The invention relates to a device and a method to acquire the direction and noise level of a sound field at an observation point as a function of time. It also relates to a set of devices and a method to combine the results of several measurement points with cross- bearing techniques to locate dominant sound sources with their geographical coordinates and to correlate the results with source-related audio-visual information. More in particular the present invention relates to a directional sound measurement device, comprising at least two pressure gradient microphones having substantially the same directional characteristics, co-located in a mutually different orientation, and a processor adapted to combine the output signals of the microphones for obtaining the sound level and the direction of a dominant sound source in each time window. Herein the expression 'co-located' is understood to express that they are virtually at the same position in relation to the angles with respect to the sound source.

A well-known method to acquire the direction of a sound wave from its wave front direction is to combine the outputs of several closely-spaced microphones to form a so- called intensity probe. A disadvantage of this method is that the microphones must be very identical in amplitude and phase characteristics, which will make the system expensive. Besides that, there remains the problem that the finite difference

approximations lead to errors for high frequencies as is well known from p-p intensity probes as disclosed in F.J. Fay, Sound Intensity, St Edmundsbury Press, Suffolk, Great Britain, 1989. Another approach is to make use of four pressure-gradient microphones that are placed on the surfaces of a regular tetrahedron as is known from the so-called Soundfield microphone, which is disclosed in GB-A-1 512 514. The proposed method makes use of such a configuration. In the normal application of the Soundfield microphone, a mix of the audio signals of the four microphones is taken to make outputs with variable directivity in different directions. Use could be made of this principle, but the result depends on the similarity of the microphone characteristics, while further phase errors at high frequencies may occur. To avoid these disadvantages the invention proposes a directional sound-measurement device, comprising of at least two pressure-gradient microphones having substantially the same directional characteristics, located in their vicinity (see note above) and in mutually different orientations, and a processor adapted to divide the time in time windows, determine the mean squared value or the root mean squared value of the output signals of the microphones in each time window, and execute goniometric combinations to the squared signals in each time window with the purpose of obtaining the sound level and the direction of a dominant sound source for each time window. Consequently there is no need for phase sensitive signal mixing and no use of finite difference approaches, which makes the method a preferred for practical applications, as the signals are combined after eliminating the phase dependency of the signals.

The invention also provides a corresponding method.

Subsequently the present invention will be elucidated with the help of the following drawings, wherein depict:

Figure 1 : a spherical coordinate system with azimuth a and elevation Θ;

Figure 2 : a diagram explaining the positions of the microphones in a special embodiment; and

Figure 3 : a flow chart of the post processing of signals in the embodiment shown in figure 2.

A sound field is characterized by its spatial and temporal pressure and particle velocity field. If the sound field is due to a single source and the propagation of the sound is in a stationary, homogeneous and isotropic medium without reflections taking place, the direction of the source is the same as the direction of the particle velocity in the point of observation. The same is valid for the intensity vector of the sound field. If we measure the sound field in the far field of the source, a local plane wave approximation is valid. The particle velocity is then related to the sound pressure and the source direction by: v(r,f) = (r,f)n _s (l)

s

with Z _s the specific acoustic impedance of the medium (usually air), equal to p ₀ C, the product of the mass density p ₀ of the medium and the sound velocity c, r being the vector of the spatial coordinates of the observation point and n _s the normal vector of the wave front of the sound field that equals the direction from the source to the observation point.

The intensity of the sound field is given by:

l (r) = p(r, f)v(r, f) = pL/Z _s , (2) where the overbar denotes time averaging.

From the measurement of the sound pressure, the immission level is normally found as L = 201og(p _mB /A,) [dB] (3) with p _rrrE being the root mean squared value of the sound pressure and p ₀ = 20 μPa. The source direction is related to the three vector-components of the particle velocity and to the vector components of the intensity. For the characterization of the direction of the sound source we will use the azimuth and elevation angles as defined in figure 1.

