous amplitude A(t), the instantaneous phase Φ(ί) and the instantaneous frequency f(t). The instantaneous amplitude A(t) represents the call envelope.

A(f) = \ k _a (t) \

0(t) = arg(fc _a (t))

/ω = έ£ω (2)

The instantaneous phase difference is the difference in phase between channels A and B, i.e. ^Α"Β Φ(ί)=Φ(ί)= ^Α Φ(ί)- ^Β Φ(ί), where ^Α Φ(ί) and ^Β Φ(ί) are the instantaneous phases measurements for channels A and B respectively.

These time variant quantities can be substituted in to Equation 1 , which will now produce N estimates of the angle to the source 0(t) over the duration of the call. A final estimate of the call angle can be deduced statistically from a selection of the instantaneous phases; the mean over the call envelope weighted by the amplitude for example.

Phase unwrapping

The change in path length ΔΙ_ increases with call angle, Θ. When the geometry allows for the case where ΔΙ_ > λ, ΔΙ_ becomes ambiguous and can have values:

The conditions under which this occurs is a function of call frequency and microphone separation distance d. An ideal instrument design would have a separation, d, small enough to preclude phase wrapping. In practice the separation is limited by the radius of the microphones (12.7 mm for the SM2+ ultrasonic microphones), and adjusting the separation for a particular frequency is not possible when targeting multiple species. The implication of equation 3 is that Θ is also ambiguous (equation 4). Therefore, under conditions where the phase may wrap, we need to determine n in order to calculate Θ.

9=sin ^"1 [((φ-φ _Μ ι)/2π+η) v/fd] (4)

For a sequence of calls it is obvious when the phase has wrapped from the discontinuity in the time-series. Determining the value of n for a call relative to the value of n for other calls in the sequence is not difficult. Determining the absolute value of n is more problematic, but method to do this are described below.

Methods to validate the time invariant and frequency modulated calls

The time-variant and invariant methods were validated experimentally as follows. The simple invariant case was tested in a laboratory setting with simulated calls emitted over a range of angles to the interferometer. For the time-variant method, we recorded the calls of Soprano pipistrelles as they flew over the interferometer after emerging from a roost. For both tests we used SM2+ sound recorder with smx-41 ultrasonic microphones from Wildlife Acoustics Inc., Maynard, MA, USA. The sample rate was set to 192 kHz, stereo mode, and no high-pass filter. The microphones were taped together, giving a microphone separation of 12.7 mm (the diameter of the microphones). The gain on the pre-amplifier was adjusted to suit the call volumes for each case.

A Wildlife Acoustics Ultrasonic Calibrator was used to generate simulated animal calls for the laboratory study. This generates a 40 kHz sine wave modulated by a square wave pulse that breaks the source into 100 ms pulses. Calls were recorded at 13 different positions relative to the microphones, between -30° and +30° at 5° intervals. Ten second recordings were made at each angle to produce a .wav file of approximately 24 simulated calls for each position. Each wav file contained two channels of 16-bit integers. For each call that was analysed, a start location was found on the file corresponding to a sample near the beginning of the call. A section of the call with 4096 samples was taken from each channel and these arrays were used as the values kn as the input to the FFT. The call angle Θ was calculated from the simulated calls from Equation 1 , using the value of Φ from the difference in phases from FFT for each channel. A calibration offset of 1.77 radians (2.3 mm) was used to correct for bias (see discussion). Phase wrapping was corrected from the call amplitude. Calls below an amplitude threshold, determined empirically, were adjusted with a value of ±1 for n depending on the sign of the phase. Θ for calls above this threshold were calculated with n=0.

Validation of the time variant method used recordings of real animal calls; soprano pipistrelles emerging from their roost. The recordings contained sequences of calls emitted by individual animals as they exited the roost. The interferometer was positioned 1 m from the building where they were roosting, and the exit hole in the building was 7 m above ground level. Several groups of calls were recorded. In each a sequence of distinct calls was observed with a separation between calls of 0.08 seconds. The call sequences were superficially similar, and a single group was used in the analysis. The phase was unwrapped manually from time-series discontinuities. Results

From the laboratory simulation it was found that the phase difference at the interferometer (Figure 3a) varies with the angle between the interferometer and the source of the call, θ _β , and passes through zero when θ _β is zero with the phase correction 0 _ca i applied. The phase wraps at ±20°. This was corrected from the call amplitude (Figure 4a) using a threshold of -4 dB, to give values for n. The angle between the interferometer and the source of the call, Θ, was calculated from equation 4. It is clear that the value for the angle that we estimate from interferometry, Θ, corresponds closely to the angle at which the emitter was placed in the experiment, θ _β (Figure 4b).

