WO2019178802A1

WO2019178802A1 - Method and device for estimating direction of arrival and electronics apparatus

Info

Publication number: WO2019178802A1
Application number: PCT/CN2018/079993
Authority: WO
Inventors: Sebastien CURDY
Original assignee: Goertek Inc
Current assignee: Goertek Inc
Priority date: 2018-03-22
Filing date: 2018-03-22
Publication date: 2019-09-26
Anticipated expiration: 2020-09-22
Also published as: CN108702558A; CN108702558B

Abstract

The present invention discloses a method and device for estimating direction of arrival and an electronics apparatus. The method comprises: digitalizing input audio signals from a pair of microphones in a microphone array within a certain time frame; buffering the digitalized signals; extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth; calculating phrase shifts in each of the multiple sub-bands for the pair of microphones; performing linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones; and calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones.

Description

METHOD AND DEVICE FOR ESTIMATING DIRECTION OF ARRIVAL AND ELECTRONICS APPARATUS

FIELD OF THE INVENTION

The present invention relates to the technical field of microphone, and more specifically, to a method for estimating direction of arrival, a device for estimating direction of arrival and an electronics apparatus.

BACKGROUND OF THE INVENTION

Estimation of direction of arrival is widely used in microphone technology. For example, it can be used for uplink noise cancellation.

The aim of estimating direction of arrival is to determine from which angular direction a single audio point source is located relative to a microphone array. Generally, the direction of arrival is represented by an angle of arrival, which is an angle between an impinging direction and a normal direction of the plane of the microphones.

In the prior art, this task is performed by means of beam-forming and statistical analysis.

In this prior art, the amount of calculation is relatively high and the efficiency is relatively low.

SUMMARY OF THE INVENTION

One object of an embodiment is to provide a new technical solution for estimating direction of arrival.

According to a first aspect, there is provided a method for estimating direction of arrival, comprising: digitalizing input audio signals from a pair of microphones in a microphone array within a certain time frame; buffering the digitalized signals; extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth; calculating phrase shift in each of the multiple sub-bands for the pair of microphones; performing linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones; and calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones.

According to a second aspect, there is provided a device for estimating direction of arrival, comprising: an A/D converter, which converts input audio signals from a pair of microphones in a microphone array within a certain time frame into digitalized signals; a buffer, which buffers the digitalized signals; and a processing device, which performs the following processes: extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth; calculating phrase shift in each of the multiple sub-bands for the pair of microphones; performing linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones; and calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones.

According to a third aspect, there is provided an electronics apparatus, including a device for estimating direction of arrival according to an embodiment.

According to an embodiment, computing resources for estimating direction of arrival can be reduced.

Further features of the present invention and advantages thereof will become apparent from the following detailed description of exemplary embodiments according to the present invention with reference to the attached drawings.

BRIEF DISCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the description thereof, serve to explain the principles of the invention.

Fig. 1 is a schematic diagram showing time difference of arrival from a sound source to a microphone array.

Fig. 2 is a schematic graph showing the relationship between frequency components and the phase differences.

Fig. 3 is a schematic flow chart of a method for estimating direction of arrival according to an embodiment.

Fig. 4. is a schematic graph showing the relationship coefficients between frequency components and the phase differences.

Fig. 5 is a schematic diagram showing an exemplary processing of estimating direction of arrival.

Fig. 6 is a schematic block diagram of a device for estimating direction of arrival according to another embodiment.

Fig. 7 is a schematic diagram of an electronics apparatus to which the solution of an embodiment can be applied.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Various exemplary embodiments of the present invention will now be described in detail with reference to the drawings. It should be noted that the relative arrangement of the components and steps, the numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise.

The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

Techniques, methods and apparatus as known by one of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.

In all of the examples illustrated and discussed herein, any specific values should be interpreted to be illustrative only and non-limiting. Thus, other examples of the exemplary embodiments could have different values.

