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CN115290130B - Distributed information estimation method based on multivariate probability quantization - Google Patents

Distributed information estimation method based on multivariate probability quantization Download PDF

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CN115290130B
CN115290130B CN202211229494.1A CN202211229494A CN115290130B CN 115290130 B CN115290130 B CN 115290130B CN 202211229494 A CN202211229494 A CN 202211229494A CN 115290130 B CN115290130 B CN 115290130B
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黄川�
崔曙光
何萌
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Chinese University of Hong Kong Shenzhen
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Abstract

本发明公开了一种基于多元概率量化的分布式信息估计方法，包括以下步骤：S1.构建分布式信息估计场景：包括一个位于无线通信网络中心的融合中心FC和多个分布在无线通信网络边缘的传感器；S2.构建传感器对本地观测数据进行量化的多元概率量化器；S3.优化多元量化概率函数的设计参数

Figure 493582DEST_PATH_IMAGE001
；S4.融合中心FC设计量化融合估计器并进行优化得到最优估计函数
Figure 495036DEST_PATH_IMAGE002
；S5.基于
Figure 910580DEST_PATH_IMAGE001
和
Figure 48300DEST_PATH_IMAGE002
的多元概率量化分布式信息估计。本发明能够适应量化结果存在多元的情况，并保持较高的估计性能。

Figure 202211229494

The invention discloses a distributed information estimation method based on multivariate probability quantification, which includes the following steps: S1. Construct a distributed information estimation scene: including a fusion center FC located at the center of the wireless communication network and multiple distributed at the edge of the wireless communication network S2. Construct a multivariate probability quantizer for quantifying the local observation data by the sensor; S3. Optimize the design parameters of the multivariate quantization probability function

Figure 493582DEST_PATH_IMAGE001
; S4. The fusion center FC designs a quantized fusion estimator and optimizes it to obtain the optimal estimation function
Figure 495036DEST_PATH_IMAGE002
; S5. Based on
Figure 910580DEST_PATH_IMAGE001
and
Figure 48300DEST_PATH_IMAGE002
Multivariate Probability Quantification for Distributed Information Estimation. The present invention can adapt to the situation that there are multiple quantization results, and maintains high estimation performance.

Figure 202211229494

Description

一种基于多元概率量化的分布式信息估计方法A Distributed Information Estimation Method Based on Multivariate Probability Quantification

技术领域technical field

本发明涉及分布式信息估计，特别是涉及一种基于多元概率量化的分布式信息估计方法。The invention relates to distributed information estimation, in particular to a distributed information estimation method based on multivariate probability quantization.

背景技术Background technique

基于量化数据的分布式信息估计一直是一个活跃的研究领域。在典型的分布式估计框架中，本地传感器将对原始信息的本地观测数据发送到融合中心。融合中心接收从不同本地传感器发送过来的数据，利用估计算法来估计未知的原始信息。然而，由于带宽/能量限制，传感器上的本地观测数据通常在传输到融合中心之前需要被量化。所有传感器使用相同的量化器是一种被广泛采用的方案，因为它简化了设计问题。Estimation of distributed information from quantitative data has been an active research area. In a typical distributed estimation framework, local sensors send local observations of raw information to a fusion center. The fusion center receives data sent from different local sensors, and uses estimation algorithms to estimate unknown raw information. However, due to bandwidth/energy limitations, local observations on sensors usually need to be quantized before being transmitted to the fusion center. Using the same quantizer for all sensors is a widely adopted solution because it simplifies the design problem.

然而，很多传统技术方案主要考虑了在理想无观测噪声存在的环境下，量化器优化的问题。而对考虑观测噪声条件下的量化器设计缺少进一步的研究。此外，很多关于最优量化器的性能分析及理论，都只考虑了二元量化的情况，即传感器上量化数据的长度被限制在1比特。对于传感器上，将观测数据量化成为多比特数据，即量化结果存在多元可能时的情况，相应的量化器设计方案同样缺少研究。However, many traditional technical solutions mainly consider the problem of quantizer optimization in an ideal environment without observation noise. However, there is a lack of further research on quantizer design under the condition of considering observation noise. In addition, many performance analyzes and theories about optimal quantizers only consider the case of binary quantization, that is, the length of quantized data on the sensor is limited to 1 bit. For the sensor, the observation data is quantized into multi-bit data, that is, when the quantization result has multiple possibilities, the corresponding quantizer design scheme is also lack of research.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足，提供一种基于多元概率量化的分布式信息估计方法，能够适应量化结果存在多元的情况，并保持较高的估计性能。The purpose of the present invention is to overcome the deficiencies of the prior art and provide a distributed information estimation method based on multivariate probability quantization, which can adapt to the situation of multivariate quantification results and maintain high estimation performance.

本发明的目的是通过以下技术方案来实现的：一种基于多元概率量化的分布式信息估计方法，包括以下步骤：The purpose of the present invention is achieved through the following technical solutions: a distributed information estimation method based on multivariate probability quantification, comprising the following steps:

S1.构建分布式信息估计场景：包括一个位于无线通信网络中心的融合中心 FC和多个分布在无线通信网络边缘的传感器；S1. Construct a distributed information estimation scenario: including a fusion center FC located at the center of the wireless communication network and multiple sensors distributed at the edge of the wireless communication network;

每一个传感器都对融合中心需要的原始信息

Figure 100002_DEST_PATH_IMAGE001
进行观测，并得到自己的本地观测数据，对本地的观测数据进行多元概率量化操作，将连续的观测数据转化为能够被用于数字通信的二进制离散数据，并发送给融合中心FC；FC融合中心根据所有传感器发送过来的量化数据对原始信息进行估计；Each sensor has the raw information required by the fusion center
Figure 100002_DEST_PATH_IMAGE001
Make observations and get your own local observation data, perform multiple probability quantification operations on the local observation data, convert continuous observation data into binary discrete data that can be used for digital communication, and send it to the fusion center FC; FC fusion center Estimate raw information based on quantitative data sent from all sensors;

S2.构建传感器对本地观测数据进行量化的多元概率量化器；S2. Construct a multivariate probability quantizer for quantifying local observation data by sensors;

S3.优化多元量化概率函数的设计参数

Figure 100002_DEST_PATH_IMAGE002
；S3. Optimizing the design parameters of the multivariate quantitative probability function
Figure 100002_DEST_PATH_IMAGE002
;

S4.融合中心FC设计量化融合估计器并进行优化得到最优估计函数

Figure 100002_DEST_PATH_IMAGE003
；S4. The fusion center FC designs a quantized fusion estimator and optimizes it to obtain the optimal estimation function
Figure 100002_DEST_PATH_IMAGE003
;

S5.基于

Figure 503964DEST_PATH_IMAGE002
和
Figure 280159DEST_PATH_IMAGE003
的多元概率量化分布式信息估计。S5. Based on
Figure 503964DEST_PATH_IMAGE002
with
Figure 280159DEST_PATH_IMAGE003
Multivariate Probability Quantification for Distributed Information Estimation.

本发明的有益效果是：本发明的多元量化概率方法在网络的总比特数变化的情况下，仍然保持了随总量化比特数近似线性递减的能力，在分布式无线传感器网络中的高效估计性能。The beneficial effects of the present invention are: the multivariate quantization probability method of the present invention still maintains the ability of approximately linear decrease with the total quantization bit number under the condition that the total number of bits of the network changes, and the efficient estimation in the distributed wireless sensor network performance.

