- Research
- Open Access

# Joint estimation of pitch and direction of arrival: improving robustness and accuracy for multi-speaker scenarios

- Stephan Gerlach
^{1, 4}Email author, - Jörg Bitzer
^{1, 2}, - Stefan Goetze
^{1, 4}and - Simon Doclo
^{3, 4}

**2014**:31

https://doi.org/10.1186/s13636-014-0031-8

© Gerlach et al.; licensee Springer. 2014

**Received: **6 September 2013

**Accepted: **16 July 2014

**Published: **12 August 2014

## Abstract

In many speech communication applications, robust localization and tracking of multiple speakers in noisy and reverberant environments are of major importance. Several algorithms to tackle this problem have been proposed in the last decades. In this paper, we propose several extensions to a recently presented joint direction of arrival (DOA) and pitch estimation method, increasing its robustness in multi-speaker scenarios, noise, and reverberation. First, a spectral comb filter is added to the original algorithm to better cope with concurrent speakers. Second, the well-known generalized cross-correlation with phase transform (GCC-PHAT) is used as an additional weighting function to improve the DOA estimation accuracy in terms of correct hits. Third, using multiple microphone pairs, the multi-channel cross-correlation approach is incorporated to improve the robustness against noise and reverberation. In order to improve tracking for moving and even intersecting speakers, a particle filter is used. Experiments with real-world recordings in realistic acoustic conditions show that the proposed extensions increase the DOA hit rate by about 33% compared to the original algorithm for two step-wise moving sources at a signal-to-noise ratio (SNR) of 15 dB and a reverberation time RT_{60} of 560 ms.

## Keywords

## 1 Introduction

Automatic detection, localization, and tracking of speaker are of high interest in several applications such as hands-free speech communication and video conferencing, as well as for computational auditory scene analysis and human-machine interfaces. For example, in current high-quality video-conferencing systems, the users are typically not located close to the microphones, and furthermore, several users may be talking simultaneously.

To distinguish between multiple concurrent speakers, it is desirable to be able to differentiate between their directions of arrival (DOAs) and their voice characteristics. This information can then be used to, e.g., enhance automatic speech recognition, indicate active speakers, steer the camera of a video-conferencing system, or to suppress undesired acoustic disturbances.

A common method for DOA estimation is to first estimate the time difference of arrival (TDOA) between different microphone pairs. An overview of these methods, as well as related references, can be found in [1],[2]. A well-known TDOA estimation method is the generalized cross-correlation with phase transform (GCC-PHAT), first introduced in [3] and intensively investigated for speech signals in, e.g., [4]–[7]. The dual delay line algorithm in [8] is another method to estimate the azimuths of sound sources by analyzing the coincidences along two-channel delay-line pairs. Other methods for DOA estimation are based on blind channel identification, such as the adaptive eigenvalue decomposition algorithm (AEDA) [9],[10], or subspace methods such as multiple signal classification (MUSIC) [11]. Another category of DOA estimation algorithms are energy-based methods which only use the measured signal energy at each microphone [12], or combined methods using both TDOA and energy information [13],[14].

The spectro-temporal characteristics of speech signals, e.g., the fundamental frequency (pitch), can also be analyzed to distinguish between concurrent speakers [15]. Traditional pitch estimation methods are based on, e.g., zero crossing rate analysis, detection of harmonics in the autocorrelation function, and cepstrum analysis [16]. Recently, a pitch estimation filter with amplitude compression (PEFAC) in the spectral domain has been proposed in [17], and methods for joint pitch and model order estimation have been proposed in [18]–[20]. Multi-pitch estimation has also become a topic of research, and several approaches are summarized in [21].

