EP1771034A2 - Microphone calibration in a RGSC-beamformer - Google Patents

Abstract

An acoustic RGSC (Robust Generalised Sidelobe Canceller) beamformer has a microphone calibration filter unit (CAL) with calibration filters (C0-2) for component tolerance calibration microphones (M0-2) feeding signals (X0-2) to a fixed beamformer (FBF) with adaptive Block matrix (ABM) and interference suppressor (AIC). An independent claim is included for a method of operating an RGSC beamformer.

Description

The invention relates to a circuit arrangement and a method for microphone calibration in an RGSC beamformer.

Out Wolfgang Herbordt: "Combination of Robust Adaptive Beamforming with Acoustic Echo Cancellation for Acoustic Human / Machine Interface", dissertation, Friedrich-Alexander-University Erlangen / Nuremberg, submitted on 03.12.2003, page 99 ff , is an RGSC beamformer known.

From the US 2005/0047611 A1 For example, a system and a method for recording audio signals are known in which an interference signal is reduced compared to a useful signal using a microphone array. For this purpose, the microphones of the microphone arrays are connected by means of a filter unit and a summation element to a beamformer. In the cited document, the filter unit of the Beamformers is not referred to in a non-standard way as a calibration filter.

Generally, in a beamformer, multiple microphones are interconnected to form a microphone system having a directional characteristic. As a result, acoustic input signals are attenuated differently in the microphone system depending on their direction of incidence in the microphone system. In the case of a beamformer, the signal transmission functions of the microphones used must be very precisely matched in order to achieve a desired directivity. Deviations in the signal transmission functions due to tolerances or aging effects considerably worsen the function of the beamformer, so that, if necessary, a desired noise suppression can no longer be ensured to a sufficient extent with the microphone system used. This is particularly true for beamformers with microphone arrays with very small aperture, which are used for example in hearing aid applications, in which often differential or super-directive beamformer algorithms.

It is known to follow the microphones of a Beamformers calibration filter to compensate for component tolerances of the microphones used. Here, the signal transmission behavior of the microphones is determined once and filter coefficients of calibration filters, which are connected downstream of the microphones, adjusted so that the component tolerances are compensated. However, this approach has the disadvantage that aging effects can not be taken into account.

The object of the present invention is therefore to specify an RGSC beamformer in which age-related component tolerances of the microphones used are automatically compensated.

This object is achieved by an RGSC beamformer having the features according to claim 1. Further, the object is achieved by a method for operating an RGSC beamformer having the features according to claim 6.

In the context of the invention, the calculation of a filter is understood as meaning the calculation of the transfer function of the relevant filter or the calculation of the corresponding filter coefficients for determining this transfer function.

The invention offers the advantage that an automatic calibration of the microphones takes place during operation of the beamformer. As a result, time-variant microphone mismatches, for example due to aging, moisture, dirt, etc., can be compensated for, without the need for elaborate separate recalibration.

The RGSC beam former known from the cited prior art and illustrated in FIG. 1 will be described below briefly described with reference to an embodiment with three microphones:

At least two microphones are required to construct an RGSC beamformer. Theoretically, however, any number of microphones can be used. In the exemplary embodiment, the beamformer comprises the three microphones M ₀ , M ₁ and M ₂ . The microphones are followed by the calibration filters C ₀ , C ₁ and C ₂ to compensate for component tolerances. To compensate for existing component tolerances of the microphones used their transmission behavior is measured. Subsequently, the filter coefficients of the calibration filter C ₀ , C ₁ and C ₂ are adjusted so that the microphones in conjunction with the downstream calibration filters show at least approximately the same signal transmission behavior. The calibration filters are followed by the beamformer filters W ₀ , W ₁ and W ₂ in the signal paths of the microphones. Subsequently, the filtered microphone signals for generating a directional characteristic in the adder S are added.

It should be noted that in the circuit shown, the calibration of the microphones and the beam shaping can be performed even if in only two microphone signal paths calibration filters or in only two microphone signal paths Beamformer filter are available. The three calibration filters C ₀ , C ₁ and C ₂ are together called the calibration filter unit CAL and the beamformer filters W ₀ , W ₁ and W ₂ in conjunction with the summer S together are referred to as fixed beamformer FBF. The microphones M ₀ , M ₁ and M ₂ in conjunction with the calibration filter unit CAL and the fixed beamformer FBF already form a microphone system with a directional characteristic. An acoustic signal (useful signal) arriving from the preferred direction of the directional microphone thus formed is thus raised in relation to an acoustic signal (interference signal) arriving from another direction.