Recordings of the soprano pipistrelles showed a modulation over the duration of the call (Figure 5). The sampled waveforms for the first six calls within the group chosen are shown in Figure 5, the instantaneous amplitude A(t) (a), frequency f(t) (b) and phase difference Φ(ί) (c) are shown in Figure 6, and the call angle 0(t) for all eight calls is shown in Figure 7. Deviations from the mean value correlate with low values in either ^A A(t) or ^B A(t). The final call angle was calculated as the weighted mean of the call angles across the window, with the weights being taken from the normalised product of the instantaneous amplitudes in each channel. The standard deviation weighted by the amplitude product was used to give the error in the call angle.

The angle from the interferometer to the source of the call for the group is shown in Figure 8a, and the distance of the bat from the edge of the building is shown in Figure 8b. Call 8 had a 2π phase correction applied manually. The unwrapped value is also shown in both plots. We calculated the flight speed of the animal perpendicular to the building at 5 ms ^"1 . Discussion

The amplitude threshold for shifting must, of course, be calculated for each species due to the differences in call frequency and microphone response. A novel method to locate the position of bats, to track their movements and to calculate their speed from a sequence of echolocation calls has been validated as described hereinbefore. The method has an accuracy that is useful to both academic and commercial ecologists. If the complexities of real bat calls and removed and a pure sine wave is considered as an input to our method, an error has been found in the angle Θ of 0.25° which corresponds to a positional accuracy of 30 cm at a distance of 7 m (the height of the bats recorded in the field).

There was some variation in the error associated with the call angle Θ from the recordings of soprano pipistrelles. The larger errors come from two different sources. Call 3 showed larger modulations over the call envelope than other calls. The recording of call 7 was poor quality, had a low amplitude, decreasing the SNR.

All the calls showed some modulation over the call envelope, but this was particularly noticeable in call 3. The modulation in each channel is different. This suggests that (at least in part) the modulations seen in the calls are not a property of the call itself, but are a recording artefact. Sonograms for each call in the group show an echo. The likely explanation is a reflection from the wall of the building where the pipistrelles were roosting. The modulations are therefore interference fringes caused by the interference between the direct and reflected signals. It is expected that the modulation would be different in each channel because of the difference on path length. Calls earlier in the recording before the recorder was placed by the roost did not show these echoes. If the microphones were acoustically coupled (touching), it is possible that crosstalk between the two channels could contribute to a similar distortion of the calls. The call angle 0(t) for call 7 was flat over the window (Figure 7g), but the scatter around the mean was relatively high due to the low signal to noise ratio. The error in call angle Θ for both calls was 4° (± 0.5 m error in position at 7m) despite the poor quality. An error in the call angle Θ of 4° is therefore likely to be a worst case, and errors of 1° or less will be more typical for scenarios where the recorder not situated in a location that is susceptible to reflections and the SNR is good. The mean error in angle over the group of 8 calls was 2.1° and the mean error in position was 260 mm. If we reject the two poor quality calls these reduce to 1.5° and 179 mm, although all the calls in the group were compromised by interference from the reflection off the building. Our single night's recording did not include any calls that were strong (good SNR) and without the reflections. We did record some weak calls before the recorder was placed next to the building. These had a low SNR, no echoes, and the errors in angle for these calls were around 0.6°.

The results presented here are from a single evening's recording. We will gather many more recordings over the next season of fieldwork and try to understand this behaviour. The error in our angle estimate is likely to reduce as we understand the data better. It may also be possible to improve on the statistical method of estimating the location from the measurements across the call window. Despite these errors, the method provides accurate estimates of the call angle, and we were able to deduce the location, speed and direction of flight as the bat flew over the interferometer.