DOA and pitch estimation are typically treated separately, and only a couple of attempts have been made for joint DOA and pitch estimation. A possible solution is a two-step approach. In the first step, the position of a source is estimated from (multiple) microphone pairs. In the second step, the microphone signals are combined using a beamformer to obtain a single-channel output signal which is used to estimate the pitch using a single-channel pitch estimation method. In [22], a joint position and pitch (PoPi) estimation method has been proposed which is based on either cross-correlations or cross-power spectral densities (CPSDs). Several extensions have been proposed using cepstral weighting [23], gammatone-like weighting [24], time-domain GCC-PHAT replacement [25], particle filtering [26], and speaker-dependent subgrouping [27]. In [28], a different method based on a recurrent timing neural network is used for joint DOA and pitch estimation. Other methods make use of the 2D-Capon method [29],[30], a subspace approach termed as multi-channel multi-pitch harmonic MUSIC (MC-HMUSIC) [31], a minimum variance distortionless response (MVDR) beamformer [32] which additionally estimates the model order to determine the number of harmonics of the source signal, and a non-linear least squares (NLS)-based method [33], all using a harmonic signal model to jointly estimate the DOA and pitch. When jointly estimating DOA and pitch, the parameter estimation typically mutually benefits from each other. Although these joint estimation methods perform quite well for clean speech signals (i.e., without noise and no reverberation), their performance typically degrades considerably in adverse acoustic environments.

The focus of this paper is to improve joint DOA and pitch estimation for multiple speakers in terms of accuracy and robustness in realistic acoustic situations. We have taken the CPSD-based method proposed in [22] combined with cepstral weighting [23], gammatone-like weighting [24], and a subsequent particle filtering [26] as the core algorithm, and we propose several extensions to improve both accuracy and robustness in this paper. As a first extension, a frequency-domain comb filter is introduced to improve the performance for simultaneously active speakers. As a second extension, a GCC-PHAT weighting function is introduced, resulting in an improved DOA estimation accuracy. As a third extension, instead of simply averaging the multiple microphone pair results, the multi-channel cross-correlation (MCCC) method, presented in [34], is adapted to the joint DOA and pitch estimator, leading to a robustness improvement especially for noisy conditions.

This paper is structured as follows: In Section 2, we introduce the core algorithm for joint DOA and pitch estimation and describe each of the proposed extensions. In Section 3, the core algorithm and its extensions are evaluated for different amounts of reverberation and signal-to-noise ratios (SNRs). Finally, the paper concludes with the most relevant findings from the proposed extensions in Section 4.

## 2 Algorithm

### 2.1 Scenario and notation

*Q*speech sources are recorded using

*M*microphones in a noisy and reverberant environment. The

*i*th microphone signal

*y*

_{ i }[

*k*], with

*k*the discrete time index, is first transformed to the frequency domain using the short-time Fourier transform (STFT), i.e.,

*n*=1…

*N*and frame index

*λ*. The STFT spectra can be modeled as

_{ i }[

*n*,

*λ*]=[h

_{i 1}[

*n*,

*λ*],…,h

_{ iQ }[

*n*,

*λ*]]

^{T}denotes the acoustic transfer functions between the speech sources s [

*n*,

*λ*]=[s

_{1}[

*n*,

*λ*],…,s

_{ Q }[

*n*,

*λ*]]

^{T}and the

*i*th microphone, and x

_{ i }[

*n*,

*λ*] and v

_{ i }[

*n*,

*λ*] represent the speech and noise components in the

*i*th microphone signal, respectively. The superscript T denotes the transpose operation. Each acoustic transfer function h

_{ iq }[

*n*,

*λ*] can be expressed as

where *A*_{
iq
} [*n*,*λ*] and *ψ*_{
iq
} [*n*,*λ*] represent the amplitude and the phase of the acoustic transfer function, respectively.

_{ i }[

*n*,

*λ*] is applied, in order to improve multi-speaker detection, i.e.,

*g*indicates the frequency group number, which results in

*G*(partially overlapping) spectra. We used a gammatone-like weighting function g

^{(g)}[

*n*] as depicted in Figure 2.

*i*th and the

*ℓ*th microphone is computed for each subgroup

*g*, where E{·} denotes the expectation operator, and complex conjugate terms are marked by the operator (·)

^{∗}. In practice, the CPSD is estimated using a recursive smoothing procedure corresponding to a first-order low-pass filter [35], i.e.,

*α*<1 is a smoothing factor. Please note that in our case, the CPSD calculation in Equation 7 is performed in

*G*subspectra. Afterwards, the CPSDs are normalized by the maximum of each subspectrum and recombined, i.e.,

where max*n*{·} denotes the maximum operator over index *n*. The normalization of each subspectrum in Equation 8 attempts to emphasize all speech source components in the recombined representation, as described in [24]. This is because in multi-speaker scenarios, harmonic speech sources have a different influence on the subspectra, and the narrowband CPSD ${\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}^{\phantom{\rule{0.3em}{0ex}}\left(g\right)}\phantom{\rule{0.3em}{0ex}}\left[n,\lambda \right]$ may be dominated by different signal components.