A further improvement of the signal-to-noise ratio results in the known directional microphone system through the use of an adaptive interference canceler AIC (Adaptive Interference Canceller). The output of the fixed beamformer FBF serves as the reference signal for the adaptive interference suppressor. An adaptive blocking matrix ABM with blocking filters B ₀ , B ₁ and B ₂ blocks the useful signal so that only the estimation of an interference signal is present at each output of the adaptive blocking matrix ABM. The AIC uses this estimate to suppress the disturbance in the reference signal (and hence the wanted signal).

The adjustment of the filter coefficients of the calibration filter CAL takes place in the circuit known from the prior art by means of a one-time measurement of the signal transmission behavior of the microphones used. To compensate for aging phenomena, this measurement would have to be repeated from time to time. In contrast, the invention proposes an automatic, continuous or repeated calibration of the microphones. This is achieved according to the invention in that a calibration filter calculation unit (CALBE) is integrated into the circuit known from the prior art according to FIG. The resulting block diagram is illustrated for the special case of a beamformer with three microphones M ₀ , M ₁ and M ₂ in FIG. In this case, the basic mode of operation of the beamformer corresponds to the mode of operation of the beamformer illustrated and described in FIG. 1, with the difference that in the beamformer according to the invention an automatic calibration of the microphones takes place. For this purpose, the beamformer according to the invention comprises the calibration filter calculation unit CALBE. These are the signal outputs of the blocking filter B ₀ , B ₁ and B ₂ supplied as input. One of these output signals of the blocking filters is used as a reference signal. In the exemplary embodiment, this is the output signal of the blocking filter B ₁ . Finally, in the calibration filter calculation unit CALBE, the calibration filters C ₀ 'and C ₂ ' are adaptively determined such that the energy of the reference signal subtracted, with the calibration filters C ₀ 'and C ₂ ' filtered output signals of the blocking filter B ₀ or B _{2 is} minimized. The calibration filters thus determined are subsequently used as new calibration filters C ₀ and C ₂ connected downstream of the microphones M ₀ and M _2, respectively.

In summary, the calibration algorithm calculates optimized calibration filters in the calibration filter calculation unit CALBE. These are then copied to the calibration filter unit CAL, where they replace the previously valid calibration filters. The filtered output signal of the fixed beamformer FBF thus produces the input signals to the adaptive algorithm for the determination of new, improved calibration filters of the calibration filter unit. An analysis shows that the filtered output signals of the Fixed Beamformer are very well suited for the determination of the calibration filters and lead to optimized calibration filters (Wiener solution).

A significant advantage of the invention is that the output signal of the fixed beamformer FBF has a better signal-to-noise power ratio SNR (signal-to-noise ratio) than the microphone signals. This means that the inputs of the adaptive algorithm are hardly disturbed by noise. This leads to a fast convergence and a good calibration. Furthermore, with increasing convergence of the calibration filter, the signal-to-noise power ratio in the output of the fixed beamformer FBF improves, so that both the convergence of the blocking filters and the further convergence of the calibration filters are supported. Since the calibration according to the invention runs automatically, continuously or repeatedly, even time-variant microphone mismatches, for example due to aging, moisture, contamination, etc., can be compensated without the need for time-consuming manual recalibration.

The proposed method for calibrating the microphones of an RGSC beamformer can be realized both in the time domain and in the frequency domain.

In the context of the invention, the procedure described in the example for a beamformer with three microphones can also be analogously applied to beamformers with an arbitrary number of microphones (≥ 2).

The theoretical background in microphone calibration according to the invention is shown below:

analysis

The following analysis is based on a time-discrete Fourier space. It is further assumed that all sensor signals are static and ergodic. The superscript T and the asterisk (*) mark the transposed and the complex conjugate matrix, respectively.

wobei H^T(ω) = [H₀(ω),H₁(ω),H₂(ω)] gilt. Das Mikrofonsignal X_m(ω) wird mit dem korrespondierenden Kalibrierfiltergewicht C_m(ω) gefiltert. Ohne Beschränkung der Allgemeinheit kann das Signal X₁(ω) als Referenzsignal angenommen werden. Daher gilt C₁(ω) = 1. Sei W_m(ω) die Übergangsfunktion des FBF (Fester Beamformer) für das m-te Mikrofon. Dann ist das FBF-Ausgangssignal Y_f(ω) gegeben durch $$Y_f\left(\omega \right)={\displaystyle \sum _{m=0}^2}{W}_m\left(\omega \right)C_m\left(\omega \right)X_m\left(\omega \right)=S\left(\omega \right){\displaystyle \sum _{m=0}^2}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\mathrm{.}$$