Notice that similar reference numerals and letters refer to similar items in the following figures, and thus once an item is defined in one figure, it is possible that it need not be further discussed for following figures.

Generally, for a single point sound source located far enough (usually D >> d, for example, typically D is 10 times longer than d) , where D is the distance between the sound source and a microphone array and d is the inter-element distance between the microphones of the microphone array, the waves impinging the microphone array are considered as parallel. The frequency content of the impinging signal is assumed to be wideband (in the sense of the superposition of several frequencies covering a wide spectrum range) . Here, the micro array can be a linear microphone array.

The time difference of arrival between two microphones of the microphone array is directly correlated to a phase shift with respect to each frequency component of the impinging signal. This is illustrated in Fig 1. As shown in Fig. 1, the sound source S emits sound waves, which impinge the microphone array. The microphone array includes microphones mic1, mic2, …, micN. The phrases of frequency component ω at time t of the input sound signals from the microphones are

i=1…N, respectively. The angle of arrival at time t is θ (t) . D is the distance between the sound source S and a microphone array, and d is the distance between two consecutive microphones of the microphone array.

The time difference of arrival τ between two consecutive microphones can be expressed as follow:

where θ is the angle of arrival, and C is the speed of sound in the air. Here, because D >>d, the impinging waves are deemed to be parallel.

For each frequency component of the source signal, the time difference of arrival τ can be expressed as a phase shift difference. Let

be the phase of the frequency component ω at the time t of the sound signal input from the k-th microphone and let

be the phase of the frequency component ω at the time t of the sound signal input from the k+1-th microphone. The first order phase difference can be then expressed as:

The expression can be re-written in terms of time difference of arrival:

There exists a direct proportional relationship between the frequency component ω and the 1st order phase difference

for a given angle of arrival θ:

This relationship can be expressed as:

with

This direct proportional relationship is shown in Fig. 2. As shown in Fig. 2, the slope α (θ) is proportional to θ. So, θ can be derived from this relationship.

Fig. 3 is a schematic flow chart of a method for estimating direction of arrival between a sound source and a microphone array according to an embodiment.

Step S1100, digitalizing input audio signals from a pair of microphones in a microphone array within a certain time frame;

Step S1200, buffering the digitalized signals;

Step S1300, extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth;

Step S1400, calculating phrase shift in each of the multiple sub-bands for the pair of microphones;

Step S1500, performing linear regression according to the phrase shifts and the frequencies of the sub-bands to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones;

Step S1600, calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones in a microphone array.

As above, the solution in this embodiment provides a new solution for calculating an angle of arrival. In this solution, a signal from a pair of microphones in a microphone array is divided into multiple sub-bands. The

obtained from respective sub-bands are linearly fitted, to obtain a fitted relationship coefficient. The angle of arrival for the microphone can directly be derived form one single inverse sine transform, without performing inverse sine transforms for every sub-bands and taking mean of the obtained angles of them as an optimized angle of arrival. This approach is relatively simple in computation and has a relatively low amount of data processing. The efficiency of this approach is relatively high.

In the below, the steps of the method will be described in more details. As shown in Fig. 3, at step S1100, input audio signals from a pair of microphones in a microphone array within a certain time frame are digitalized. For example, the two microphones of the pair of microphones are consecutive. Generally, the certain time frame may be in a range of 10～20 ms.

At step S1200, the digitalized signals are buffered.

At step S1300, multiple sub-bands are extracted from each of the buffered signals, which covers a predefined bandwidth.

Usually, a filter-bank may be used to extract the N sub-bands. The filter-bank is a well-known overlap-adding FFT based method, for example, with 40%, 50%or 60%overlapping. The filter-bank is an array of band-pass filters that that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal.

For example, N is a power of 2. N can be chosen to be a value of the closest power of 2 (e.g. 2, 4, 8, 16, 32…) that will cover the 10-20 milliseconds time frame. Here, the FFT algorithm will be more efficient if N is a power of 2.