附图说明Description of drawings

图1为本发明的方法流程图；Fig. 1 is method flowchart of the present invention;

图2为分布式信息估计场景示意图；Figure 2 is a schematic diagram of a distributed information estimation scenario;

图3为多元概率量化器结构图；Fig. 3 is a structural diagram of a multivariate probability quantizer;

图4为量化函数结构图；Fig. 4 is a quantization function structural diagram;

图5为量化融合估计器结构图；Fig. 5 is the structural diagram of quantitative fusion estimator;

图6为整个网络总量化比特数变化的情况下，网络对原始信息估计的MSE示意图。Fig. 6 is a schematic diagram of the MSE estimated by the network for the original information when the total number of quantized bits of the entire network changes.

具体实施方式detailed description

下面结合附图进一步详细描述本发明的技术方案，但本发明的保护范围不局限于以下所述。The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

针对未来无线通信网络中基于带宽/能量受限的分布式无线传感器的信息估计问题，本发明设计了一种基于多元概率量化的分布式信息估计方案：包括位于传感器上的多元概率量化器设计及相应的多元量化概率函数优化算法；位于融合中心上的量化融合估计器设计及相应的估计函数优化算法。考虑一个分布式无线传感器网络对一个未知原始信息进行估计的一般化场景，网络包含位于网络中心节点的融合中心（fusion center, FC）和分布于网络边缘的不同位置的多个传感器。原始信息可能是网络需求的任意一类数据，由网络具体的需求决定，如常见的定位信息或者是天气信息等。每一个传感器都对原始信息进行观测，并得到自己的本地观测数据，通常在实际环境中由于环境噪声对观测的影响，本地的观测数据与原始信息间存在误差。对于带宽/能量受限的传感器来说，需要先对本地的观测数据进行量化操作，将连续的观测数据转化能够被用于现代数字通信的二进制离散数据，才能顺利发送自己的观测数据给FC。FC只能使用从所有传感器发送过来的量化数据对原始信息进行估计。原始信息估计性能的衡量指标，一般使用原始信息与其估计值的均方误差（mean squared error, MSE），越小的MSE意味着更精确的估计以及越更好的估计性能；Aiming at the problem of information estimation based on distributed wireless sensors with limited bandwidth/energy in future wireless communication networks, the present invention designs a distributed information estimation scheme based on multivariate probability quantization: including the design of multivariate probability quantizers located on sensors and Corresponding optimization algorithm of multivariate quantization probability function; design of quantization fusion estimator located on fusion center and corresponding estimation function optimization algorithm. Consider a generalized scenario where a distributed wireless sensor network estimates an unknown original information. The network includes a fusion center (FC) located at the central node of the network and multiple sensors distributed at different locations on the edge of the network. The original information may be any type of data required by the network, determined by the specific requirements of the network, such as common positioning information or weather information. Each sensor observes the original information and obtains its own local observation data. Usually, in the actual environment, due to the influence of environmental noise on the observation, there is an error between the local observation data and the original information. For sensors with limited bandwidth/energy, it is necessary to quantify the local observation data first, convert the continuous observation data into binary discrete data that can be used in modern digital communication, and then send their own observation data to FC smoothly. FC can only estimate raw information using quantitative data sent from all sensors. The measurement index of the original information estimation performance generally uses the mean squared error (mean squared error, MSE) of the original information and its estimated value. The smaller the MSE, the more accurate the estimation and the better the estimation performance;

如图1所示，一种基于多元概率量化的分布式信息估计方法，包括以下步骤：As shown in Figure 1, a distributed information estimation method based on multivariate probability quantification includes the following steps:

S1.构建分布式信息估计场景：如图2所示，包括一个位于无线通信网络中心的融合中心 FC和多个分布在无线通信网络边缘的传感器；S1. Build a distributed information estimation scenario: as shown in Figure 2, including a fusion center FC located at the center of the wireless communication network and a plurality of sensors distributed at the edge of the wireless communication network;

每一个传感器都对融合中心需要的原始信息

Figure 100002_DEST_PATH_IMAGE004
进行观测，并得到自己的本地观测数据，对本地的观测数据进行多元概率量化操作，将连续的观测数据转化为能够被用于数字通信的二进制离散数据，并发送给融合中心FC；FC融合中心根据所有传感器发送过来的量化数据对原始信息进行估计；Each sensor has the raw information required by the fusion center
Figure 100002_DEST_PATH_IMAGE004
Make observations and get your own local observation data, perform multiple probability quantification operations on the local observation data, convert continuous observation data into binary discrete data that can be used for digital communication, and send it to the fusion center FC; FC fusion center Estimate raw information based on quantitative data sent from all sensors;

S2.构建传感器对本地观测数据进行量化的多元概率量化器：S2. Construct a multivariate probability quantizer for sensor quantification of local observation data:

多个分布在网络边缘的传感器，共同对融合中心需要的原始信息

Figure 512426DEST_PATH_IMAGE004
进行观测，分别得到自己的本地观测。这里考虑所有传感器观测时，受环境影响的观测噪声是独立同分布的。因此，为了降低传感器设计及部署时的难度，我们同样考虑所有的传感器上使用完全相同的多元概率量化器结构，包括量化器上任何可调节的设计参数也是相同的。Multiple sensors distributed at the edge of the network jointly collect the original information required by the fusion center
Figure 512426DEST_PATH_IMAGE004
Observations are made to get their own local observations respectively. When all sensor observations are considered here, the observation noise affected by the environment is independent and identically distributed. Therefore, in order to reduce the difficulty of sensor design and deployment, we also consider using exactly the same multivariate probability quantizer structure on all sensors, including any adjustable design parameters on the quantizer.

因为考虑了所有传感器上独立同分布的观测噪声，以及使用相同的多元量化器。我们在这里以任意一个传感器（忽略传感器序号）举例，来描述传感器上的观测和数据量化的过程，及多元概率量化器的结构、功能及设计方案。如图3所示，传感器观测原始信息