A desired source S (ω) with a known position will irradiate the microphone array consisting of M = 3 sensors. Let H _m (ω) be the transition function from the source to the mth microphone. Then the microphone signals
X ^T (ω) = [X ₀ (ω), X ₁ (ω), X ₂ (ω)] are written as: $${\mathrm{X}}^T\left(\omega \right)=S\left(\omega \right){\mathrm{H}}^T\left(\omega \right).$$

where H ^T (ω) = [H ₀ (ω), H ₁ (ω), H ₂ (ω)]. The microphone signal X _m (ω) is filtered with the corresponding calibration filter weight C _m (ω). Without limiting the generality, the signal X ₁ (ω) can be assumed as the reference signal. Therefore, C ₁ (ω) = 1. Let W _m (ω) be the transition function of the FBF (Fixed Beamformer) for the mth microphone. Then the FBF output Y _f (ω) is given by $$Y_f\left(\omega \right)={\displaystyle \underset{m=0}{\overset{2}{\Sigma }}}{W}_m\left(\omega \right)C_m\left(\omega \right)X_m\left(\omega \right)=S\left(\omega \right){\displaystyle \underset{m=0}{\overset{2}{\Sigma }}}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\mathrm{,}$$

The transition function B _m (ω) of the m-th adaptive blocking matrix (ABM) filter is determined by minimizing the mean square of the m-th ABM output signal Y _{b, m} (ω), where $$Y_{b.m}\left(\omega \right)=X_m\left(\omega \right)-B_m\left(\omega \right)Y_m\left(\omega \right)\mathrm{,}$$

wobei Φ_YfYf(ω) die spektrale Leistungsdichte am FBF-Ausgang und Φ_XmYf(ω) die Kreuzspektraldichte zwischen dem m-ten Mikrofonsignal und dem FBF-Ausgang bezeichnet. Mit den Gleichungen (1) und (2) folgt: $$B_m\left(\omega \right)={\mathrm{\Phi }}_{\mathit{SS}}\left(\omega \right)H_m\left(\omega \right){\left({\displaystyle \sum _{m=0}^2}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\right)}^{*}{\left({\mathrm{\Phi }}_{Y_f{Y}_f}\left(\omega \right)\right)}^{-1}\mathrm{.}$$

Φ _SS(ω) = S(ω)S*(ω) bezeichnet die spektrale Leistungsdichte des gewünschten Signals. Sei $$\mathrm{\Psi }\left(\omega \right)={\mathrm{\Phi }}_{\mathit{SS}}\left(\omega \right){\left({\displaystyle \sum _{m=0}^2}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\right)}^{*}{\left({\mathrm{\Phi }}_{Y_f{Y}_f}\left(\omega \right)\right)}^{-1},$$

dann gilt: $$B_m\left(\omega \right)=\mathrm{\Psi }\left(\omega \right)H_m\left(\omega \right)\mathrm{.}$$

With the principle of orthogonality, the transition function for the optimal filter can be derived as follows: $$B_m\left(\omega \right)=\frac{{\mathrm{\Phi }}_{X_m{Y}_f}\left(\omega \right)}{{\mathrm{\Phi }}_{Y_f{Y}_f}\left(\omega \right)}$$

where Φ _YfYf (ω) _denotes the spectral power density at the FBF output and Φ _XmYf (ω) the cross spectral density between the _{mth microphone signal} and the FBF output. With equations (1) and (2) follows: $$B_m\left(\omega \right)={\mathrm{\Phi }}_{\mathit{SS}}\left(\omega \right)H_m\left(\omega \right){\left({\displaystyle \underset{m=0}{\overset{2}{\Sigma }}}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\right)}^{*}{\left({\mathrm{\Phi }}_{Y_f{Y}_f}\left(\omega \right)\right)}^{-1}\mathrm{,}$$

Φ _SS (ω) = S (ω) S * (ω) denotes the spectral power density of the desired signal. Be $$\mathrm{\Psi }\left(\omega \right)={\mathrm{\Phi }}_{\mathit{SS}}\left(\omega \right){\left({\displaystyle \underset{m=0}{\overset{2}{\Sigma }}}{W}_m\left(\omega \right)C_m\left(\omega \right)H_m\left(\omega \right)\right)}^{*}{\left({\mathrm{\Phi }}_{Y_f{Y}_f}\left(\omega \right)\right)}^{-1}.$$

then: $$B_m\left(\omega \right)=\mathrm{\Psi }\left(\omega \right)H_m\left(\omega \right)\mathrm{,}$$