For example, the phase

can be derived, where k∈ [0, M-1] , M is the number of microphones in the microphone array, ω∈ [ω ₀, ω _N-1] covering a predefined bandwidth, and N is the number of sub-bands. It will be appreciated by a person skilled in the art that the sub-bands are narrow enough so that frequencies ω can be used to represent them, respectively, in practice.

The selection of the predefined bandwidth may depend on the application of the solution and on the microphone array topology such as the number of microphones, inter-element distance and so on.

In one embodiment, the application of the solution is speech. Commonly, a speech is contained in the bandwidth from 150Hz to 7000Hz for a high intelligibility. Most of the speech energy is in the low-frequency part of this bandwidth. However, low frequencies are less directional than high frequencies. In other words, it is more difficult to find out from which direction the low frequencies are coming than the high frequencies.

In another aspect, the plane waves propagating to adjacent microphones create delays in the microphone’s channels. These delays are translated into phase shifts for every individual frequencies of which the signals of interest are composed.

Consequently, the distance between two microphones determines the lowest frequency whose phase shift can be measured. The closer is the distance, the smaller is the phase shift.

On the other hand, a close distance helps to detect high frequencies. Here, in order to avoid a “time aliasing” phenomena, the predefined bandwidth is selected so that the distance d between the two microphones of the pair of microphones is less than half of the wavelength of the highest frequency in the N sub-bands, i.e. d < 0.5*wavelength of the highest frequency measured.

To sum up, the closer the microphones are, the better high frequencies can be detected and the lesser low frequencies can be detected. The distance between the two microphone is then a trade-off between the lowest frequency and highest frequency which the signal of interest contains.

In addition, in order to measure the phase shift introduced into the direction of arrival, the sampling rate is considered. The higher the sampling rate is, the more accurate small phase shift can be measured, especially, when the phase shift corresponds to a fraction of a single sample, i.e. phase shift < 1 sample time Ts = 1/Fs, where Fs is the sampling rate.

In this regard, the selection of the predefined bandwidth shall be a trade-off between microphone distance and sampling rate.

So, in an example, the predefined bandwidth is a relatively high part of the effective bandwidth of the input audio signals. Here, the effective bandwidth of the input audio signals contains effective energy of the signal, and the relatively high part is used to make the detection of the direction of arrival more accurate. Here the effective bandwidth is in a range from 150 Hz to 7000 Hz.

At step S1400, phrase shift in each of the multiple sub-bands for the pair of microphones is calculated.

Here, two adjacent microphones (or consecutives microphones) may be selected to derive

for each of the N sub-bands. For example,

where ω∈ [ω ₀, ω _N-1] . This phase shift may also be called as a 1st order phase difference. As shown in Fig. 4, the phrase shifts of the N sub-bands produce a scatter of points in the plane of

and ω. Generally, it is deemed that the

and ω are in a linear relationship. The regression line between the

axis and ω axis is an ideal distribution of the phase shifts, and the derived

are around the regression line.

At step S1500, linear regression is performed according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones.

For example, the linear regression is performed according to the phrase shifts and frequencies of the sub-bands based on Least Mean Square LMS or Normalized Least Mean Square NLMS, to estimate the estimated relationship coefficient.

In an example, the linear regression is performed to estimate the estimated relationship coefficient based on the following relationships:

where the phase shift of each of the N sub-bands is

the frequency of each of the N sub-bands is

and the estimated relationship coefficient is

As shown in Fig. 4, the natural presences of background noise, electronics noise and/or reverberation in real life acoustical environment tend to diffuse the distribution of those phrase shift points outside the theoretical proportionality relationship line in the plane of

and ω. In order to overcome this problem, a linear regression algorithm based on a LMS or NLMS regulation control is used here in order to estimate the relationship coefficient

such that the estimation will minimize the variance of the scattered points along the regression line (the line surrounded by the points in Fig. 4) . As shown in Fig. 4, an estimated relationship coefficient

between frequency component and the phase shift may be obtained. The estimated relationship coefficient

can be deemed as the slope of the regression line.