A CPSD-based voice activity detection (VAD) [36] is used to determine speech segments. Only the time frames in which voice activity has been detected are considered in the following processing. Please note that in the remainder of this paper, we will omit the frame index *λ* for simplification where it is not needed.

### 2.2 Joint DOA and pitch estimation

_{1}[

*n*] impinging with DOA

*φ*on a uniform linear array (ULA), as shown in Figure 3a,b, the relationship between the

*i*th and

*l*th microphone signal is equal to

*ψ*

_{ i ℓ }describes the phase, depending on the center frequency

*f*

_{ n }at frequency index

*n*, the distance

*d*

_{ i ℓ }between microphones

*i*and

*ℓ*, and the speed of sound

*c*. Figure 3b depicts the definition of the DOA relative to the microphone array used throughout this paper. Without additional noise, the CPSD can then be understood as

*f*

_{0}(pitch) and multiple harmonics. We use a harmonic sieve in order to estimate the pitch of the speech signal. This is shown in Figure 4, where the underlying concept of a harmonic sieve is presented, assuming different pitch values up to the fourth harmonic. The indices of the analyzed frequency bins of the harmonic sieve are defined as

where *p* denotes the harmonic, *N* is the frame size, and *f*_{s} is the sampling frequency. Only signal components corresponding to the harmonic sieve will be considered for the estimation. The harmonic sieve is computed for all values in the considered pitch range. For the exemplary harmonic sieve in Figure 4, the third example (*f*_{0}=200 Hz) would result in the best estimate, since the pitch of the signal and the harmonic sieve match. In [22], two different types of harmonic sieves are proposed, either based on cross-correlation or based on the CPSD. In this paper, we will only consider the CPSD-based version.

*ψ*

_{ i ℓ }[

*n*] of the CPSD. To this end, the harmonic sieve is applied to the recombined CPSD in Equation 8, where the amplitude $\left|{\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}\right[\phantom{\rule{0.3em}{0ex}}n\left]\phantom{\rule{0.3em}{0ex}}\right|$ and the phase

*ψ*

_{ i ℓ }[

*n*] are treated differently to obtain the 2D DOA/pitch pattern

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}) as follows:

*f*

_{0}and DOA

*φ*. The sum is taken over the

*P*discrete frequency bins

*n*

_{ p }belonging to the harmonic sieve. The amplitude $\left|{\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]\right|$ encodes pitch information due to the harmonic multiples of

*f*

_{0}, whereas DOA information is encoded in the phase ${\widehat{\psi}}_{\mathit{\text{i}}\ell}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$. The result for all considered combinations of pitch values

*f*

_{0}and DOA values

*φ*are stored in the 2D pattern

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}). For computational efficiency, the values

*n*

_{ p }and ${\psi}_{\mathit{\text{i}}\ell}^{0}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$ can be calculated beforehand and stored in look-up tables. Figure 5 shows the magnitude and phase spectrum of the harmonic sieve filter for a speech signal. The example depicts the case in which the harmonic sieve fits to the pitch of the speaker.

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}), which are all real-valued, even, and 2

*π*periodic functions [22]. These transforms increase the impact of the phase weighting on the harmonic sieve (cf. Equation 13). The transform used in this contribution is the one proposed in [22], i.e.,

*χ*, we use the mismatch between ${\psi}_{\mathit{\text{i}}\ell}^{0}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$ and ${\widehat{\psi}}_{\mathit{\text{i}}\ell}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$ as stated in Equation 13, where the parameter 0<

*β*≤1 affects the width of the preferred direction. A small mismatch from 0 or a multiple of 2

*π*causes a large weighting factor. Accordingly, a large mismatch in

*χ*leads to a small weighting factor. Hence, if the pair

*φ*,

*f*

_{0}corresponds to a source, the amplitude $\left|{\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]\right|$ is weighted more. Figure 6 depicts the case in which ${\psi}_{\mathit{\text{i}}\ell}^{0}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$ corresponds to the measured phase ${\widehat{\psi}}_{\mathit{\text{i}}\ell}\phantom{\rule{0.3em}{0ex}}\left[{n}_{p}\right]$, and the transform T{·} is large for the analyzed frequency bins (marked by vertical dashed lines).

