广义相关法在时间延迟估计中的应用
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"这篇论文是关于广义互相关方法在时延估计中的应用，发表在1976年的IEEE Transactions on Acoustics, Speech, and Signal Processing期刊上。作者通过对比分析，探讨了在不同输入信号（如高斯噪声和电视信号）下，小型计算机的性能标准。此外，论文还讨论了有限位宽对数字滤波器精度的影响，并介绍了自适应量化器的理论。文章提出了一种最大似然（ML）估计器，用于在两个空间上分离的传感器接收到不相关噪声的信号时确定时间延迟。该ML估计器由一对预滤波器和一个交叉相关器组成，当相关器达到最大值时的时间参数即为时延估计。作者将ML估计器与其他方法进行了比较，深入研究其性能优势和潜在应用场景。"
这篇论文的核心知识点包括：
1. **广义互相关方法**：这是一种信号处理技术，用于计算两个信号之间的相似性，尤其在存在噪声或非理想条件下的时间对齐。在本论文中，广义互相关被应用于时延估计，帮助确定信号到达不同传感器的时间差。
2. **时延估计**：在多传感器系统中，精确地估计信号传播的时间差对于定位、同步和信号处理至关重要。本文提出了一种基于最大似然估计的时延估计算法，它能在有噪声环境下提供较好的性能。
3. **最大似然估计器**：这是统计学中的一种常见估计方法，旨在找到最可能生成观测数据的参数值。在本文中，这个估计器由预滤波器和交叉相关器构成，通过寻找相关函数的最大值来估计时间延迟。
4. **预滤波器**：预处理信号的滤波器，可以去除噪声，改善信号质量，以便更准确地估计时延。
5. **交叉相关器**：计算两个信号之间延迟的相关性的设备，用于找到使两个信号相关程度最大的时间点，即时延估计。
6. **不相关噪声**：在信号传输过程中引入的随机干扰，与原始信号没有固定的关系。在本文中，考虑的是这种噪声如何影响时延的估计。
7. **数字滤波器**：用于处理数字信号的算法或硬件设备，可以去除噪声，提取信号特征等。论文指出有限的位宽会限制滤波器的精度。
8. **自适应量化器**：一种能够根据输入信号自动调整其量化级别的量化器，常用于提高信号编码效率和减少通信系统的噪声影响。
9. **性能比较**：论文通过对比分析，评估了提出的ML估计器与其他方法在时延估计上的表现，展示了其优越性。
这些知识点不仅反映了信号处理领域的基础理论，还展示了实际应用中解决问题的策略和技术。对于从事声学、语音识别、信号处理以及通信工程等领域研究的学者和工程师来说，这些内容具有很高的参考价值。
320
IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING,
VOL.
ASSP-24, NO.
4,
AUGUST
1976
[7] J.
L.
Butler, “Comparative criteria for minicomputers,”
Instrum.
and computer simulation results
for
Gaussian and television
Technol.,
vol. 17, pp. 67-82, Oct. 1970.
input signals,” Bell
Syst.
Tech.
J.,
vol. 45,
pp.
117-142, Jan.
[8]
B. Liu, “Effect
of
finite word length
on
accuracy
of
digital
1966.
filters-A review,”
IEEE
Trans. Circuit Theory,
vol. CT-18,
[lo]
D.
J.
Goodman and
A.
Gersho, “Theory
of
an adaptive quan-
pp. 670-677, NOV. 1971. tizer,”
IEEE
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Commun.,
vol. COM-22, pp. 1037-1045,
[9] J.
B.
O’Neal, Jr., “Delta modulation quantizing noise analytical
Aug.
1974.
The Generalized Correlation Met
r
of
Time
Abstruct-A
maximum likelihood (ML) estimator is developed for
determining time delay between signals received at
two
spatially sepa-
rated sensors in the presence of uncorrelated noise. This ML estimator
can be realized
as
a pair of receiver prefilters followed by a cross
correlator. The time argument at which the correlator achieves a
maximum is the delay estimate. The ML estimator
is
compared with
several other proposed processors of similar form. Under certain con-
ditions the
ML
estimator is shown
to
be identical
to
one proposed by
Hannan and Thomson
[
101
and MacDonald and Schultheiss
[
2
11
.
Qualitatively, the role
of
the prefiiters is
to
accentuate the signal
passed
to
the correlator at frequencies for which the signal-to-noise
(S/N) ratio is highest and, simultaneously,
to
suppress the noise power.
The same type of prefiitering is provided by the generalized Eckart
fiiter, which maximizes the
S/N
ratio of the conelator output.
For
low
S/N
ratio, the ML estimator is shown
to
be equivalent
to
Eckart
prefiltering.
A
INTRODUCTION
SIGNAL emanating from a remote source and moni-
tored in the presence of noise at two spatially sepa-
rated sensors can be mathematically modeled as
Xl(t>
=
Sl(t)
+n1(t)
(1
a)
x2
(t)
=
as
1
(t
+
0)
+
nz
(t),
(1b)
where
sl(t),
nl(t),
and
nz(t)
are real, jointly stationary ran-
dom processes. Signal
sl(t)
is assumed to be uncorrelated with
noise
n
(t)
and
nz
(t).
There are many applications in which
it
is of interest to esti-
mate the delay
D.
This paper proposes a maximum likelihood
(ML) estimator and compares it with other similar techniques.
While the model of the physical phenomena’ presumes sta-
tionarity, the techniques to be developed herein are usually
employed in slowly varying environments where the character-
Manuscript received July 24, 1975; revised November 21, 1975 and
C.
H.
Knapp is with the Department
of
Electrical Engineering and
G.
C. Carter is with the Naval Underwater Systems Center, New
February 23,1976.
Computer Science, University
of
Connecticut, Storrs,
CT
06268.
London Laboratory, New London, CT 06320.
istics of the signal and noise remain stationary only for finite
observation time
T.
Further, the delay
D
and attenuation
a
may also change slowly. The estimator is, therefore, con-
strained to operate on observations of a finite duration.
Another important consideration
in
estimator design is the
available amount of
a
priori
knowledge of the signal and
noise statistics.
In
many problems, this information is negli-
gible. For example, in passive detection, unlike the usual
communications problems, the source spectrum is unknown
or only known approximately.
One common method of determining the time delayD and,
hence, the arrival angle relative to the sensor axis
[l]
is to
compute the cross correlation function
where
E
denotes expectation. The argument
7
that maxi-
mizes
(2)
provides an estimate of delay. Because of the finite
observation time, however,
RxIx,(7)
can only be estimated.
For example, for ergodic processes
(2,
p.
3271
,
an estimate
of the cross correlation is given by
where
T
represents the observation inter@. In order to im-
prove the accuracy of the delay estimate
D,
it is desirable to
prefdter
xl(t)
and
xz(t)
prior to the integration in
(3).
As
shown
in
Fig.
1,
xi
may be fdtered through
Hi
to yieldyi for
i
=
1,
2.
The resultant
yi
are multiplied, integrated, and
squared for a range of time shifts,
T,
until the peak is obtained.
The time shift causing the peak
is
an estimate of the true
d,elay
D.
When the fdters
HI
(f)
=
If2
(f)
=
1,
Vf,
the estimate
D
is simply the abscissa value at which the cross-correlation
function peaks. This paper provides for a generalized correla-
tion through the introduction of the fdters
H1
(f)
and
Hz
(f)
which, when properly selected, facilitate the estimation of
delay.
The cross correlation between
xl(t)
and
xZ(t)
is related to
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