At step S1600, the direction of arrival is calculated through the estimated relationship coefficient for the pair of microphones.

For example, the direction of arrival is calculated based on the speed of sound in the air, the distance between the two microphones of the pair of microphones and the estimated relationship coefficient.

In an example, the direction of arrival is an estimated angle of arrival

which is an angle between an impinging direction and a normal direction of the plane of the pair of microphones.

The direction of arrival can be calculated through the following relationship:

with

wherein C is the speed of sound in the air , d is the distance between the two microphones of the pair of microphones, and

is the estimated relationship coefficient. The sign of

will determine whether

is a positive or a negative angle.

It will be appreciated by a person skilled in the art that since the estimated relationship coefficient contains the angle information inherently, many other approaches, other than the angle of arrival, may be used to represent the direction of arrival based on the relationship coefficient.

In the embodiment, a linear regression is used to take advantage of the linear relationship between the phase shift and the frequency. Here, the proportionality coefficient

is first estimated and optimized and then only one single inverse sine transform is made to obtain an estimated angle of arrival

Compared with the prior art, this embodiment is computationally more optimal and is also more robust to diffuse noise as explained above.

Optionally, the microphone array includes at least two pairs of microphones. Angles of arrival of the at least two pairs of microphones can be estimated as above and are

The estimated angles of arrival

are placed into a histogram to obtain an optimized estimated angle of arrival. The histogram can be used for statistical analysis in order to ensure an angular region whose resolution is to be defined by the application and the microphone array characteristics. Here, the estimated angles of arrival obtained from the pairs of microphones are statistically processed to select the most likely angle of arrival or a scope for angle of arrival, as the direction of arrival with respect to the microphone array.

Fig. 5 is a schematic diagram showing an exemplary processing of estimating direction of arrival. In Fig. 5, the microphone array includes three microphones mic1, mic2 and mic3. The impinging waves are received by the three microphones and then are passed as input signal to the processing unit A1, A2 and A3, in which they are digitalized and buffered. Then, N sub-bands are extracted from the input signals in A1, A2 and A3. Then, phases

of the N sub-bands are calculated. Based on the phases of the N sub-bands, phase shifts

of the two corresponding sub-bands for mic1 and mic2,

of the N sub-bands are obtained. Here, although the phase shifts of consecutive microphones are obtained, it will be appreciated by a person skilled in the art that phase shift of other microphones is also possible, for example, the phase shift between the first microphone mic1 and the third microphone mic3.

By using the phase shifts

of the N sub-bands, an estimated relationship coefficient

is obtained through linear regression based on LMS or NLMS. Likewise, an estimated relationship coefficient

is also obtained.

Estimated angles of arrival

can be derived from the coefficients

Finally, the estimated angles of arrival

are put into a histogram to obtain an optimized estimated angle of arrival

Fig. 6 is a schematic block diagram of a device for estimating direction of arrival according to another embodiment. As shown in Fig. 6, the device 20 for estimating direction of arrival is connected to a microphone array 10 and receives input audio signals from the microphone array 10.

The device 20 for estimating direction of arrival comprises: an A/D converter 21, a buffer 22, and a processing device 23.

The A/D converter 21 receives input audio signals from a pair of microphones in a microphone array within a certain time frame and converts them into digitalized signals. The buffer 22 buffers the digitalized signals. For example, the pair of microphones includes two adjacent microphones in the microphone array. The certain time frame may be in a range of 10～20 ms.