A cepstral weighting (cf. Figure 1) of the 2D pattern *ρ*_{
i
ℓ
}(*φ*,*f*_{0}), based on the cepstrum of the cross-correlation, was proposed in [23] to further increase the pitch estimation for disturbed input signals. The cepstrum is computed on the inverse STFT of the logarithm of the amplitude of the spectrum y_{
i
}[ *n*]. This transform leads to an additive representation of the signal components rather than a multiplicative one in the superimposed spectrum [33]. Thus, the so-called quefrency [35] for a dominant peak can be interpreted as a pitch candidate and the pitch relevant part of the cepstrum can be used as a weighting function.

*ρ*(

*φ*,

*f*

_{0}), combined of DOA and pitch estimate. The particle filter tries to represent an unknown probability function by using a sequential Monte Carlo simulation with a set of particles and respective probabilities. The particles

*ν*

^{ u }[

*λ*] for frame

*λ*incorporate the DOA

*φ*

^{ u }[

*λ*], angular velocity

*ω*

^{ u }[

*λ*], and pitch ${f}_{0}^{u}\left[\phantom{\rule{0.3em}{0ex}}\lambda \right]$, i.e.,

where *U* denotes the total number of particles.

*ν*

^{ u }[

*λ*] has a weight

*ξ*

^{ u }representing its probability. The evolution of the particles can be described in two stages. First, the state of a particle is predicted using the particle

*ν*

^{ u }[

*λ*−1] from the previous frame, taking into account possible physical restrictions. The pitch change is described using

*r*is a Gaussian distributed random variable, and

*β*

_{ f }is the pitch shift prediction value. In addition, it is assumed that the pitch only changes within a certain range. The DOA change is described using the so-called

*Langevin Model*[37], i.e.,

*β*

_{ φ }is the DOA shift prediction value. In the second stage, we use the 2D pattern

*ρ*(

*φ*,

*f*

_{0}) as a pseudo-likelihood function to determine the weights

*ξ*

^{ u }, i.e.,

*λ*is obtained by summing all weighted particles, i.e.,

To avoid the so-called degeneracy problem, we use the systematic resampling approach, as proposed in [38], and an additional module for removal and addition of particles, as proposed in [26]. The advantages of a particle filter compared to a simple maximum search is based on its inherent tracking capabilities and its robustness against reverberation [37]. This is because in adverse conditions, the 2D pattern *ρ*(*φ*,*f*_{0}) does not exhibit a clear main peak at the source positions, but instead a fuzzy sometimes biased area with multiple peaks is observable. The particle filter can be considered as a self-adapting smoothing function of the estimate due to the predicted source behavior and the imposed physical restrictions of this behavior.

### 2.3 Methods to increase the robustness

For a single speaker scenario and clean speech recordings, the basic DOA and pitch estimation algorithm in [23] performs quite well. However, its performance decreases in noisy and reverberant conditions as well as in multi-speaker scenarios. Different extensions have been proposed in [23]–[27] to increase the robustness of the algorithm in various aspects. The above stated subgrouping of the spectra (cf. Equation 5) as well as the already mentioned cepstral weighing [23], both part of the core algorithm and discussed in Section 2.2, are two of these extensions.

In the following sections, we will explain three novel extensions, namely, a spectral comb filter to better cope with concurrent speakers, a generalized cross-correlation (GCC)-phase transform (PHAT) weighting function to improve the DOA estimation accuracy, and a multi-channel cross-correlation approach to improve the robustness against noise and reverberation. The order of the extensions corresponds to their occurrence in the algorithm, cf. Figure 1.

#### 2.3.1 Spectral comb filter

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}). Assuming the number of sources

*Q*is known, we propose to introduce a comb filter

*γ*[

*n*] in order to suppress components of the CPSD ${\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}\left[\phantom{\rule{0.3em}{0ex}}n\right]$ corresponding to already estimated sources, i.e.,

*β*

_{ c }indicates the width of one tooth of the comb filter, and

*P*denotes the number of teeth in the comb filter, which is equal to the number of considered harmonics in Equation 12. The comb filter

*γ*[

*n*] only depends on already estimated pitch values ${\widehat{f\phantom{\rule{0.3em}{0ex}}}}_{\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}0}$, i.e.,