Our errors scale linearly with the distance between the interferometer and the call. The main sources of error from triangulation of arrival times will be the timing accuracy, the error in cross-correlation of the sampled calls, number of calls picked up, and the angles of triangulation. Timing accuracy is not a function of distance; it should be scale independent. The number of calls recorded for each location was constant (the volume was set so that calls would be recorded at all the sound recorders - it is not clear if the volumes were typical for the species). The cross-correlation error may become larger as distance increases due to a higher SNR. Mennill's survey area was larger than the distance between our interferometer and the calls in the group we report here, and they report a higher accuracy with 25 m spacing (1.5 m) than 50 m spacing (3 m). We can compare the accuracy of our method by extrapolating the error in angle Θ to the size of the interior of their survey area. At 25 m our mean error would be 0.9 m and at 50 m it would be 1.9 m. Our errors at these distances might be worse than those derived from this simple calculation due to the decreasing SNR with distance. Low amplitude calls without reflection interference were more accurate than those within the group of 8 calls. The distance to these calls is, of course, unknown, but will be further from the sound recorder than 7 m. The inventors intend to make recordings of several British species of bat, test the accuracy, and investigate which method is best for each one. It is possible that the Fourier method will give better results for the two horseshoe species for example, because the frequency is more consistent over the call duration than for other species. We will also attempt to cross-calibrate the positions with other survey methods, for example I R video recordings.

The 0cai correction was too large to be due to microphone misalignment (we taped the microphones together for the experiment but the accuracy was better than 2.3 mm). The likely explanation is a timing discrepancy between the two channels on the SM2. Further experimentation will show if the correction required is common to all SM2 units or if the correction needs to be found for each SM2/microphone pair.

A complication of the method outlined above is the ambiguity in the phase angle Φ due to phase wrapping. There are a number of ways of addressing this problem and in practical field situations it can be overcome in most situations. The method that we used to unwrap the simulated calls treats each call on its own and applies a phase shift depending on an amplitude threshold. Often, calls recorded in a field situation can be considered as a sequence rather than as individual calls. This makes the process of phase unwrapping much easier. It is usually obvious where phase wrapping has occurred and the correction can be made manually. For example, in the sequence of calls shown in Figure 8, call 8 wrapped and was corrected. The uncorrected measurement is shown on both plots in figure 8 to demonstrate this. Automatic phase unwrapping is not difficult. An algorithm to do this is to simply apply a 2π phase shift at the discontinuities in order to make the sequence continuous. We used the unwrap() function in the Python numpy library to unwrap the instantaneous phase across individual calls during our exploration of the data. The algorithm was able to apply the correct phase shift at each discontinuity despite the phase wrapping over many times. The same algorithm could be used to unwrap the phase between calls without difficulty. It is, therefore, a trivial process to find the relative number of phase shifts required to correct for phase wrapping. Finding the absolute number of phase shifts required is a harder problem. If Φ passes through zero over a sequence of calls, a minimum will be observed in the unwrapped value of Φ and ddVdt, and Θ will change sign, indicating the point at which the absolute number of wraps is zero.

If this is not the case, we have two pieces of information that can help to find the absolute phase. First, we have the call amplitude. (We used this to unwrap individual calls in our experiment with simulated calls). It is likely that we could determine the case where the phase comes from calls within the cone where the phase has not yet wrapped. These calls would be above the microphones and would have correspondingly high amplitudes. However, this relies on the animal's flight path crossing the cone that corresponds with the condition where the number of times that the phase has wrapped is zero.

Secondly we have the rate of change in phase ddVdt between sequential calls. This is a function of frequency, microphone separation (constant within a group of calls), call angle, and the speed of flight parallel to the interferometer baseline. We can, therefore, make deductions about the phase angle given constraints on the speed of flight. In many situations it should be possible to determine the absolute number of phase shifts to apply from the available information, and this will be a topic for future work.

The most obvious solution is to reduce the microphone spacing d to a distance that prevents phase wrapping from happening. The plot in figure 9 shows the point at which phase wrapping will occur for any combination of frequency and microphone separation. It shows that very small microphones are needed for species such as horseshoes with high call frequencies if phase wrapping is to be prevented.