Figure 100002_DEST_PATH_IMAGE005
得到本地观测值
Figure 100002_DEST_PATH_IMAGE006
，用
Figure 100002_DEST_PATH_IMAGE007
来表示观测值
Figure 606503DEST_PATH_IMAGE006
相对于被观测的
Figure 79597DEST_PATH_IMAGE005
的条件概率密度函数，以描述它们之间的随机性。传感器得到观测值
Figure 495535DEST_PATH_IMAGE006
后将其输入多元概率量化器，并输出最终的量化结果
Figure 100002_DEST_PATH_IMAGE008
，量化结果
Figure 100002_DEST_PATH_IMAGE009
是一个包含
Figure 100002_DEST_PATH_IMAGE010
比特的二进制数据。在量化器的内部，输入的观测值
Figure 625819DEST_PATH_IMAGE006
首先被送入一个多元量化概率控制函数
Figure 100002_DEST_PATH_IMAGE011
，被映射为一个
Figure 100002_DEST_PATH_IMAGE012
维的概率向量
Figure 100002_DEST_PATH_IMAGE013
，概率向量
Figure 100002_DEST_PATH_IMAGE014
中的所有元素都是在
Figure 100002_DEST_PATH_IMAGE015
区间取值，同时满足相加之和为1，即Because the independent and identically distributed observation noise on all sensors is considered, and the same multivariate quantizer is used. Here we take any sensor (ignoring the serial number of the sensor) as an example to describe the process of observation and data quantification on the sensor, as well as the structure, function and design scheme of the multivariate probability quantizer. As shown in Figure 3, the sensor observes the original information
Figure 100002_DEST_PATH_IMAGE005
get local observations
Figure 100002_DEST_PATH_IMAGE006
,use
Figure 100002_DEST_PATH_IMAGE007
to represent the observed value
Figure 606503DEST_PATH_IMAGE006
compared to the observed
Figure 79597DEST_PATH_IMAGE005
The conditional probability density function of , to describe the randomness among them. The sensor gets the observed value
Figure 495535DEST_PATH_IMAGE006
Then input it into the multivariate probability quantizer, and output the final quantization result
Figure 100002_DEST_PATH_IMAGE008
, the quantitative result
Figure 100002_DEST_PATH_IMAGE009
is a containing
Figure 100002_DEST_PATH_IMAGE010
bits of binary data. Inside the quantizer, the input observations
Figure 625819DEST_PATH_IMAGE006
is first fed into a multivariate quantized probability control function
Figure 100002_DEST_PATH_IMAGE011
, is mapped to a
Figure 100002_DEST_PATH_IMAGE012
A probability vector of dimension
Figure 100002_DEST_PATH_IMAGE013
, the probability vector
Figure 100002_DEST_PATH_IMAGE014
All elements in the
Figure 100002_DEST_PATH_IMAGE015
The value of the interval, at the same time, the sum of the addition is 1, that is

Figure 100002_DEST_PATH_IMAGE016
（1）
Figure 100002_DEST_PATH_IMAGE016
(1)

其中，

Figure 100002_DEST_PATH_IMAGE017
是一个由设计参数
Figure 100002_DEST_PATH_IMAGE018
控制的可变函数，有in,
Figure 100002_DEST_PATH_IMAGE017
is a design parameter
Figure 100002_DEST_PATH_IMAGE018
The variable function of the control has

Figure 100002_DEST_PATH_IMAGE019
（2）
Figure 100002_DEST_PATH_IMAGE019
(2)

其中

Figure 100002_DEST_PATH_IMAGE020
包含了
Figure 100002_DEST_PATH_IMAGE021
中所有可调节的参数，
Figure 100002_DEST_PATH_IMAGE022
是设计参数的个数。从公式(2)中不难看出，通过改变设计参数
Figure 100002_DEST_PATH_IMAGE023
的取值，相应改变参数函数
Figure 602215DEST_PATH_IMAGE021
的函数表达式和结构。从
Figure 333411DEST_PATH_IMAGE021
输出的概率向量
Figure 100002_DEST_PATH_IMAGE024
接着被送入量化函数
Figure 100002_DEST_PATH_IMAGE025
中（
Figure 985497DEST_PATH_IMAGE025
的具体结构在下文及图4中有详细说明），输出一个十进制的一维离散值
Figure 100002_DEST_PATH_IMAGE026
，接着我们通过将十进制的
Figure 100002_DEST_PATH_IMAGE027
转化为二进制的量化结果
Figure 100002_DEST_PATH_IMAGE028
。对于量化函数
Figure 100002_DEST_PATH_IMAGE029
，它的输出
Figure 100002_DEST_PATH_IMAGE030
一共有
Figure 100002_DEST_PATH_IMAGE031
不同的结果，期望是使得
Figure 582569DEST_PATH_IMAGE027
取每一种结果的概率完全由
Figure 381898DEST_PATH_IMAGE031
维的概率向量
Figure 100002_DEST_PATH_IMAGE032
控制，即实现in
Figure 100002_DEST_PATH_IMAGE020
contains
Figure 100002_DEST_PATH_IMAGE021
All adjustable parameters in
Figure 100002_DEST_PATH_IMAGE022
is the number of design parameters. It is not difficult to see from formula (2) that by changing the design parameters
Figure 100002_DEST_PATH_IMAGE023
value, change the parameter function accordingly
Figure 602215DEST_PATH_IMAGE021
function expressions and structures. from
Figure 333411DEST_PATH_IMAGE021
output probability vector
Figure 100002_DEST_PATH_IMAGE024
is then fed into the quantization function
Figure 100002_DEST_PATH_IMAGE025
middle(
Figure 985497DEST_PATH_IMAGE025
The specific structure is described in detail below and in Figure 4), outputting a decimal one-dimensional discrete value
Figure 100002_DEST_PATH_IMAGE026
, then we pass the decimal
Figure 100002_DEST_PATH_IMAGE027
Quantized results converted to binary
Figure 100002_DEST_PATH_IMAGE028
. For the quantization function
Figure 100002_DEST_PATH_IMAGE029
, which outputs
Figure 100002_DEST_PATH_IMAGE030
A total of
Figure 100002_DEST_PATH_IMAGE031
different results, the expectation is that the
Figure 582569DEST_PATH_IMAGE027
The probability of taking each outcome is entirely determined by
Figure 381898DEST_PATH_IMAGE031
A probability vector of dimension
Figure 100002_DEST_PATH_IMAGE032
to control, to achieve

Figure 100002_DEST_PATH_IMAGE033
（3）
Figure 100002_DEST_PATH_IMAGE033
(3)

其中

Figure 100002_DEST_PATH_IMAGE034
表示在给定输入多元概率量化器的观测值
Figure 100002_DEST_PATH_IMAGE035
的前提下，量化输出
Figure 100002_DEST_PATH_IMAGE036
取值为
Figure 100002_DEST_PATH_IMAGE037
的概率。in
Figure 100002_DEST_PATH_IMAGE034
represents the observations at the given input multivariate probability quantizer
Figure 100002_DEST_PATH_IMAGE035
Under the premise that the quantized output
Figure 100002_DEST_PATH_IMAGE036
The value is
Figure 100002_DEST_PATH_IMAGE037
The probability.

为了实现上述描述的多元概率量化器对本地观测数据进行概率量化的功能，我们对多元概率量化器中的量化函数

Figure 72992DEST_PATH_IMAGE029
设计如图4所示的结构。In order to realize the function of the multivariate probability quantizer described above to quantify the probability of local observation data, we quantify the quantization function in the multivariate probability quantizer
Figure 72992DEST_PATH_IMAGE029
Design the structure shown in Figure 4.

其中量化函数

Figure 100002_DEST_PATH_IMAGE038
的输入是
Figure 100002_DEST_PATH_IMAGE039
维的概率向量
Figure 100002_DEST_PATH_IMAGE040
，输出是一维离散值
Figure 100002_DEST_PATH_IMAGE041
，它由
Figure 100002_DEST_PATH_IMAGE042
个串行的具有相同结构的子层组成，具体的结构功能如下：where the quantization function
Figure 100002_DEST_PATH_IMAGE038
The input is
Figure 100002_DEST_PATH_IMAGE039
A probability vector of dimension
Figure 100002_DEST_PATH_IMAGE040
, the output is a one-dimensional discrete value
Figure 100002_DEST_PATH_IMAGE041
, which consists of
Figure 100002_DEST_PATH_IMAGE042
It consists of a series of sub-layers with the same structure, and the specific structural functions are as follows:

输入：输入

Figure 817351DEST_PATH_IMAGE039
维的概率向量
Figure 100002_DEST_PATH_IMAGE043
，及初始的量化值
Figure 100002_DEST_PATH_IMAGE044
。input: input
Figure 817351DEST_PATH_IMAGE039
A probability vector of dimension
Figure 100002_DEST_PATH_IMAGE043
, and the initial quantization value
Figure 100002_DEST_PATH_IMAGE044
.