Using estimated pitch values ${\widehat{f\phantom{\rule{0.3em}{0ex}}}}_{\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}0}$, the spectral comb filter is build to suppress the influence of the already estimated speech sources in the CPSD; this leads to a more robust estimation of the remaining speech sources. If the concurrent sources are not yet estimated in the current frame, the pitch estimate from the previous timeframe *λ*−1 is used. Accordingly, if there is no previous estimate available, the very first pitch estimate is determined using the unmodified $\left|{\widehat{\mathsf{\Phi}}}_{\mathit{\text{i}}\ell}\right[\phantom{\rule{0.3em}{0ex}}n\left]\phantom{\rule{0.3em}{0ex}}\right|$ in Equation 13.

#### 2.3.2 GCC-PHAT weighting

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}) exhibits a wide spread of the peaks with regard to the DOA

*φ*. Similar to the cepstral weighting, which aims to improve the pitch estimation, we propose a second weighting function

*w*

_{ i ℓ }(

*φ*) which aims to improve the DOA estimation accuracy. This extension is derived from the GCC-PHAT algorithm [3], not used as a DOA estimator itself, but only as a weighting function of the 2D pattern

*ρ*

_{ i ℓ }(

*φ*,

*f*

_{0}), i.e.,

*i*and

*ℓ*using the phase transform PHAT weighting [3]. The weighting function

*w*

_{ i ℓ }(

*φ*) can be interpreted as a warped extract of the cross-correlation with respect to the DOA

*φ*and the microphone distance. In Figure 8, the upper graph depicts an example of a complete GCC-PHAT, whereas the lower graph only shows the relevant part for the DOA estimation, which is used as a weighting function.

Please note that in [25], a different GCC-PHAT extension was proposed, in which the central part of the unweighted cross-correlation is replaced with the GCC-PHAT weighted cross-correlation. Afterwards, in contrast to the GCC-PHAT weighing proposed here, a time-domain-based harmonic sieve is applied to the cross-correlation to obtain the 2D pattern *ρ*_{
i
ℓ
}(*φ*,*f*_{0}).

#### 2.3.3 Multi-channel cross-correlation

*i*and

*ℓ*. An intuitive approach to combine multiple microphone pairs is the arithmetic mean of all 2D pattern, as already performed in [22]. However, averaging is sensitive to microphone malfunctions and mutual cancelation of opposite erroneous estimates. Therefore, we introduce a more sophisticated method based on the multi-channel cross-correlation (MCCC) [34], which exploits the redundancy among multiple microphones pairs and can be understood as the generalized multi-channel extension of the cross-correlation. We adapted the MCCC to the joint DOA and pitch estimation problem, in order to generate an overall 2D pattern using multiple microphone pairs. First, a

*M*×

*M*matrix P(

*φ*,

*f*

_{0}) with the 2D pattern of all microphone pairs is constructed, i.e.,

*ρ*

_{ il }(

*φ*,

*f*

_{0})=

*ρ*

_{ li }(

*φ*,

*f*

_{0}). Similarly to [34], the determinant det(P(

*φ*,

*f*

_{0})) of this matrix is subsequently used to define the overall 2D pattern, i.e.,

Although it has been shown in [34] that the MCCC always lies between 0 and 1, this does not hold anymore for *ρ*(*φ*,*f*_{0}) defined in Equation 32.

The adaptation of the MCCC algorithm shows two advantages compared to the arithmetic mean. Firstly, it is robust against malfunctions of single microphones. In case of defective microphones, only the remaining microphones are taken into account for the estimation. Secondly, if two microphone signals, highly or perfectly, match (with regard to the considered pitch and DOA combination), the overall result becomes 1, independent of the remaining microphones and opposite erroneous estimates no longer cancel themselves.

## 3 Evaluation

We have conducted experimental evaluations for different acoustic conditions and scenarios. Three different scenarios with increasing complexity are evaluated. In Scenario 1, two simultaneous speakers at fixed positions are simulated. In Scenario 2, the two speakers move stepwise while speaking. In the most difficult Scenario 3, the two speakers move stepwise on intersecting pathways. Measured and simulated room impulse responses (RIRs) are used to generate the microphone signals. Reverberation times RT_{60} ranging from 0 to 560 ms, SNRs from 0 to 20 dB, and noise free simulations (SNR=*∞*) are used. A performance comparison between the core algorithm discussed in Section 2.2 and the extensions proposed in Section 2.3 will be presented in terms of DOA estimation hit rate *A*_{
φ
} and pitch estimation hit rate *A*_{
f
}, as well as root-mean-square error (RMSE) of the DOA estimates.