In the arrangement described hereinbefore, just two microphones 10, 12 are used. It will be appreciated that such an arrangement is useful in that it allows the direction from which a call is emitted to be identified. It is effectively a one dimensional arrangement and does not provide sufficient information to allow the exact location of the animal that emitted the call to be derived as the distance of the animal from the microphones 10, 12 is not known. Also, in 3D space, there will be an infinite number of directions for which the phase difference is the same. Accordingly, additional information is required if the 3D location of the animal is to be identified.

Depending upon the application in which the invention is used, and other information that may be available, the information derived using the arrangement described hereinbefore may allow the animal location to be derived. For example, if the animal is at a roost location that can be treated as a one dimensional space, the information provided using the invention may allow the location of the animal on the roost to be derived to a high degree of accuracy, or if the animal is travelling along a known path, the location of the animal along the path may be derived. The orientation of the apparatus may be selected to maximise the usefulness of the information provided therefrom. By way of example, mounting the microphones 10, 12 so that they are horizontally spaced may be of benefit when monitoring the movement of a ground based animal along a known path, whilst mounting them so that they are vertically spaced may be more appropriate with flying animals. However, in general, where it is desired to identify the location of an animal, the location or path of which is unconstrained and so additional information regarding the animal location is limited, then the arrangement described hereinbefore may be insufficient to allow the exact location of the animal to be determined.

Referring next to Figure 10a, if two interferometers 20, 22 of substantially the form described hereinbefore are used in combination, the interferometers 20, 22 being spaced apart from one another, for example by a distance of several meters, the movement of an animal 14 along a path can be studied in such a manner that additional positional information can be derived. By way of example, in the case shown the movement of a bat following the path of a hedge 26 is studied, and the outputs of the interferometers 20, 22 in combination may be used to identify the height of the bat as well as its position along the hedge. The arrangement thus provides 2D position information. Depending upon the application in which the invention is employed, other orientations and spacing of the interferometers 20, 22 may be preferred.

Figure 10b illustrates an arrangement in which the first interferometer 20 (including microphones 20a, 20b) is arranged with the microphones thereof located at the same height as one another but spaced apart laterally from one another by a small distance. The arrangement further includes a second interferometer 22 (including microphones 22a, 22b). The microphones of the second interferometer are located at the same height as one another, and are spaced apart by a small distance in a direction perpendicular to the direction of the spacing of the microphones of the first interferometer. In other words, the interferometers 20, 22 are located orthogonally relative to one another. The use of the interferometers 20, 22 in combination in relation to the same animal sound or call provides additional location information by extending the location detection scheme from a one dimensional scheme (as shown in Figure 1) to a two dimensional scheme allowing azimuth and elevation information of a source relative to the interferometers to be derived.

Using a pair of arrangements of the form shown in Figure 10b in combination would allow a unique location of the animal in 3D space to be derived. Figure 11 illustrates an alternative to the arrangement of Figure 10b in which the two interferometers 20, 22 share a common reference microphone 24. The system thus comprises two microphones 20a, 22a mounted orthogonally with respect to the third reference microphone 24 which is common to both interferometers 20, 22. Having a common reference microphone 24 eliminates the need for precise timing between the two interferometers. This geometry would generate a unit vector pointing in the direction of the call source. In the case of the soprano pipistrelle site we would record the distance from the building and also the direction in which the bat flew. This information could help ecologists count the numbers of individuals using different foraging sites, for example. It would also show the movements of foraging behaviour, and avoidance around landscape features for example.

Our calculation for the distance from the building depended upon knowledge of the height of the exit hole in the roost building. An estimate of height could be measured directly by positioning two interferometers along a flightpath. This would generate two call angles separated by a known distance. The height can then be calculated from the intersection of the two angles. Rotating this geometry through 90 degrees would provide a system for tracking ground dwelling species in the area immediately in front of the interferometer pair. This would produce a similar dataset to the method described by Mennill et al. (2012).