第m子层，m=1,2,…,M: 第m子层的输入（如果m=1，其输入是

Figure 449189DEST_PATH_IMAGE045
和
Figure 100002_DEST_PATH_IMAGE046
）是上一个子层（第m-1子层）输出的
Figure 380105DEST_PATH_IMAGE047
维的向量
Figure 100002_DEST_PATH_IMAGE048
和量化值
Figure 100002_DEST_PATH_IMAGE049
；首先，在第m子层中，将输入的
Figure 100002_DEST_PATH_IMAGE050
分为两个相同长度的子向量，分别包含
Figure 207597DEST_PATH_IMAGE050
前半段的所有元素和后半段的所有元素，即两个
Figure 100002_DEST_PATH_IMAGE051
维的子向量
Figure 100002_DEST_PATH_IMAGE052
和
Figure 100002_DEST_PATH_IMAGE053
；接着，第m子层利用
Figure 100002_DEST_PATH_IMAGE054
和
Figure 100002_DEST_PATH_IMAGE055
输出量化值
Figure 100002_DEST_PATH_IMAGE056
，其中The mth sublayer, m=1,2,...,M: The input of the mth sublayer (if m=1, its input is
Figure 449189DEST_PATH_IMAGE045
with
Figure 100002_DEST_PATH_IMAGE046
) is the output of the previous sublayer (m-1th sublayer)
Figure 380105DEST_PATH_IMAGE047
vector of dimensions
Figure 100002_DEST_PATH_IMAGE048
and quantized value
Figure 100002_DEST_PATH_IMAGE049
; First, in the mth sublayer, the input
Figure 100002_DEST_PATH_IMAGE050
Divide into two sub-vectors of the same length, containing
Figure 207597DEST_PATH_IMAGE050
All elements of the first half and all elements of the second half, i.e. two
Figure 100002_DEST_PATH_IMAGE051
Dimension subvector
Figure 100002_DEST_PATH_IMAGE052
with
Figure 100002_DEST_PATH_IMAGE053
; Next, the mth sublayer uses
Figure 100002_DEST_PATH_IMAGE054
with
Figure 100002_DEST_PATH_IMAGE055
output quantized value
Figure 100002_DEST_PATH_IMAGE056
,in

Figure 100002_DEST_PATH_IMAGE057
（4）
Figure 100002_DEST_PATH_IMAGE057
(4)

Figure 100002_DEST_PATH_IMAGE058
是[0,1]区间均匀分布的随机噪声，函数
Figure 100002_DEST_PATH_IMAGE059
输入非负数会输出1，反之输入负数会输出0。定义
Figure 100002_DEST_PATH_IMAGE060
，第m子层输出
Figure 100002_DEST_PATH_IMAGE061
维的向量
Figure 100002_DEST_PATH_IMAGE062
，其中
Figure 100002_DEST_PATH_IMAGE058
is random noise uniformly distributed in the [0,1] interval, the function
Figure 100002_DEST_PATH_IMAGE059
Inputting a non-negative number will output 1, otherwise inputting a negative number will output 0. definition
Figure 100002_DEST_PATH_IMAGE060
, the output of the mth sublayer
Figure 100002_DEST_PATH_IMAGE061
vector of dimensions
Figure 100002_DEST_PATH_IMAGE062
,in

Figure 100002_DEST_PATH_IMAGE063
（5）
Figure 100002_DEST_PATH_IMAGE063
(5)

输出：量化函数

Figure 100002_DEST_PATH_IMAGE064
的输出量化值
Figure 100002_DEST_PATH_IMAGE065
即为其第
Figure 100002_DEST_PATH_IMAGE066
子层输出的量化值
Figure 100002_DEST_PATH_IMAGE067
，即
Figure 100002_DEST_PATH_IMAGE068
。output: quantization function
Figure 100002_DEST_PATH_IMAGE064
The output quantization value of
Figure 100002_DEST_PATH_IMAGE065
is its first
Figure 100002_DEST_PATH_IMAGE066
Quantized value of sublayer output
Figure 100002_DEST_PATH_IMAGE067
,Right now
Figure 100002_DEST_PATH_IMAGE068
.

通过如图4的结构，量化函数

Figure 484643DEST_PATH_IMAGE064
实现了使其输出的量化值
Figure 100002_DEST_PATH_IMAGE069
取其每一种可能结果的概率完全由概率向量
Figure 100002_DEST_PATH_IMAGE070
来控制，实现了公式(3)中的功能。Through the structure shown in Figure 4, the quantization function
Figure 484643DEST_PATH_IMAGE064
implements the quantized value that makes it output
Figure 100002_DEST_PATH_IMAGE069
The probability of each possible outcome is completely determined by the probability vector
Figure 100002_DEST_PATH_IMAGE070
To control, realize the function in the formula (3).

S3.优化多元量化概率函数的设计参数

Figure 100002_DEST_PATH_IMAGE071
;S3. Optimizing the design parameters of the multivariate quantitative probability function
Figure 100002_DEST_PATH_IMAGE071
;

如公式(2)和(3)中所示，通过调节传感器上的多元概率量化器中多元量化概率控制函数

Figure 100002_DEST_PATH_IMAGE072
的设计参数
Figure 100002_DEST_PATH_IMAGE073
的取值，我们可以相应地改变
Figure 731341DEST_PATH_IMAGE072
的函数表达式，进而改变传感器上的量化数据相对于本地观测数据及原始信息的概率分布。这意味着针对服从不同随机分布的原始信息，和不同观测环境下的具有不同随机特性的观测噪声，我们可以通过优化多元量化概率函数
Figure 872472DEST_PATH_IMAGE072
的设计参数
Figure 698346DEST_PATH_IMAGE073
，以获得适应当前环境的最优量化数据概率分布。通过利用贝叶斯估计理论，我们考虑通过算法最小化由
Figure 63468DEST_PATH_IMAGE073
决定的，传感器对本地观测进行量化后，在融合中心使用量化后的数据能达到的估计的MSE下界，以找到适应当前观测环境下的最优设计参数
Figure 100002_DEST_PATH_IMAGE074
，及传感器上对应的使用最优设计参数
Figure 138740DEST_PATH_IMAGE074
的最优多元量化概率函数
Figure 83562DEST_PATH_IMAGE071
。As shown in equations (2) and (3), by adjusting the multivariate quantization probability control function in the multivariate probability quantizer on the sensor
Figure 100002_DEST_PATH_IMAGE072
design parameters
Figure 100002_DEST_PATH_IMAGE073
value, we can change accordingly
Figure 731341DEST_PATH_IMAGE072
The function expression of the sensor can change the probability distribution of the quantitative data on the sensor relative to the local observation data and original information. This means that for the original information subject to different random distributions, and the observation noise with different random characteristics under different observation environments, we can optimize the multivariate quantization probability function
Figure 872472DEST_PATH_IMAGE072
design parameters
Figure 698346DEST_PATH_IMAGE073
, to obtain the optimal quantitative data probability distribution suitable for the current environment. By utilizing Bayesian estimation theory, we consider algorithmically minimizing by
Figure 63468DEST_PATH_IMAGE073
Determined, after the sensor quantifies the local observations, the estimated MSE lower bound can be achieved using the quantified data in the fusion center to find the optimal design parameters for the current observation environment
Figure 100002_DEST_PATH_IMAGE074
, and the corresponding optimal design parameters on the sensor
Figure 138740DEST_PATH_IMAGE074
The optimal multivariate quantified probability function for
Figure 83562DEST_PATH_IMAGE071
.