A comparison with other state-of-the art joint DOA and pitch estimators (cf. Section 1) was not conducted since those algorithms assume single-source scenarios and do not support estimation of multiple sources without introducing further extensions which is beyond the scope of this paper.

### 3.1 Setup and performance measures

*M*=6 microphones (inter-microphone distance 0.22 m), resulting in 15 microphone pairs. A loudspeaker was used as signal source at nine different positions with a distance of approximately 3.3 m to the microphones at a similar height of 1.21 m to the microphones. The distance between the loudspeaker positions was 0.5 m. The real RIRs were measured at a sampling rate of 48 kHz using the sine sweep method [39]. The reverberation time of the conference room is approximately 560 ms with a direct-to-reverberant ratio (DRR) of 6.2 dB.

To investigate the performance for different reverberation times, we used simulated RIRs that were generated with the image method [40],[41]. The same relative microphone and loudspeaker positions were used, but inside a simulated rectangular room of size *l*=4.6 m×*w*=5.1 m×*h*=2.5 m. Reverberation times of RT_{60}={0,100,250, and 560 ms} with direct-to-reverberant ratios of DRR={*∞*,9.1,2.5, and −3.6 dB} were simulated.

The clean microphone signals were generated by convolving the measured or simulated RIRs with clean speech recordings which consisted of male and female speech in German and English. Uncorrelated speech-shaped noise was used as interference signal, played back from all loudspeakers simultaneously. Speech and noise recordings were mixed at six different broadband SNR values (measured at the first microphone) ranging from −5 to 20 dB.

Only the time frames labeled to contain active speech, determined using a VAD [36], are considered for the joint DOA and pitch estimation. These time frames are not further distinguished in voiced or unvoiced speech, assuming the most dominant part of speech is voiced speech.

For the STFT processing, the frame size was set to 85 ms (4,096 samples at 48 kHz sampling rate) using a von Hann window with an overlap of 50*%*. The resulting spectrum was subdivided in *G*=64 partly overlapping gammatone-like weighted subspectra. It should be noted that the choice of the frame size is a trade-off between frequency resolution of the harmonic sieve (cf. Equation 12) and tracking capability of the particle filter (cf. Equations 18 and 20).

The smoothing parameter for the CPSD estimation in Equation 7 was set to *α*=0.1, which is chosen quite low to better deal with simultaneous speech sources. The number of considered harmonics in Equation 12 was set to *P*=5. In practice, the number of harmonics *P* is unknown or changes over time and has to be estimated [18]–[20],[32]. The parameter *β* for the phase transform in Equation 16 was set to *β*=0.2. The teeth width of the proposed spectral comb filter extension in Equation 27 was set to *β*_{
c
}=1.

In order to generate the 2D pattern *ρ*(*φ*,*f*_{0}) in Equation 13, the DOA values were analyzed from 0° to 180° with an interval of 1°, where 90° is perpendicular to the microphone axis (cf. Figure 3), and pitch frequencies were analyzed from 70 to 280 Hz with an interval of 1 Hz. Due to the test setup from Figure 9, only the estimates in front of the array are considered to be valid source positions.

For the particle filter, we used *U*=50 particles per source to simulate and track the source motion over time, where the steady-state angular velocity was set to $\stackrel{\u0304}{\omega}=1$ rad/s; for the DOA shift prediction value, we used *β*_{
φ
}=10 s^{−1}, and for the pitch shift prediction we used *β*_{
f
}=5 Hz/s.

The resulting performance was measured in terms of hit rate *A*_{
φ
} (DOA) and *A*_{
f
} (pitch) for all processed time frames with a fault tolerance of Δ_{
φ
}=±10° and Δ_{
f
}=±10 Hz compared to the true source characteristics. Results with a smaller tolerance interval, i.e., Δ_{
φ
}=±5° and Δ_{
f
}=±5 Hz, have also been calculated, which lead to an overall reduced hit rate, but showing the same performance comparison between the algorithms under test. Although, it is known that beamformers can be designed to have a more narrow beam width, a tolerance interval of Δ_{
φ
}=±10° and Δ_{
f
}=±10 Hz allows for more robust beamformers in case of erroneous DOA estimates.