It will be appreciated that the concept illustrated in Figure 11 may be viewed as allowing provision of one, two or three dimensional interferometer arrangements. In each case, the arrangement includes a reference microphone and one or more microphones spaced from the reference microphone in the direction or axis in which the arrangement is to be sensitive. A three dimensional arrangement would thus be similar to the arrangement of Figure 1 1 , but include another microphone spaced from the reference microphone in a direction perpendicular or orthogonal to the directions in which the other two microphones are spaced from the reference microphone. The use of two (or more) spaced interferometers of any of these forms in combination may provide additional position information, for example as shown in Figure 10a. Depending upon the types of interferometer used, this can allow a 3D position of the animal to be derived. Greater spatial resolution may be gained from an array of several microphones (conveniently equally spaced apart) analogous to a diffraction grating rather than using just two microphones per interferometer as described hereinbefore. Phase coherence between recorders could be derived from an audio or electronic timing signal (an audio signal might be detected by the bats, influencing behaviour). A common reference signal could be used for all recorders (as described above), although this would be expensive because an extra 2-channel recorder would be required for each additional microphone. This might be overcome by using a low-cost single board computer and multiple high-quality sound cards instead of a dedicated wildlife acoustic recorder. Figure 12a illustrates a simple one dimensional array. A two dimensional array would provide elevation and azimuth. A system might be constructed in the shape of a cross (see Figure 12b), giving a unit vector pointing towards the call from the centre of the cross. This is analogous to some directional dipole radio telescopes, such as the Mills Cross telescope (Christiansen and Hogbom, 1969).

Other configurations are also possible, and it is thought that the optimum geometry for a two-dimensional interferometer is based on a hexagonal geometry (Camps et al. 1997), giving options of triangular layouts (see Figure 12c), or Y shaped layouts (see Figure 12d) analogous to the NRAO Very Large Array.

The precision with which the flight trajectory of a bat can be calculated makes the method we have described here particularly well suited to observations of bat ecology at a very fine scale such as whether and where bats cross roads, the effectiveness of gantries or flight patterns at turbines. We also propose that our method could be used by ecological consultants for emergence surveys.

As it is an offence to disturb a roost, it is usually necessary to survey buildings where renovations or clearances are planned to see whether bats emerge from holes in the wall, from behind climbing plants or from under eaves (Hundt, 2012). Surveys begin at 30 minutes before sunset and last for several hours to allow consultants to monitor activity in the area by which time it is dark. By using the SM2+ for emergence surveys there might be less chance of an emerging bat being missed and emerging bats could be detected long after dark. Our method has several advantages over alternative technologies and other methods that based on the analysis of acoustic recordings. As it is based on acoustic data, our method is non-invasive which minimises disturbance to bats and does not require users to have a license as is the case with radio tags. Unlike infra-red cameras, the SM2+ is autonomous, requiring little human input , and can be left in-situ for several nights. At the same time as providing precise information about the movement of individual bats, activity levels and species assemblages can also be monitored. Overall, our method is very economical: the quantity and detail of the data that can be generated is very high compared to the time, effort and money invested.

The method has advantages over the similar method of triangulation from call arrival times. It is particularly suited to observations of flying species such as bats, and also birds. The fundamental measurement that we produce is a measure of angle rather than position; a unit vector pointing towards the source of the call. This can give an intuitive understanding of the behaviour of individual animals around features in the landscape, and can help pinpoint exit holes and flightpaths.

The TDOA triangulation method is two-dimensional. It gathered positions over a plane parallel to the ground. This could be extended to three dimensions with the addition of sound recorders mounted above ground level. Two dimensional measurements could be made by rotating the plane through 90° and having two recorders at ground level and two above ground, making a rectangle perpendicular to the ground.

Our method is superficially similar to the TDOA technique in that we use acoustic data recorded on SM2+ bat detectors to locate the position of bats. However, the TDOA technique requires a great deal more equipment (4 SM2+ units, 8 microphones and 4 GPS units to synchronize the microphones). In order to triangulate the location of bats, detectors must be positioned at some height off the ground whereas our method achieves this with all equipment at ground level. The most important difference is the greater accuracy offered by our method: in the TDOA technique the average location accuracy is typically in the region of 1.87+_0.13m whereas we report a mean accuracy of 0.2m.

The discussion set out hereinbefore relates primarily to detecting the location of bats. It will be appreciated, however, that the invention is not restricted in this regard. It may be applied to other flying animals, to climbing animals and to ground based animals, provided that the animals in question make sounds that can be detected by the microphones to allow the location information to be derived. The locations information derived through the use of the invention may be employed in a number of applications. By way of example, it may be used in studying animal behaviours and behavioural patterns. It may also be used to derive information regarding population sizes.

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