我们假设一共有

Figure 100002_DEST_PATH_IMAGE075
个独立的传感器分布在整个网络中，所有传感器上都使用如图3所示的多元概率量化器结构，并且我们在所有的多元概率量化器中使用完全相同的多元量化概率函数
Figure 761013DEST_PATH_IMAGE072
和相应的设计参数
Figure 562616DEST_PATH_IMAGE073
，以降低整个网络的设计成本和难度。
Figure 594025DEST_PATH_IMAGE075
个传感器分别对原始信息
Figure 100002_DEST_PATH_IMAGE076
进行观测，分别得到自己的带有观测噪声的本地观测数据
Figure 100002_DEST_PATH_IMAGE077
。我们这里考虑各个传感器上存在独立同分布的观测噪声，并定义概率密度函数
Figure 100002_DEST_PATH_IMAGE078
来描述观测噪声的分布：对于第
Figure 100002_DEST_PATH_IMAGE079
个传感器，它的本地观测数据
Figure 100002_DEST_PATH_IMAGE080
经过本地的多元概率量化器，被量化成
Figure 100002_DEST_PATH_IMAGE081
比特的二进制数据
Figure 100002_DEST_PATH_IMAGE082
,并被发送给网络中心的FC。所以
Figure 762445DEST_PATH_IMAGE075
个传感器一共产生了
Figure 500594DEST_PATH_IMAGE075
个
Figure 676360DEST_PATH_IMAGE081
比特的量化数据
Figure 100002_DEST_PATH_IMAGE083
并发送给了FC，FC需要利用所有接收到的量化数据来对原始信息进行估计。We assume that there are
Figure 100002_DEST_PATH_IMAGE075
independent sensors are distributed throughout the network, all sensors use the multivariate probability quantizer structure shown in Figure 3, and we use exactly the same multivariate quantization probability function in all multivariate probability quantizers
Figure 761013DEST_PATH_IMAGE072
and the corresponding design parameters
Figure 562616DEST_PATH_IMAGE073
, to reduce the design cost and difficulty of the entire network.
Figure 594025DEST_PATH_IMAGE075
sensor to the original information
Figure 100002_DEST_PATH_IMAGE076
Make observations to obtain their own local observation data with observation noise
Figure 100002_DEST_PATH_IMAGE077
. Here we consider that there is independent and identically distributed observation noise on each sensor, and define the probability density function
Figure 100002_DEST_PATH_IMAGE078
to describe the distribution of observation noise: for the first
Figure 100002_DEST_PATH_IMAGE079
sensor, its local observation data
Figure 100002_DEST_PATH_IMAGE080
After the local multivariate probability quantizer, it is quantized as
Figure 100002_DEST_PATH_IMAGE081
bit of binary data
Figure 100002_DEST_PATH_IMAGE082
, and sent to the FC in the network center. so
Figure 762445DEST_PATH_IMAGE075
sensors produced a total of
Figure 500594DEST_PATH_IMAGE075
indivual
Figure 676360DEST_PATH_IMAGE081
quantized data in bits
Figure 100002_DEST_PATH_IMAGE083
And sent to FC, FC needs to use all the quantized data received to estimate the original information.

通过贝叶斯概率理论，所有传感器上的量化数据在给定

Figure 100002_DEST_PATH_IMAGE084
的情况下也是独立同分布的。因此，基于量化数据的概率分布，首先计算当FC接收到量化数据
Figure 726225DEST_PATH_IMAGE083
时，对原始信息
Figure 12850DEST_PATH_IMAGE084
进行估计所能达到的估计MSE的下界，即Through Bayesian probability theory, the quantitative data on all sensors are in a given
Figure 100002_DEST_PATH_IMAGE084
is also independent and identically distributed. Therefore, based on the probability distribution of quantized data, first calculate when FC receives quantized data
Figure 726225DEST_PATH_IMAGE083
, for the original information
Figure 12850DEST_PATH_IMAGE084
The lower bound of the estimated MSE that can be achieved by performing the estimation, that is,

Figure 100002_DEST_PATH_IMAGE085
Figure 100002_DEST_PATH_IMAGE086
（6）
Figure 100002_DEST_PATH_IMAGE085
Figure 100002_DEST_PATH_IMAGE086
(6)

其中

Figure 100002_DEST_PATH_IMAGE087
，
Figure 100002_DEST_PATH_IMAGE088
表示FC接收到的所有从传感器发送过来的量化数据，
Figure 100002_DEST_PATH_IMAGE089
表示FC利用量化数据
Figure 100002_DEST_PATH_IMAGE090
所能实现的对
Figure 100002_DEST_PATH_IMAGE091
的任意估计值，相应地公式中不等式左边的
Figure 100002_DEST_PATH_IMAGE092
表示原始信息
Figure 841391DEST_PATH_IMAGE091
和其估计值
Figure 100002_DEST_PATH_IMAGE093
之间的MSE，
Figure 100002_DEST_PATH_IMAGE094
表示求取数学期望的操作，公式（6）中不等式右边表示求取的MSE下界，
Figure 100002_DEST_PATH_IMAGE095
是数学定义中的组合数，in
Figure 100002_DEST_PATH_IMAGE087
,
Figure 100002_DEST_PATH_IMAGE088
Indicates all the quantitative data sent from the sensor received by the FC,
Figure 100002_DEST_PATH_IMAGE089
Indicates that FC utilizes quantified data
Figure 100002_DEST_PATH_IMAGE090
what can be achieved
Figure 100002_DEST_PATH_IMAGE091
Any estimated value of , corresponding to the left side of the inequality in the formula
Figure 100002_DEST_PATH_IMAGE092
Indicates the original information
Figure 841391DEST_PATH_IMAGE091
and its estimated value
Figure 100002_DEST_PATH_IMAGE093
MSE between,
Figure 100002_DEST_PATH_IMAGE094
Indicates the operation of obtaining the mathematical expectation, and the right side of the inequality in formula (6) represents the lower bound of the obtained MSE,
Figure 100002_DEST_PATH_IMAGE095
is the combination number in the mathematical definition,

Figure 100002_DEST_PATH_IMAGE096
（7）
Figure 100002_DEST_PATH_IMAGE096
(7)