Please note that the exact pitch of real speech signals, required to calculate the hit rate *A*_{
f
}, is unknown and can only be estimated. We used the overall mean of the PEFAC pitch estimate [17] of the clean speech signal as ground-truth pitch.

#### 3.1.1 Scenario 1: two speech sources at fixed positions

*A*

_{ φ }and

*A*

_{ f }separately. We chose a scenario where two persons (male and female) were simultaneously speaking at fixed positions. The signals were about 5 s long, wherein each speaker is pronouncing one sentence. These signals were processed with different extensions enabled, resulting in five different setups shown in Table 1.

**Setup specification of used extensions**

Setup | Specification |
---|---|

I | Core algorithm |

II | Core algorithm and spectral comb filter |

III | Core algorithm and spectral comb filter and GCC-PHAT weighting |

IV | Core algorithm and spectral comb filter and MCCC |

V | Core algorithm and spectral comb filter and GCC-PHAT weighting |

and MCCC |

_{60}=0 and 560 ms. The results shown in Figure 10 are separated into DOA and pitch results for every source separately.

As seen from Figure 10, the core algorithm in Setup I performs moderately at SNR=*∞* and in an anechoic environment, but deteriorates fast in adverse conditions for both DOA and pitch estimation. Setup I seems to be particularly susceptible to reverberation.

With the spectral comb filter activated in Setup II, the two sources are estimated equally good for the scenarios without reverberation (top panel in Figure 10). Unfortunately, there is no improvement observable for the scenarios with RT_{60}=560 ms (bottom panel in Figure 10). Nevertheless, if the spectral comb filter is missing, as in Setup I, we can see that the algorithm preferably estimates the dominant source. Hence, in our implementation, this filter is beneficial for tracking of two sources simultaneously. Considering that we are exploring multi-source localization, in all following scenarios, the spectral comb filter will be a ctivated using Setups II to V.

Using Setup III, focusing on the GCC-PHAT weighting as our second extension, we can observe that especially the DOA estimate improves considerably in all four SNR and RT_{60} combinations, compared to Setup I. In comparison to Setups I and II, no substantial difference in the pitch estimation can be identified.

In case of low reverberation, the MCCC extension (Setup IV) also improves the DOA estimation compared to Setup I, but deteriorates strongly with larger reverberation times. The simulation results of Setup V, in which all proposed extensions are enabled, show a good overall performance for all different acoustic conditions. It seems that the GCC-PHAT weighting has the largest influence in terms of DOA estimation, in that the DOA hit rates *A*_{
φ
} of Setup III are equal or better than those of Setup V. However, especially for RT_{60}=560 ms and SNR=15 dB, Setup V shows the best hit rate compared to all other setups.

At an SNR of 15 dB and a reverberation time RT_{60} of 560 ms, we obtained DOA hit rates of *A*_{
φ
}=72*%* with Setup V, compared to DOA hit rates of 5% obtained with Setup II.

#### 3.1.2 Scenario 2: two stepwise moving speech sources

Figure 12(a) shows the results for several SNR conditions from 20 to −5 dB without reverberation. It is apparent that the proposed algorithm (Setup V) outperforms Setup II for all conditions, resulting in mean hit rates ${\u0100}_{\phi}=87.1\%$ for Setup V over all SNR (bottom panel in column (a)) and 55.3% for Setup II (top panel in column (a)). The proposed algorithm (Setup V) results in high hit rates even at low SNR.

_{60}=560 ms and varying SNRs. For both setups, II and V, the hit rate decreases compared to RT

_{60}=560 ms. However, the proposed algorithm (Setup V) still outperforms Setup II by 25.7

*%*on average for all conditions. Figure 12(c) shows the results for different reverberation times without noise (SNR =

*∞*). Comparing the mean hit rates ${\u0100}_{\phi}$, the proposed algorithm (Setup V) achieves a hit rate of 87.7

*%*and surpasses the core algorithm with the spectral comb filter (Setup II) by 37

*%*. Additionally, Figure 13 shows the RMSEs of the DOA estimates for the same setups (II and V) and conditions as in Figure 12.