One component of the particle velocity can directly be obtained from a microphone with a so-called figure of eight directivity. Such microphones are sensitive to the first order gradient of the sound pressure, which is related to the particle velocity by Euler's equation:

This means that in a plane propagating wave field the sensitivity of such a microphone equals

G(cp) = G ₀ coscp (5) with φ being the angle between the source direction and the main direction of the microphone. G ₀ is the microphone sensitivity in the main direction. The gradient can be obtained from a microphone that makes use of the pressure difference at the two sides of the microphone membrane. It can also be obtained from measurements with two closely spaced pressure sensitive microphones and taking a finite difference

approximation of Eq. (4). The particle velocity can also be measured with a very fast flow sensor, such as the Micro flown, as described in patent application

WO-A-1996000488. If we place three gradient microphones in the x- y- and z-direction of the coordinate system of figure 1 at a coincident place in the centre, the outputs of the microphones are respectively:

x ₂ (f) = (since sin0 )s(f) . (6) x ₃ ( = (cose)s(

It is assumed here that the microphones have been calibrated such that S(f) equals the sound pressure of the sound source at the position of the microphones. In the following discussions we will use the mean squared and the root mean squared values of the measured signals.

The mean s uared value of signal x(f) is defined as:

and the root mean squared value as

In practice the time integral is taken over a sufficiently long time to get a statistically stable output. From the measurements with the gradient microphones according to Eq. (6), the sound pressure level can easily be found from

L = 101og((x _{l ms} + x _{2 ms} + x _{3 ms} ) / p ₀ ² ) . (9)

However, it is not so easy to calculate and Θ because this has to be done based on the time dependent signals and not on the ms or rms values. That is because quadratic averaging would destroy the correct signs of the goniometric factors. Therefore direct application of the output of gradient microphones is not preferred.

The components of the intensity vector can be obtained with microphone probes that apply Eq. (2) by multiplying the time dependent pressure and particle velocity and averaging the result. Such probes can be combined to form a three-dimensional intensity probe. The outputs of such a three-dimensional probe give the following components:

/ _y = (since sine )p Z _a . (10) l _z = (cosQ )p _ms / Z _s The sound pressure level equals

L = 101og(^ + /; + / _z ² / / ₀ ) (11) with / ₀ = p ₀ ² / Z _s .

The azimuth and elevation angles can be calculated as follows:

= arctan(/ / / _x ) (12)

To obtain over the full angular range between 0 and 2π, Eq. (13) can be computed with the well-known atan2 function.

It must be noted that intensity probes are very sensitive to deviations from the ideal characteristics due to errors causes by phase differences and finite difference approaches. This is mainly caused by the fact that outputs of the individual microphones of these probes must be combined as the time dependent signals and cannot be applied to the ms or rms values. This makes the application of intensity probes expensive.

The principle of our invention is the use of pressure-gradient microphones that are placed close together in such a way that the sound pressure level and the azimuth and elevation angles can be found in an easy way by post processing of ms or rms output values. In a preferred implementation this can be done with only four microphones. The directivity characteristic of a pressure-gradient microphone is given by;

G((p) = G ₀ (l + jbcos(p) /(l + ib) . (14)

The variable b is normally taken > 0 and depends on the directivity characteristic of the microphone. For an omnidirectional microphone b = 0, for a cardioid b = 1 and for a velocity-type (or figure of eight) microphone, b » 1.

The basis of our invention can easily be understood by first looking at a one- dimensional situation where we want to find the angle φ of the incident plane sound wave. Therefore we will make use of two pressure-gradient microphones with the same characteristic (same b) and place these microphones in opposite directions. With the sound pressure of the sound field at the microphone position given by S(f) (we omit the sensitivity of the microphone as an extra multiplication factor here), we have: 1

*ι(0 = (l + Jbcoscp)s(f) (15a)

(l + b)

1

x ₂ ( = (l - bcos )s(t) (15b)

(l + b)

We can easily find the sound pressure signal S t) as

(16) and φ = arccos x.(Q- *2(Q (17)

6(^(0+ ₂ ( )

Due to symmetry, φ can only be obtained over an angular range between 0 and π. Note that the processing of Eq. 16 and 17 is done on the time dependent signals and is therefore sensitive to phase differences caused by the microphone characteristics and due to the fact that the microphones have a slightly different position in the sound field. In our invention we realize that equivalent relations can be found for the root mean squared output signals of these microphones.