是由多元量化概率函数

Figure 100002_DEST_PATH_IMAGE097
的设计参数
Figure 100002_DEST_PATH_IMAGE098
和原始信息
Figure 100002_DEST_PATH_IMAGE099
决定的一系列中间计算项。从公式（6）中可以看出，在原始信息
Figure 496713DEST_PATH_IMAGE099
的概率分布和观测噪声分布
Figure 100002_DEST_PATH_IMAGE100
都确定的情况下，FC利用量化数据对
Figure 502715DEST_PATH_IMAGE099
进行估计的MSE,即
Figure 100002_DEST_PATH_IMAGE101
，其下界完全由多元量化概率函数
Figure 124190DEST_PATH_IMAGE097
的设计参数
Figure 571351DEST_PATH_IMAGE098
决定。因此，通过算法最小化公式（6）中不等式右边，由
Figure 100002_DEST_PATH_IMAGE102
决定的FC使用量化数据对原始信息估计的MSE的下界，以找到适应当前观测环境下的最优设计参数
Figure 100002_DEST_PATH_IMAGE103
，及对应的最优多元量化概率函数
Figure 100002_DEST_PATH_IMAGE104
。is a multivariate quantified probability function
Figure 100002_DEST_PATH_IMAGE097
design parameters
Figure 100002_DEST_PATH_IMAGE098
and original information
Figure 100002_DEST_PATH_IMAGE099
A sequence of intermediate calculation terms for a decision. It can be seen from formula (6) that in the original information
Figure 496713DEST_PATH_IMAGE099
The probability distribution and the observation noise distribution of
Figure 100002_DEST_PATH_IMAGE100
When both are determined, FC uses quantized data to
Figure 502715DEST_PATH_IMAGE099
Estimated MSE, ie
Figure 100002_DEST_PATH_IMAGE101
, whose lower bound is entirely given by the multivariate quantized probability function
Figure 124190DEST_PATH_IMAGE097
design parameters
Figure 571351DEST_PATH_IMAGE098
Decide. Therefore, by algorithmically minimizing the right side of the inequality in formula (6), by
Figure 100002_DEST_PATH_IMAGE102
The determined FC uses quantitative data to estimate the lower bound of the MSE of the original information to find the optimal design parameters for the current observation environment
Figure 100002_DEST_PATH_IMAGE103
, and the corresponding optimal multivariate quantified probability function
Figure 100002_DEST_PATH_IMAGE104
.

基于上述分析，我们考虑如下的一种迭代算法，基于从实际观测环境收集到的原始信息与传感器本地观测数据的一系列样本，在算法的每次迭代中近似求解关于设计参数的优化问题，并在迭代过程中逐渐逼近最优的设计参数

Figure 216484DEST_PATH_IMAGE103
。Based on the above analysis, we consider an iterative algorithm as follows, based on a series of samples of the original information collected from the actual observation environment and the local observation data of the sensor, the optimization problem about the design parameters is approximately solved in each iteration of the algorithm, and Gradually approach the optimal design parameters in the iterative process
Figure 216484DEST_PATH_IMAGE103
.

初始化：传感器总数为

Figure 100002_DEST_PATH_IMAGE105
，样本集
Figure 100002_DEST_PATH_IMAGE106
,
Figure 100002_DEST_PATH_IMAGE107
为样本集包含的总样本数，
Figure 100002_DEST_PATH_IMAGE108
是原始信息样本，
Figure 100002_DEST_PATH_IMAGE109
表示样本的序号，而
Figure 100002_DEST_PATH_IMAGE110
表示传感器对原始信息样本
Figure 490208DEST_PATH_IMAGE108
总共观测
Figure 100002_DEST_PATH_IMAGE111
次得到的
Figure 670302DEST_PATH_IMAGE111
个观测样本；设定初始的设计参数
Figure 100002_DEST_PATH_IMAGE112
,将迭代的容忍门限设定为
Figure 100002_DEST_PATH_IMAGE113
，设定初始的迭代计数为
Figure 100002_DEST_PATH_IMAGE114
。Initialization: The total number of sensors is
Figure 100002_DEST_PATH_IMAGE105
, sample set
Figure 100002_DEST_PATH_IMAGE106
,
Figure 100002_DEST_PATH_IMAGE107
is the total number of samples contained in the sample set,
Figure 100002_DEST_PATH_IMAGE108
is the original information sample,
Figure 100002_DEST_PATH_IMAGE109
represents the serial number of the sample, and
Figure 100002_DEST_PATH_IMAGE110
Represents the sensor’s response to raw information samples
Figure 490208DEST_PATH_IMAGE108
total observations
Figure 100002_DEST_PATH_IMAGE111
times obtained
Figure 670302DEST_PATH_IMAGE111
observation samples; set the initial design parameters
Figure 100002_DEST_PATH_IMAGE112
, set the tolerance threshold of the iteration as
Figure 100002_DEST_PATH_IMAGE113
, set the initial iteration count as
Figure 100002_DEST_PATH_IMAGE114
.

步骤一：在第

Figure 100002_DEST_PATH_IMAGE115
次迭代中，按照公式（7）对
Figure 100002_DEST_PATH_IMAGE116
的定义，对
Figure 100002_DEST_PATH_IMAGE117
，计算由第
Figure 100002_DEST_PATH_IMAGE118
次迭代中得到的多元量化概率函数设计参数
Figure 100002_DEST_PATH_IMAGE119
决定的一系列中间计算项
Figure 100002_DEST_PATH_IMAGE120
，其中Step 1: In the
Figure 100002_DEST_PATH_IMAGE115
In iterations, according to formula (7) for
Figure 100002_DEST_PATH_IMAGE116
definition of
Figure 100002_DEST_PATH_IMAGE117
, calculated by the
Figure 100002_DEST_PATH_IMAGE118
The multivariate quantitative probability function design parameters obtained in the second iteration
Figure 100002_DEST_PATH_IMAGE119
A series of intermediate calculation items determined
Figure 100002_DEST_PATH_IMAGE120
,in

Figure 100002_DEST_PATH_IMAGE121
（8）
Figure 100002_DEST_PATH_IMAGE121
(8)

步骤二：利用公式（8）中的

Figure 100002_DEST_PATH_IMAGE122
和样本集
Figure 100002_DEST_PATH_IMAGE123
，将式（6）中不等式右边的MSE下界近似计算为Step 2: Using the formula (8)
Figure 100002_DEST_PATH_IMAGE122
and sample set
Figure 100002_DEST_PATH_IMAGE123
, the MSE lower bound on the right side of the inequality in equation (6) is approximately calculated as

Figure 100002_DEST_PATH_IMAGE124
Figure 100002_DEST_PATH_IMAGE125
（9）
Figure 100002_DEST_PATH_IMAGE124
Figure 100002_DEST_PATH_IMAGE125
(9)

然后利用内点法和梯度下降法，解决如下最小化问题Then use the interior point method and gradient descent method to solve the following minimization problem

Figure 100002_DEST_PATH_IMAGE126
（10）
Figure 100002_DEST_PATH_IMAGE126
(10)

求解之后得到新的设计参数

Figure 100002_DEST_PATH_IMAGE127
。After solving, the new design parameters are obtained
Figure 100002_DEST_PATH_IMAGE127
.

步骤三：计算并查看收敛条件

Figure 100002_DEST_PATH_IMAGE128
是否成立。Step 3: Calculate and view the convergence conditions
Figure 100002_DEST_PATH_IMAGE128
Whether it is established.