For RT_{60}=0 ms (Figure 13(a)), Setup II achieves a mean RMSE of 15.7°, whereas the mean RMSE of Setup V decreases to 8.5°. For RT_{60}=560 ms (Figure 13(b)), the mean RMSE for both setups increases to 19.6° for Setup II and to 15.9° for Setup V. For different reverberation times (Figure 13(c)), Setup V achieves a mean RMSE of 7.9°), which is 10° better than the mean RMSE of Setup II.

_{60}=560 ms. It can be observed that the proposed algorithm (Setup V) achieves less scattered estimates than Setup II.

The hit rates *A*_{
φ
} in Scenario 2 are considerably higher than in Scenario 1, especially for the core algorithm with the spectral comb filter (Setup II). This is because wrong DOA estimates tend to be located in the frontal direction (around *φ*=90°), as can be seen in Figure 14a. Due to the scenario definition, in which the sources move towards *φ*=90°, it occurred that erroneous estimates are actually counted as correct hits, e.g., for time frames around *λ*=400, which does not necessarily indicate a more reliable estimation but still increases the *A*_{
φ
} value. At an SNR of 15 dB and a reverberation time RT_{60} of 560 ms, we obtained DOA hit rates of *A*_{
φ
}=73*%* with Setup V, compares to DOA hit rates of *A*_{
φ
}=40*%* obtained with Setup II.

#### 3.1.3 Scenario 3: two intersecting speech sources

The proposed algorithm is intended to be capable of tracking stepwise intersecting sources by using the particle filter. Therefore, in the third scenario, we considered two speakers on crossing paths while speaking. The intersecting source movement can be considered as the most ambitious, but also the most realistic scenario in this evaluation. The movement of the two concurrent speakers was, again, simulated with a stepwise switching between subsequent loudspeaker positions. Hence, at a certain position, the two speech signals were emitted by a single loudspeaker. Similar to Scenario 2, we performed three experiments in which either the reverberation time RT_{60} or the SNR was kept constant and the other value varied over the range of interest.

_{60}=560 ms (cf. Figure 15(b)) is 54.6

*%*for Setup V and only 34.5

*%*for Setup II.

_{60}=0 ms), 17° (RT

_{60}=560 ms), and 17.2° (SNR=

*∞*), but Setup V achieves better mean RMSE of 11.3°, 15.6°, and 10.4°, respectively.

*λ*for an SNR of 15–dB and a reverberation time of 560 ms. The corresponding DOA hit rates are

*A*

_{ φ }=63.2

*%*for Setup V and

*A*

_{ φ }=36.6

*%*for Setup II.

Due to the spectral comb filter, it is impossible for the proposed algorithm to exactly estimate two sources coming from a single direction. Nevertheless, Figure 17 shows that the proposed algorithm is still capable to estimate the movement of intersecting speakers. In particular, when the speakers are crossing (at frames 400<*λ*<550), it can be seen that the proposed algorithm estimates the sources to be in close proximity to each other; however, they never overlap.

## 4 Conclusion

In this paper, several extensions to the core joint DOA and pitch estimation algorithm were proposed, which were shown to increase the robustness and hit rate even for difficult acoustic situations. In particular, the generalized cross-correlation GCC-PHAT weighting achieves a considerable improvement of the DOA estimation accuracy. To cope with multi-speaker situations, the spectral comb filter was proposed, which achieves that the proposed method is less unaffected by dominant sources and more or less estimates the DOA and pitch of all sources to the same extent. Furthermore, the MCCC extension improves the robustness and accuracy and, in addition, makes the algorithm less sensitive to microphone malfunctions. Even intersecting sources can be tracked by usage of a particle filter.

At an SNR of 15 dB and a reverberation time RT_{60} of 560 ms, the proposed algorithm (Setup V) achieved DOA hit rates of *A*_{
φ
}=72*%*,73*%*, and 63.2*%* for two fixed, moving, and intersecting speech sources, respectively, compared to *A*_{
φ
}=5*%*,40*%*, and 36.6*%* achieved with the core algorithm including the spectral comb filter (Setup II).

## Declarations

### Acknowledgements

This work was partly supported by the Research Unit FOR 1732 ‘Individualized Hearing Acoustics’, funded by the German Research Foundation (DFG), and EcoShopping ’Energy efficient & cost competitive retrofitting solutions for shopping buildings’ grant no. 609180, funded by the European Commission.

## Authors’ Affiliations

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