The processing device 23 extracts multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth. For example, the predefined bandwidth is a relatively high part of the effective bandwidth of the input audio signals and the effective bandwidth is in a range from 150 Hz to 7000 Hz. For example, the predefined bandwidth is selected so that the distance d between the two microphones of the pair of microphones is less than half of the wavelength of the highest frequency in the N sub-bands. The predefined bandwidth may be a relatively high part of the effective bandwidth of the input audio signals. N may be a power of 2..

The processing device 23 calculates phrase shift in each of the multiple sub-bands for the pair of microphones.

The processing device 23 performs linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones. For example, the linear regression is performed according to the phrase shifts and frequencies of the sub-bands based on Least Mean Square LMS or Normalized Least Mean Square NLMS, to estimate the estimated relationship coefficient.

where the phase shift of each of the N sub-bands is

the frequency of each of the N sub-bands is

and the estimated relationship coefficient is

The processing device 23 calculates the direction of arrival through the estimated relationship coefficient for the pair of microphones. For example, the processing device 23 further performs the following process: calculating the direction of arrival based on the speed of sound in the air, the distance between the two microphones of the pair of microphones and the estimated relationship coefficient.

For example, the direction of arrival is an estimated angle of arrival

which is an angle between an impinging direction and a normal direction of the plane of the pair of microphones, wherein the processing device 23 calculates the direction of arrival based on the following relationship:

with

wherein C is the speed of sound in the air , d is the distance between the two microphones of the pair of microphones and

is the estimated relationship coefficient.

Optionally, the microphone array includes at least two pairs of microphones. In such a situation, the processing device 23 produces estimated angles of arrival

of the at least two pairs of microphones, respectively. The device 20 for estimating direction of arrival further comprises a histogram unit, which receives

and places them into a histogram to obtain an optimized estimated angle of arrival.

The components 21-23 may be implemented along or separately by software, hardware or a combination thereof. For example, they can be implemented through a combination of a computing unit such as a CPU or a MPU and a memory storing instructions for controlling the computing unit to implement the respective functions during the running thereof. Alternatively, they can be implemented in a programmable logic circuitry, field-programmable gate arrays (FPGA) , programmable logic arrays (PLA) , or an application-specific integrated circuit (ASIC) . Under the teaching of this disclosure, all there implementations are feasible. It will be understood by a person skilled in the prior art that a software is equivalent to a hardware except for some of the mechanical components such a speaker, a microphone and so on. In this regard, a person skilled in the art can conceive, under the teaching of this disclosure that the implementations of hardware manner, software manner and/or combination thereof are equivalent. In this regard, this disclosure will not limit the implementation manners of the components 21-23. A person skilled in the art can choose the implementation manners under the teaching of this disclosure in consideration of the cost, the market availability and so on.

In Fig. 7, the electronics apparatus 30 includes a device for estimating direction of arrival as above. In Fig. 7, an earphone 30 is shown, and it includes a control box 31. The device for estimating direction of arrival may be placed in the control box 31. It would be appreciated by a person skilled in the art that the electronics apparatus can be any type of electronic apparatus, such as an ear-bud, a headphone, a smart phone, a tablet, a laptop and so on.

Although some specific embodiments of the present invention have been demonstrated in detail with examples, it should be understood by a person skilled in the art that the above examples are only intended to be illustrative but not to limit the scope of the present invention.

Claims

A method for estimating direction of arrival, comprising:

digitalizing input audio signals from a pair of microphones in a microphone array within a certain time frame;

buffering the digitalized signals;

extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth;

calculating phrase shift in each of the multiple sub-bands for the pair of microphones;

performing linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones; and

calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones.
The method according to claim 1, wherein performing linear regression further comprises:

performing linear regression according to the phrase shifts and frequencies of the sub-bands based on Least Mean Square LMS or Normalized Least Mean Square NLMS, to estimate the estimated relationship coefficient.
The method according to claim 1 or 2, wherein performing linear regression further comprises:

performing linear regression to estimate the estimated relationship coefficient based on the following relationships:

where the phase shift of each of the N sub-bands is
the frequency of each of the N sub-bands is ω _i, i=1…N, and the estimated relationship coefficient is
The method according to claim 1 or 2, wherein calculating the direction of arrival further comprises:

calculating the direction of arrival based on the speed of sound in the air, the distance between the two microphones of the pair of microphones and the estimated relationship coefficient.
The method according to claim 4, wherein the direction of arrival is an estimated angle of arrival
which is an angle between an impinging direction and a normal direction of the plane of the pair of microphones,

wherein calculating the direction of arrival further comprises:

calculating the direction of arrival based on the following relationship:

with

wherein C is the speed of sound in the air , d is the distance between the two microphones of the pair of microphones, and
is the estimated relationship coefficient.
The method according to claim 5, wherein the predefined bandwidth is selected so that d is less than half of the wavelength of the highest frequency in the N sub-bands.
The method according to claim 5, wherein the microphone array includes at least two pairs of microphones and estimated angles of arrival of the at least two pairs of microphones are

wherein
are placed into a histogram to obtain an optimized estimated angle of arrival.
The method according to claim 1, wherein the pair of microphones includes two adjacent microphones in the microphone array.
The method according to claim 1, wherein the predefined bandwidth is a relatively high part of the effective bandwidth of the input audio signals and the effective bandwidth is in a range from 150 Hz to 7000 Hz.
A device for estimating direction of arrival, comprising:

an A/D converter, which converts input audio signals from a pair of microphones in a microphone array within a certain time frame into digitalized signals;

a buffer, which buffers the digitalized signals; and

a processing device, which performs the following processes:

extracting multiple sub-bands from each of the buffered signals, which covers a predefined bandwidth;

calculating phrase shift in each of the multiple sub-bands for the pair of microphones;

performing linear regression according to the phrase shifts and frequencies of the sub-bands, to estimate an estimated relationship coefficient between the phrase shifts and the frequencies of the sub-bands corresponding to the pair of microphones; and

calculating the direction of arrival through the estimated relationship coefficient for the pair of microphones.
The device according to claim 10, wherein the processing device further performs the following process:

performing linear regression according to the phrase shifts and frequencies of the sub-bands based on Least Mean Square LMS or Normalized Least Mean Square NLMS, to estimate the estimated relationship coefficient..
The device according to claim 10 or 11, wherein the processing device further performs the following process:

performing linear regression to estimate the estimated relationship coefficient based on the following relationships:

where the phase shift of each of the N sub-bands is
the frequency of each of the N sub-bands is ω _i, i=1…N, and the estimated relationship coefficient is
The device according to claim 10 or 11, wherein the processing device further performs the following process:

calculating the direction of arrival based on the speed of sound in the air, the distance between the two microphones of the pair of microphones and the estimated relationship coefficient.
The device according to claim 10 or 11, wherein the direction of arrival is an estimated angle of arrival
which is an angle between an impinging direction and a normal direction of the plane of the pair of microphones, and the processing device further performs the following process:

calculating the direction of arrival based on the following relationship:

with
wherein C is the speed of sound in the air , d is the distance between the two microphones of the pair of microphones, and
is the estimated relationship coefficient.
The device according to claim 14, wherein the predefined bandwidth is selected so that d is less than half of the wavelength of the highest frequency in the N sub-bands.
The device according to claim 14, further comprising a histogram unit,

wherein the microphone array includes at least two pairs of microphones and the processing device produces estimated angles of arrival of the at least two pairs of microphones
respectively,

wherein the histogram unit receives
and places them into a histogram to obtain an optimized estimated angle of arrival.
The device according to claim 10, wherein the pair of microphones includes two adjacent microphones in the microphone array.
The device according to claim 10, wherein the predefined bandwidth is a relatively high part of the effective bandwidth of the input audio signals and the effective bandwidth is in a range from 150 Hz to 7000 Hz.
An electronics apparatus, including a device for estimating direction of arrival according to any of claims 10-18.