1

Lrms ^' (l + bcosq>)s _n (18a)

(l + b)

1

2,rms ^' (l - /3cosq>)§. (18b)

(l + b)

A restriction is that Eqs. (18) are only valid as long as (1 + jbcoscp) > 0, so in general, taking all angles of incidence into account, for b < 1. Pressure-gradient microphones with 0 < b < 1 are called sub-cardioid microphones. The post-processing equations are now:

and φ = arccos (20)

These relations do not depend on the already mentioned phase differences and take much less computing power, because they are applied on the averaged signals only. The principle as outlined here can easily be extended to three dimensions by using additional microphone pairs in orthogonal directions. If we label the microphone pairs in the ±x-directions with 1 and 3, in the ±y-direction with 2 and 4 and in the ±z-direction with 5 and 6, the microphone signals for a sound field from the direction ( ,θ) are given by: j(f) = ^~ ^(! + kcosa sin9 ) s t) x ₂ (t) = (l + Jbsin sine ) s(f) x ₃ (f) =— !— (l - Jbcos sin9 ) s(f)

l ^b (21) x ₄ (f ) = ( 1 - Jb sin sin9 ) s(f ) x ₅ (f) =— L(l + jbcose ) s(f) 6( = ^(l + ^sine ) s(

In a first preferred method, we first measure the rms signals of the outputs of the sub- cardioid microphones, giving = (! + bcosa sine ) S _rms = ( ¹ + b sina sine ) ^χ ₃ ™ = ( ¹ - b cosa sine ) s _rms

(2: ^χ ₄ ™ = (! - ^sin sine ) = Y^( ¹ + ^cose )s _nTB

= Y^( ¹ + ^sine ) ^ _ms

Here the restriction is that b < \ . We find as a result: ms Cs _rms cosa sine

y Cs _rms sina sine

Cs^cose with C _rms = 2/5/ (1 + b). From E . (23) we can find:

a = arctan(v _{y ms} /v _{x ms} ),

With this configuration it is also possible to calculate the results after obtaining the ms- outputs of the microphones. With this method b is not restricted to values < 1 so any type of pressure-gradient microphone is applicable. We first compute the ms values of the outputs. These values can be calculated from Eq. (21) to give:

x, _™ = ( 1 + 2£>cosa sin9 + b ² cos ² a sin ² Θ ) s. χ _{1 ηκ} =—— ( 1 + 2£>sina sin9 + b ² sin ² a sin ² Θ ) S _™

' -|- ^ ' x, _m =— - T" ( 1 - 2b cos sin9 + b ² cos ² a sin ² Θ ) s„

(27) x, =—— ( 1 - 2 b sin a sin9 + b ² sin ² a sin ² Θ ) S _™

' -|- j^ ² ^ '

^{X5 mS =} (l + fe) ¹ ^ ^{+ 200089 +} ^ ^{C0S2 θ} '

We can now compute the mean squared particle velocity components as:

^V x,ms = COSOC Sin9

vy, T _B = 2,™- 4,™ = Cs _ms sin sin9 , (28)

^V z,ms ^{= X} 5,ms ~ ^X 6,ms ⁼ ^ ^S ms ^C0S ^

with C _m = 4b/ (l + bf .

From Eq. (28) we can find:

Cms

To obtain over the full angular range between 0 and 2π, Eq. (30) can be computed with the well-known atan2 function. A benefit of this preferred method is that the value of b is not restricted to values < 1.

The use of a tetrahedron as the basis for three-dimensional microphone configurations is well known. For instance the Soundfield microphone [4] makes use of four pressure- gradient microphones placed on the surfaces of a regular tetrahedron. The outputs of the microphones are called the A- format and are usually remixed to obtain the B-format, consisting of an equivalent omni-directional microphone and three figure of eight microphones in the x- y- and z-direction.