如果不成立，说明需要继续迭代，需要将

Figure 100002_DEST_PATH_IMAGE129
带入步骤A2进行下一次迭代，并更新迭代计数
Figure 100002_DEST_PATH_IMAGE130
；如果收敛条件成立，则输出
Figure 100002_DEST_PATH_IMAGE131
作为最优的设计参数。If it is not established, it means that the iteration needs to be continued, and the
Figure 100002_DEST_PATH_IMAGE129
Bring into step A2 for the next iteration and update the iteration count
Figure 100002_DEST_PATH_IMAGE130
; if the convergence condition holds, the output
Figure 100002_DEST_PATH_IMAGE131
as an optimal design parameter.

输出：最优设计参数

Figure 828095DEST_PATH_IMAGE103
Output: optimal design parameters
Figure 828095DEST_PATH_IMAGE103

通过以上算法可以得到最优的设计参数

Figure 250986DEST_PATH_IMAGE103
，及相对应的对最优多元量化概率函数
Figure 100002_DEST_PATH_IMAGE132
。The optimal design parameters can be obtained by the above algorithm
Figure 250986DEST_PATH_IMAGE103
, and the corresponding probability function for optimal multivariate quantization
Figure 100002_DEST_PATH_IMAGE132
.

S4.融合中心FC设计量化融合估计器并进行优化得到最优估计函数

Figure 100002_DEST_PATH_IMAGE133
；S4. The fusion center FC designs a quantized fusion estimator and optimizes it to obtain the optimal estimation function
Figure 100002_DEST_PATH_IMAGE133
;

如上文中提到，

Figure 293897DEST_PATH_IMAGE075
个传感器一共产生了
Figure 991595DEST_PATH_IMAGE075
个
Figure 147770DEST_PATH_IMAGE081
比特的
Figure 275650DEST_PATH_IMAGE083
并发送给了FC，FC需要利用所有接收到的量化数据来对原始信息进行估计。因此，我们首先给出FC上的量化融合估计器设计。As mentioned above,
Figure 293897DEST_PATH_IMAGE075
sensors produced a total of
Figure 991595DEST_PATH_IMAGE075
indivual
Figure 147770DEST_PATH_IMAGE081
bit
Figure 275650DEST_PATH_IMAGE083
And sent to FC, FC needs to use all the quantized data received to estimate the original information. Therefore, we first present a quantized fusion estimator design on FC.

如图5所示，FC接收到从

Figure 100002_DEST_PATH_IMAGE134
个传感器发送过来的
Figure 681224DEST_PATH_IMAGE134
个量化数据
Figure 100002_DEST_PATH_IMAGE135
，并将其输入量化融合估计器，输出对原始信息
Figure 100002_DEST_PATH_IMAGE136
的估计值
Figure 100002_DEST_PATH_IMAGE137
。在量化融合估计器中，输入的
Figure 100002_DEST_PATH_IMAGE138
个
Figure 100002_DEST_PATH_IMAGE139
比特的二进制量化数据
Figure DEST_PATH_IMAGE140
首先被转化为相应的
Figure 819163DEST_PATH_IMAGE138
个在
Figure 100002_DEST_PATH_IMAGE141
中取值十进制离散数据
Figure 100002_DEST_PATH_IMAGE142
；As shown in Figure 5, the FC receives the slave
Figure 100002_DEST_PATH_IMAGE134
sent by a sensor
Figure 681224DEST_PATH_IMAGE134
quantitative data
Figure 100002_DEST_PATH_IMAGE135
, and input it into the quantized fusion estimator, and output the original information
Figure 100002_DEST_PATH_IMAGE136
estimated value of
Figure 100002_DEST_PATH_IMAGE137
. In the quantized fusion estimator, the input
Figure 100002_DEST_PATH_IMAGE138
indivual
Figure 100002_DEST_PATH_IMAGE139
Binary Quantized Data in Bits
Figure DEST_PATH_IMAGE140
is first transformed into the corresponding
Figure 819163DEST_PATH_IMAGE138
one in
Figure 100002_DEST_PATH_IMAGE141
Median decimal discrete data
Figure 100002_DEST_PATH_IMAGE142
;

Figure 16795DEST_PATH_IMAGE138
个十进制数据
Figure 100002_DEST_PATH_IMAGE143
接着被送入Onehot函数进行独热编码操作，得到相应的
Figure 578227DEST_PATH_IMAGE138
个独热编码向量
Figure 100002_DEST_PATH_IMAGE144
。以第
Figure 100002_DEST_PATH_IMAGE145
个十进制数据
Figure 100002_DEST_PATH_IMAGE146
举例，
Figure 100002_DEST_PATH_IMAGE147
是它的对应的独热编码向量，
Figure 100002_DEST_PATH_IMAGE148
为
Figure 100002_DEST_PATH_IMAGE149
bit长度的二进制数据，给
Figure 100002_DEST_PATH_IMAGE150
中的总共
Figure 379086DEST_PATH_IMAGE149
位bit按顺序编号为
Figure 100002_DEST_PATH_IMAGE151
位，十进制数据
Figure 100002_DEST_PATH_IMAGE152
的取值范围刚好是所有bit的序号，独热编码意味着只有
Figure 100002_DEST_PATH_IMAGE153
中的第
Figure 100002_DEST_PATH_IMAGE154
位bit会被取值为1，剩下的其余所有位bit都会取值为0，即
Figure 100002_DEST_PATH_IMAGE155
，
Figure 16795DEST_PATH_IMAGE138
decimal data
Figure 100002_DEST_PATH_IMAGE143
Then it is sent to the Onehot function for one-hot encoding operation, and the corresponding
Figure 578227DEST_PATH_IMAGE138
one-hot encoded vector
Figure 100002_DEST_PATH_IMAGE144
. to the first
Figure 100002_DEST_PATH_IMAGE145
decimal data
Figure 100002_DEST_PATH_IMAGE146
For example,
Figure 100002_DEST_PATH_IMAGE147
is its corresponding one-hot encoded vector,
Figure 100002_DEST_PATH_IMAGE148
for
Figure 100002_DEST_PATH_IMAGE149
bit-length binary data, given
Figure 100002_DEST_PATH_IMAGE150
in total
Figure 379086DEST_PATH_IMAGE149
The bits are numbered sequentially as
Figure 100002_DEST_PATH_IMAGE151
bit, decimal data
Figure 100002_DEST_PATH_IMAGE152
The value range of is exactly the serial number of all bits, and one-hot encoding means that only
Figure 100002_DEST_PATH_IMAGE153
in the first
Figure 100002_DEST_PATH_IMAGE154
The bit bit will take the value 1, and all the remaining bits will take the value 0, that is
Figure 100002_DEST_PATH_IMAGE155
,

Figure 100002_DEST_PATH_IMAGE156
（11）
Figure 100002_DEST_PATH_IMAGE156
(11)

接着，

Figure 100002_DEST_PATH_IMAGE157
个独热编码向量
Figure 100002_DEST_PATH_IMAGE158
被送入平均器，得到它们的均值向量
Figure 100002_DEST_PATH_IMAGE159
；then,
Figure 100002_DEST_PATH_IMAGE157
one-hot encoded vector
Figure 100002_DEST_PATH_IMAGE158
are fed into the averager to get their mean vector
Figure 100002_DEST_PATH_IMAGE159
;