The filtered FBF output signals {F _m (ω); m = 0, 1, 2} act as an input to the adaptive calibration algorithm. Consider the calibration path for the microphone m = 0. As follows from Figure 1, this can be written as $${\mathrm{<figure-callout\; id="0"\; label="e"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">e</figure-callout>}}_0\left(\omega \right)=F_1\left(\omega \right)-C_0^{\text{'}}\left(\omega \right){\mathrm{<figure-callout\; id="0"\; label="F"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">F</figure-callout>}}_0\left(\omega \right).$$

The m-th filtered FBF output signal F _m (ω) results to $$F_m\left(\omega \right)=B_m\left(\omega \right)Y_f\left(\omega \right)\mathrm{,}$$

The optimal calibration filter results from minimizing the mean square of the error signal E ₀ (ω). With the orthogonality principle, the transition function for the optimal calibration filter is given as $$C_0^{\text{'}}\left(\omega \right)=\frac{{\mathrm{\Phi }}_{F_1<figure-callout\; id="0"\; label="\; F"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\; </figure-callout>F_{}{}_0}\left(\mathrm{<figure-callout\; id="0"\; label="\omega \; \Phi \; F"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">\omega \; </figure-callout>},\right)}{{\mathrm{\Phi }}_{F_{}}}$$

It can be seen from the equation (9) that φ _F1F0 = B ₁ (ω) B ₀ * (ω) φ _YfYF (ω) and φ _F0F0 = B ₀ (ω) B ₀ * (ω) φ _YfYf (ω). Therefore, C ₀ '= B ₁ (ω) B ₀ ^-1 (ω), provided that Φ _YfYf (ω) ≠ 0 and B ₀ (ω) ≠ 0. Equation (7) can be used to calculate the transition function for optimal calibration $$C_0^{\text{'}}\left(\omega \right)=H_1\left(\omega \right)H_0^{-1}\left(\omega \right)\mathrm{,}$$

The analysis for the second calibration filter is now performed in a similar way: $$C_2^{\text{'}}\left(\omega \right)=H_1\left(\omega \right)H_2^{-1}\left(\omega \right)\mathrm{,}$$

These are the desired transition functions for the optimal calibration filter. The analysis thus shows that the filtered FBF signals can also be used to provide calibration filters for microphones instead of microphone signals. However, they have an advantage over the conventional calibration algorithms applied directly to the microphone signals. In particular, in real situations, the filtered FBF signals are less disturbed by interfering noises than the microphone signals. This is due to the presence of the FBF, which improves the proportion of the target signal relative to interfering signals.

Adaptation

wobei µ_cal der Schrittgrößenparameter ist. P_FmFm(ω, k) ist die Leistungsschätzung für das Frequenzband um die Frequenz ω: $$P_{F_m{F}_m}\left(\omega ,,k\right)={\lambda }_c{P}_{F_m{F}_m}(\omega ,k-1)+\left(1-{\lambda }_c\right){\left|F_m\left(\omega ,,k\right)\right|}^2$$

mit dem Vergessensfaktor λ_c. k bezeichnet den Block-Zeit-Index.The calibration filters are adjusted via the nLMS (Least Mean Square Algorithm) algorithm shown below. $$C_m^{\text{'}}\left(\omega .k+1\right)=C_m^{\text{'}}\left(\omega ,,k\right)+{\mu }_{\mathit{cal}}{F}_m^{*}\left(\omega ,,k\right)e_m\left(\omega ,,k\right)P_{F_m{F}_m}\left(\omega ,,k\right).m=0.2.$$

where μ _{cal is} the step size parameter. P _FmFm (ω, k) is the power _estimate for the frequency band around the frequency ω: $$P_{F_m{F}_m}\left(\omega ,,k\right)={\lambda }_c{P}_{F_m{F}_m}(\omega .k-1)+\left(1-{\lambda }_c\right){\left|F_m\left(\omega ,,\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)\right|}^2$$

with the forgetting factor λ _c . k denotes the block time index.

adjustment controls

The ABM filters try to hide the signal components correlated between the FBF output and the sensor signals. For this reason, and so that no spatially correlated interference is hidden, the adjustment of the ABM filters may only be performed when the desired signal is present. That is, ABM filters are adjusted in situations with high signal-to-noise ratio.

The same applies to the calibration algorithm. In order to prevent the calibration element from interfering with the interference direction and the target signal direction in the case of the microphones, its adaptation must also be carried out only with a high signal-to-noise ratio.