Another approach is known from R. Hickling and A.W. Brown, "Determining the direction to a sound source in air using vector sound-intensity probes", J. Acoust. Soc. Am. 129(1), January 2011, pages 219 - 224.1. who describe a method of constructing a three dimensional intensity probe by using a finite difference approach on four omnidirectional microphones, placed at the corners of a regular tetrahedron. We mention that the principle of the Soundfield Microphone can directly be used in the preferred solutions of section 2.5, by first mixing the output to six virtual pressure- gradient microphones in the =bc- ±y- and ±z-direction. A disadvantage of this method is that the mixing of these signals relies on a very precise phase behaviour of the microphones and the microphones must also be placed very close together. Therefore we propose a preferred method that is not dependent on such phase relations because only the rms output values of the four microphones are used. The DSLM has tetrahedron geometry as shown in figure 2. The tetrahedron has edges that are surface diagonals of a cube with edges in the main directions of the carthesian coordinate system xyz. The microphones are placed on the faces of the tetrahedron, shown as circles in the figure. The orientation of the microphones is according to table 1.

Table 1 - Position and orientation of the microphones in the tetrahedron planes

Microphone Orentation Plane Direction ( X/3)

A back, left, down PQT -1 +1 -1

B front, left, up QRT +1 +1 +1

C front, right, down PQR +1-1-1

D back, right, up PRT -1-1+1

The output signals of the four microphones due to a plane wave from the direction (a, Θ) are:

3>/3Jb(-cos sin9 + sinasin9 -cos9) s(f)

-^(l + jV3Jb(+cos sin9 -sin sin9 -cos9))s(i) -sin sin9 +cos9))s(i)

The signal s(f) is the output of each of the microphones to the plane wave signal when the main axis of that microphone is pointed towards the source direction of the plane wave source. The post processing of the microphone signals follows the procedure as shown in the flow chart of figure 3. The signals are first filtered with an appropriate frequency weighting function. This can be for instance A or C weighting as indicated in the figure, but other filters such as octave or 1/3-octave filters can be used here as well. These filters can also include a frequency dependent calibration. Next the rms-outputs of the four microphone channels are computed. In this procedure it will be necessary that the pressure-gradient microphones have a value of b < 1, leading to:

⁺ 3>/3Jb(-cos sin9 +sin sin9 -cos9) s _m

^-^(l + jV3 ^~ Jb(+cos sin9 -sin sin9 -cos9))s _m

— !— (l + iV3Jb(-cos sin9 -sin sin9 +cos9

l _{+ b} \ ) '))s _rr These rms-signals are next matrixed into the following signals:

4b

= ^~ Ams + 4ms + Crn* ^{~ D} ™s = _{+ b} fi ¾™ ^{∞SCL ΆΤΐθ}

4b

^V y = + ™ + 4ms - 0™ - ^D ™s = ₊ 5™ ^{Slna SlnQ} · ( ³⁴ )

4b

V _z ^{= ~} Ams ⁺ ms ^_ -ms ⁺ D _rms = ^ fy fl ^{Srms C0S} ^

Notice that these signals look like figure of eight microphone signals, but with the procedure of our invention the goniometric functions keep the correct signs, which is not the case with rms-values obtained from figure of eight microphones.

The final post processing gives the required values for the immission level and the source angles:

_ l + b

S,ms - _{4 b} (35) a = arctan(

and

Here again, to obtain a over the full angular range between 0 and 2π, Eq. (36) can be computed with the well known atan2 function. So far we discussed several preferred methods to acquire the SPL and azimuth and elevation angles (AE) for a single DSLM. It was assumed that there is only one dominant source that is stable in position and time. In real-life applications this will not be true and instead measurements will need to be time windowed and mapped to the corresponding AE-values.

In a first preferred method this will be done by energetic summation of sound-level contributions to a grid of azimuth and elevation values. This method can be refined by retaining the statistics of the source levels in the different grid cells. This gives the possibility to characterize and identify the sources from different directions according to these statistic properties. In a second preferred method, knowledge of possible source locations can be used to localize the source positions with a cross bearing between the AE-values and the possible source locations. If for instance the DSLM is placed at a high position, the elevation of a source direction can be used to calculate its distance when we know the height of the sources above the ground.

In another preferred method a cross bearing is performed between DSMLs that are situated on different known positions. For a practical implementation of these methods each DSML should be equipped with GPS and compass sensors to find its position and orientation.

For the characterization of the measured sound sources the results may be combined with audio-visual recordings of the surrounding of the DSMLs.