语音信号基频估计：变率粒子滤波器方法
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"本文探讨了使用可变率粒子滤波器在语音信号中进行基本频率估计的方法，这是一种在非线性状态空间模型中追踪动态参数的强大贝叶斯推理方法。"
在语音信号处理领域，基本频率（Fundamental Frequency，通常称为基频）的估计是一个关键任务，对研究者和工业界都具有重要意义。基频对应于声带振动的频率，对于语音识别、情感分析以及语音合成等应用至关重要。传统的基频估计方法包括基于周期性的算法，如cepstrum分析和自相关函数等，但在噪声环境或非稳态语音中可能表现不佳。
粒子滤波器（Particle Filter, PF）作为一种贝叶斯滤波技术，因其在处理非线性和非高斯动态系统中的优秀性能而受到广泛关注。在本研究中，作者Geliang Zhang和Simon Godsill提出了一种基于时间可变源-滤波器（source-filter model）的语音模型，并利用可变率粒子滤波器（Variable Rate Particle Filter, VRPF）来估计语音信号中的基频周期。这种模型考虑了语音生成过程中的时间变化特性，从而提高了估计的准确度。
为了进一步提升性能，作者还实现了一种Rao-Blackwellised可变率粒子滤波器（RBVRPF）。Rao-Blackwell化是一种优化粒子滤波器的方法，它通过减少状态空间的维度来提高效率并降低计算复杂性。通过与现有的最先进的基频估计算法——YIN算法进行对比，模拟结果显示，即使在强背景噪声环境下，VRPF和RBVRPF也能提供更精确的基频估计。
本文的索引术语包括：可变率粒子滤波器、基频估计以及Rao-Blackwell化。这些关键词强调了该研究的核心技术及其在解决语音信号处理挑战中的应用。通过VRPF和RBVRPF的引入，研究为在复杂环境下的基频估计提供了新的解决方案，对提高语音处理系统的性能有着积极的推动作用。
892 IEEE/ACM TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 24, NO. 5, MAY 2016
Algorithm 1.
Goal: Tracking T
1:n
t
which are contained in x
1:t
,giveny
1:t
and T
1
.
1) Initialize {x
(i)
1
}
N
i=1
. Set up all the fixed hyperparame-
ters and {w
(i)
1
}
N
i=1
=
1
N
. To initialize {x
(i)
1
}
N
i=1
,usethe
joint estimation technique based on the first period of
speech data y
1:T
1
, according to (14), see later. Then sam-
ple {s
(i)
1
}
N
i=1
based on a
1
, A
1
, B
1
,T
1
according to (2)
and (5). Set P
(i)
= T
1
.
2) for t =1:t
end
do
a) for i=1:N do
i) Set n
(i)
t
= n
(i)
(t−1)
.
ii) While t>P
(i)
:
A) Add a new pitch period, n
(i)
t
← n
(i)
t
+1.
B) Sample a new pitch period and other
coefficients:
T
(i)
n
t
∼ U(max[T
(i)
n
t−1
− σ
T
,T
low
],
min[T
(i)
n
t−1
+ σ
T
,T
upp
]),
a
n
(i)
t
(i),p
∼N(a
n
(i)
t
−1
(i),p
,σ
2
a,p
),
A
n
(i)
t
(i),k
∼N(A
n
(i)
t
−1
(i),k
,σ
2
A,k
),
B
n
(i)
t
(i),k
∼N(B
n
(i)
t
−1
(i),k
,σ
2
B,k
),
C) Update P
(i)
← P
(i)
+ T
(i)
n
t
.
iii) Sample new signal value: s
t
i
based on
a
n
(i)
t
i,p
,A
n
(i)
t
i,k
,B
n
(i)
t
i,k
,T
(i)
n
(i)
t
as (2) and (5). Now
[x
(i)
1:t
]=[x
(i)
1:t−1
,x
(i)
t
], as defined in (34).
iv) Compute importance weight w
(i)
t
of each
particle:
w
(i)
t
∝ w
(i)
t−1
p(y
t
|s
(i)
t
,σ
G
).
b) end for
c) Renormalize ˜w
(i)
t
=
w
(i)
t
N
i=1
w
(i)
t
, i = 1, 2,...,N.
d) If t = k ∗ BlockSize, where k is a positive integra,
i) Resample {x
(i)
1:t
}
N
i=1
when N
eff
<N/2. N
eff
denotes the effective sample size and is calcu-
lated as N
eff
=1/
N
i=1
˜w
(i)
t
.
ii)
ˆ
T
n
t
=
N
i=1
˜w
(i)
t
T
(i)
n
t
.
3) end for
track them [17]. For example, in the case of modeling input
sources as almost periodic signals, if 20 harmonics are assumed
to be existing in the input source (K =20) and a 11-order AR
model is used (M =11), the number of parameters involved
in the whole model is 2 ∗ K + M +1, which is 52. In order
to estimate a 52-dimensional vector using a moderate number
of particles, for example, 1000 particles, it will be necessary
to have a good initialization method at the beginning of the
algorithm to make the particle filter work.
B. Joint Source-Filter Estimation Method
It has been proposed in [8] that a joint source-filter optimiza-
tion approach can be used to estimate glottal flow using the LF
model of the glottal flow derivative when the input source is
modeled as glottal pulses. It is suggested in our paper that after
some modification on the model used in the input source, this
joint source-filter optimization approach can be also applied
here when the input source is modeled as almost periodic sig-
nals as a joint source-filter estimation technique to initialize the
parameters used in the whole model. Details of how this tech-
nique can be modified to apply when input sources are modeled
as almost periodic signals here are described in Appendix A.
Here we just display the results. If we write the parameters of
the proposed almost periodic source-filter model except for T
n
,
i.e., {a
p
,A
k
,B
k
}
p=1:M, k=0:K
(upper index n
t
omitted here,
see Appendix A), into a vector a, where
a =
a
1
,...,a
M
,A
0
,...,A
K
,B
0
,...,B
K
T
(13)
Then it is possible to jointly estimate the parameters in a using
the following equation:
a = R
−1
p (14)
where
R =
R
1
−R
2
−R
T
2
R
3
(15)
where
R
1
=
⎛
⎜
⎝
C
xx
(1, 1) ... C
xx
(M,1)
.
.
. ...
.
.
.
C
xx
(1,M) ... C
xx
(M,M)
⎞
⎟
⎠
(16)
R
2
=
R
2A
R
2B
(17)
where
R
2A
=
⎛
⎜
⎝
C
0
Ax
(0, 1) ... C
K
Ax
(0, 1)
.
.
. ...
.
.
.
C
0
Ax
(0,M) ... C
K
Ax
(0,M)
,
⎞
⎟
⎠
(18)
and
R
2B
=
⎛
⎜
⎝
C
0
Bx
(0, 1) ... C
K
Bx
(0, 1)
.
.
. ...
.
.
.
C
0
Bx
(0,M) ... C
K
Bx
(0,M)
,
⎞
⎟
⎠
(19)
R
3
=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
C
0,0
CC
(0, 0) ... C
0,2K+2
CC
(0, 0)
C
1,0
CC
(0, 0) ... C
1,2K+2
CC
(0, 0)
.
.
.
.
.
. ...
.
.
.
.
.
.
C
2K,0
CC
(0, 0) ... C
2K,2K+1
CC
(0, 0)
C
2K+1,0
CC
(0, 0) ... C
2K+1,2K+1
CC
(0, 0)
,
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
(20)
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