• Figur 3 zeigt einen MSE-Plot des Kalibrierungsalgorithmus für den Amplitudenfehler von 1 dB und den Phasenfehler von -5° am vorderen Mikrofon für unterschiedliche Schrittgrößenparameter µ_c.
• Figur 4 zeigt die Spektrale Leistungsdichte des FBF-Ausgangs für ideale Mikrofone, schlecht angepasste Mikrofone (Amplitudenfehler von 1 dB und Phasenfehler von -5° am vorderen Mikrofon) sowie nachgeregelte Mikrofone nach der Kalibrierung, µ_c = 0,008.

The results of a simulation are shown in FIGS. 3 and 4:

• Figure 3 shows an MSE plot of the 1 dB amplitude error calibration algorithm and the -5 ° am phase error front microphone for different step size parameters μ _c .
• Figure 4 shows the spectral power density of the FBF output for ideal microphones, poorly matched microphones (amplitude error of 1 dB and phase error of -5 ° at the front microphone) as well as readjusted microphones after calibration, μ _c = 0.008.

Claims (10)

RGSC beamformer, comprising at least two microphones (M ₀ , M ₁ , M ₂ ) each producing a microphone signal (X ₀ , X ₁ , X ₂ ), - a Fixed Beamformer (FBF), an adaptive blocking matrix (ABM), - an adaptive interference suppressor (AIC), as well - A micro-filter downstream calibration filter unit (CAL) with at least one calibration filter (C ₀ , C ₁ , C ₂ ) to compensate for component tolerances of the microphones used Characterized by a calibration filter calculation unit (CALBE), to which signals generated for the calculation of the calibration filters (C ₀ , C ₁ , C ₂ ) in the adaptive blocking matrix (ABM) are supplied. RGSC beamformer according to claim 1, wherein the fixed beamformer (FBF) at least one beamformer filter (W ₀ , W ₁ , W ₂ ) for filtering each one of a microphone signal (X ₀ , X ₁ , X ₂ ) resulting signal and a Adder (S) for adding two of the microphone signals (X ₀ , X ₁ , X ₂ ) resulting signals. RGSC beamformer according to claim 1 or 2, wherein the adaptive blocking matrix (ABM) comprises adaptive blocking filters (B ₀ , B ₁ , B ₂ ) for filtering the output signal of the fixed beamformer (FBF) as a function of a respective microphone signal (X ₀ , X ₁ , X ₂ ). RGSC beamformer according to one of claims 1 to 3, wherein the calibration filter calculation unit (CALBE), the signal outputs of the blocking filter (B ₀ , B ₁ , B ₂ ) are supplied as signal inputs. RGSC beamformer according to one of claims 1 to 4, wherein the calibration filter calculation unit (CALBE) comprises at least one subtractor (D ₀ , D ₂ ), as a reference signal an output signal of a blocking filter (B ₁ ) is fed directly and an output signal of a blocking filter (B ₀ , B ₂ ) after filtering with an adaptive calibration filter (C ₀ ', C ₂ '). Method of operating an RGSC beamformer, the at least two microphones (M ₀ , M ₁ , M ₂ ) each producing a microphone signal (X ₀ , X ₁ , X ₂ ), - a Fixed Beamformer (FBF), an adaptive blocking matrix (ABM), - an adaptive interference suppressor (AIC), as well a calibration filter unit (CAL) connected downstream of the microphones with at least one calibration filter (C ₀ , C ₁ , C ₂ ) for compensating component tolerances of the microphones used, wherein at least one microphone signal (X _0, X _1, X ₂₎ by means of a microphone (M _0, M _1, M ₂₎ downstream Kalibrationsfilters (C _0, C _1, C ₂₎ is filtered,
characterized in that the calibration filter (C ₀ , C ₁ , C ₂ ) is adaptively calculated by signals emanating from the adaptive blocking matrix (ABM). Method according to claim 6, wherein an output signal of a blocking filter (B ₁ ) is used as a reference signal in the calculation of the calibration filter. The method of claim 6 or 7, wherein a calibration filter (C ₀ ', C _2') in the Kalibrationsfilterberechnungseinheit (CALBE) is calculated such adaptive in that the means of Kalibrationsfilters (C ₀ ', C _2') filtered output signal of the blocking filter (B ₀ , B ₂ ) is subtracted from the reference signal and the resulting output signal (E ₀ , E ₂ ) is minimized. Method according to one of claims 1 to 8, wherein the calculation of the calibration filter takes place in the time domain. Method according to one of claims 1 to 8, wherein the calculation of the calibration filter is performed in the frequency domain.

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