基于仿射算法的分布式估计算法研究

分布式算法

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"分布式估计算法基于仿射算法的研究" 分布式估计算法是指在分布式系统中实现参数估计算法的方法。该方法可以应用于各个领域，如信号处理、图像处理、机器学习等。分布式估计算法的优点在于可以充分利用分布式系统的计算资源，提高计算速度和准确性。分布式估计算法基于仿射算法的研究是指使用仿射算法来实现分布式估计算法。仿射算法是一种常用的优化算法，可以用来解决非线性最小二乘问题。在分布式估计算法中，仿射算法可以用来更新每个节点的参数，从而实现分布式估计算法。本文提出了一种基于仿射算法的分布式估计算法，该算法可以在 adaptive incremental network 中实现分布式估计算法。该算法可以克服传统的 least-mean-square (LMS) 类型的分布式自适应滤波器的收敛性问题，实现更快的收敛速度和更好的稳态性能。在该算法中，每个节点都可以独立地更新自己的参数，而不需要与其他节点进行通信。这种方式可以大大提高计算速度和准确性。同时，该算法也可以很好地适应 colored inputs，即输入信号具有色彩特性的情况。在该文中，作者们还提出了一个基于 weighted spatial-temporal energy conservation relation 的分析方法来分析算法的暂态和稳态性能。该方法可以很好地描述算法的收敛过程和稳态性能。通过计算机仿真，作者们验证了该算法的有效性。结果表明，该算法可以提供更快的收敛速度和更好的稳态性能，相比于 LMS 基础的方案。此外，该算法还可以实现可接受的 misadjustment 性能。本文提出的分布式估计算法基于仿射算法的研究可以为分布式系统的参数估计提供了一种有效的方法。该方法可以应用于各个领域，提高计算速度和准确性。知识点： 1. 分布式估计算法是指在分布式系统中实现参数估计算法的方法。 2. 仿射算法是一种常用的优化算法，可以用来解决非线性最小二乘问题。 3. 分布式估计算法基于仿射算法的研究可以克服传统的 LMS 类型的分布式自适应滤波器的收敛性问题。 4. 该算法可以在 adaptive incremental network 中实现分布式估计算法。 5. 该算法可以实现更快的收敛速度和更好的稳态性能。 6. 该算法可以很好地适应 colored inputs，即输入信号具有色彩特性的情况。 7. Weighted spatial-temporal energy conservation relation 可以用来分析算法的暂态和稳态性能。 8. 该算法可以提供更快的收敛速度和更好的稳态性能，相比于 LMS 基础的方案。 9. 该算法还可以实现可接受的 misadjustment 性能。本文提出的分布式估计算法基于仿射算法的研究可以为分布式系统的参数估计提供了一种有效的方法。该方法可以应用于各个领域，提高计算速度和准确性。

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LI et al.: DISTRIBUTED ESTIMATION OVER AN ADAPTIVE INCREMENTAL NETWORK 153

global estimation at time instant . Consider a Newton’s search

based approach to solving (9) for incremental learning within

a distributed network. The optimal tap weight

is estimated

via [17]

(10)

where

, , denotes a regu-

larization parameter with small positive value,

indicates

an appropriately chosen step-size, which is evaluated in

Section III-E, and the scheme is initialized with an

vector

For a practical scheme to realize (10), and utilizing the corre-

lation of the input signal at each node, we replace

by the following sample sliding-window estimates:

(11)

(12)

with

equal to the number of recent regressors of each node

whilst

and denote the corresponding input vector and

desired response at instant time

for the th node. Hence, using

the matrix inversion formula, recursion (10) becomes,

(13)

where the local

block data matrix and 1 data vector

are

(14)

and

is employed to avoid the inversion of a rank deﬁcient ma-

trix

. As such, recursion (13) is the distributed APA

(dAPA) learning algorithm in an incremental network, the op-

eration of which is shown in Fig. 1. At each time instant

, each

node utilizes local data

and received from its

previous node

in the cycle to update the local estimation.

At the end of the cycle, the local estimation

is employed as

the global estimation and the initial local estimation

for the next discrete time instant . The ﬁnal weight vector

shown at the bottom of Fig. 1 can either be used to generate

a ﬁlter output vector term of the form

or the vector

itself can then be used for system identiﬁcation or equaliza-

tion. The pseudo-code implementation of dAPA is described in

Table I. In addition, dAPA has intermediate computational and

memory cost between dLMS and dRLS, for certain regressor

length, which is veriﬁed in the Appendix.

Fig. 1. Data processing of the dAPA algorithm in an incremental network.

TABLE I

SEUDO-CODE IMPLEMENTATION OF D

APA

III. PERFORMANCE ANALYSIS

The convergence behaviors of classical APA-based algo-

rithms are studied in [15]–[19], exploiting arguments based on

a single adaptive ﬁlter. In order to study the performance of the

dAPA algorithm, we extend the weighted energy conservation

approach for the APA-based algorithms of [18], [19] to the

case of a distributed incremental network, which involves both

the space dimension and the time dimension. However, due to

the energy ﬂow across the interconnected ﬁlter, some of the

simpliﬁcations for a single ﬁlter case cannot be adopted. A

set of weighting matrices is particularly chosen to decouple a

set of equations and we evaluate the transient and steady-state

performances at each individual node in terms of mean-square

deviation (MSD), excess mean-square-error (EMSE) and

mean-square error (MSE). The closed-form expressions for

the theoretical results are formed under some simplifying

assumptions described below.

A. Data Model and Assumption

As deﬁned earlier, we use boldface letters as the random

quantities and assume the same model as in [9] to carry out the

performance analysis:

A1) The relation between the unknown system vector

and takes the form:

(15)

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基于仿射算法的分布式估计算法研究

2004_Robust Distributed estimation in sensor networks using the embedded polygons algorithm

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引用Distributed adaptive coverage control algorithm for mobile sensor networks

[11] G P. He, Z W. Wang, Z. Chen. Distributed Collaborative Localization Algorithm of AUV Cluster Based on Adaptive Residual Weight [J].Ship science and technology, 2022, 44(18): 101-1. 请详细解释一下，这个参考文献的格式

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greenplum Redistribute Motion

Robbins-Monro setting

Hadoop Distributed File System

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AWS Global Accelerator

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hbase row key

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