之后

Figure 100002_DEST_PATH_IMAGE160
再被送入估计函数
Figure 100002_DEST_PATH_IMAGE161
中，输出对原始信息的估计值
Figure 100002_DEST_PATH_IMAGE162
，
Figure 100002_DEST_PATH_IMAGE163
，同样是一个设计参数
Figure 100002_DEST_PATH_IMAGE164
控制的函数，即after
Figure 100002_DEST_PATH_IMAGE160
is then fed into the estimation function
Figure 100002_DEST_PATH_IMAGE161
, output an estimate of the original information
Figure 100002_DEST_PATH_IMAGE162
,
Figure 100002_DEST_PATH_IMAGE163
, is also a design parameter
Figure 100002_DEST_PATH_IMAGE164
control function, that is

Figure 100002_DEST_PATH_IMAGE165
Figure 100002_DEST_PATH_IMAGE166
（12）
Figure 100002_DEST_PATH_IMAGE165
Figure 100002_DEST_PATH_IMAGE166
(12)

其中

Figure 100002_DEST_PATH_IMAGE167
包含了
Figure 100002_DEST_PATH_IMAGE168
中所有的可调节参数。in
Figure 100002_DEST_PATH_IMAGE167
contains
Figure 100002_DEST_PATH_IMAGE168
All adjustable parameters in .

当所有传感器上使用相同的如图3所示的多元概率量化器，以及使用带有相同的最优设计参数

Figure 100002_DEST_PATH_IMAGE169
的多元量化概率函数
Figure 100002_DEST_PATH_IMAGE170
，则所有传感器发送给FC的量化数据相对于原始信息
Figure 100002_DEST_PATH_IMAGE171
是条件独立同分布的；When using the same multivariate probability quantizer as shown in Figure 3 on all sensors, and using the same optimal design parameters
Figure 100002_DEST_PATH_IMAGE169
The multivariate quantified probability function of
Figure 100002_DEST_PATH_IMAGE170
, then the quantitative data sent by all sensors to FC is relative to the original information
Figure 100002_DEST_PATH_IMAGE171
is conditionally independent and identically distributed;

此时基于贝叶斯估计理论和概率模型，计算出FC对原始信息的估计值

Figure 100002_DEST_PATH_IMAGE172
与原始信息
Figure 100002_DEST_PATH_IMAGE173
间的MSE为At this time, based on Bayesian estimation theory and probability model, the estimated value of FC to the original information is calculated
Figure 100002_DEST_PATH_IMAGE172
with original information
Figure 100002_DEST_PATH_IMAGE173
The MSE between

Figure 100002_DEST_PATH_IMAGE174
Figure 100002_DEST_PATH_IMAGE175
（13）
Figure 100002_DEST_PATH_IMAGE174
Figure 100002_DEST_PATH_IMAGE175
(13)

Figure 100002_DEST_PATH_IMAGE176
为估计MSE，
Figure 100002_DEST_PATH_IMAGE176
To estimate the MSE,

Figure 100002_DEST_PATH_IMAGE177
（14）
Figure 100002_DEST_PATH_IMAGE177
(14)

遵循公式（7）中对

Figure 100002_DEST_PATH_IMAGE178
的定义，由多元量化概率函数的最优设计参数
Figure 100002_DEST_PATH_IMAGE179
和原始信息
Figure 100002_DEST_PATH_IMAGE180
决定的一系列中间计算项；Follow formula (7) for
Figure 100002_DEST_PATH_IMAGE178
The definition of , by the optimal design parameters of the multivariate quantified probability function
Figure 100002_DEST_PATH_IMAGE179
and original information
Figure 100002_DEST_PATH_IMAGE180
A series of intermediate calculation items determined;

由公式（13）得到，在多元量化概率函数的最优设计参数

Figure 452476DEST_PATH_IMAGE179
确定的情况下，FC上对原始信息估计的MSE完全由估计函数
Figure 100002_DEST_PATH_IMAGE181
的可变设计参数
Figure 100002_DEST_PATH_IMAGE182
控制；Obtained by formula (13), the optimal design parameters of the multivariate quantitative probability function
Figure 452476DEST_PATH_IMAGE179
Under certain circumstances, the MSE estimated on the original information on FC is completely determined by the estimation function
Figure 100002_DEST_PATH_IMAGE181
The variable design parameters of
Figure 100002_DEST_PATH_IMAGE182
control;

S404.基于从实际观测环境收集到的原始信息与传感器本地观测数据的一系列样本，以及传感器上最优的多元量化概率函数

Figure 100002_DEST_PATH_IMAGE183
，求解使得FC上估计MSE最小的最优估计函数设计参数
Figure 100002_DEST_PATH_IMAGE184
。S404. A series of samples based on the original information collected from the actual observation environment and the local observation data of the sensor, and the optimal multivariate quantitative probability function on the sensor
Figure 100002_DEST_PATH_IMAGE183
, to find the optimal estimator function design parameters that minimize the estimated MSE on FC
Figure 100002_DEST_PATH_IMAGE184
.

初始化：输入传感器总数

Figure 100002_DEST_PATH_IMAGE185
，传感器上最优的多元量化概率函数
Figure 16531DEST_PATH_IMAGE183
和其相应的最优设计参数
Figure 100002_DEST_PATH_IMAGE186
，样本集
Figure 100002_DEST_PATH_IMAGE187
，遵循公式（14）中对
Figure 100002_DEST_PATH_IMAGE188
的定义，对任意的
Figure 100002_DEST_PATH_IMAGE189
，将由
Figure 100002_DEST_PATH_IMAGE190
和原始信息样本
Figure 100002_DEST_PATH_IMAGE191
决定的中间项
Figure 100002_DEST_PATH_IMAGE192
近似计算为Initialization: Enter the total number of sensors
Figure 100002_DEST_PATH_IMAGE185
, the optimal multivariate quantized probability function on the sensor
Figure 16531DEST_PATH_IMAGE183
and its corresponding optimal design parameters
Figure 100002_DEST_PATH_IMAGE186
, sample set
Figure 100002_DEST_PATH_IMAGE187
, following formula (14) for
Figure 100002_DEST_PATH_IMAGE188
definition, for any
Figure 100002_DEST_PATH_IMAGE189
, will be given by
Figure 100002_DEST_PATH_IMAGE190
and a sample of the original information
Figure 100002_DEST_PATH_IMAGE191
middle term of decision
Figure 100002_DEST_PATH_IMAGE192
Approximately calculated as

Figure 100002_DEST_PATH_IMAGE193
（15）
Figure 100002_DEST_PATH_IMAGE193
(15)

设定初始的设计参数

Figure 100002_DEST_PATH_IMAGE194
,将迭代的容忍门限设定为
Figure 100002_DEST_PATH_IMAGE195
，设定初始的迭代计数为
Figure 100002_DEST_PATH_IMAGE196
。Set initial design parameters
Figure 100002_DEST_PATH_IMAGE194
, set the tolerance threshold of the iteration as
Figure 100002_DEST_PATH_IMAGE195
, set the initial iteration count as
Figure 100002_DEST_PATH_IMAGE196
.

步骤一：在第

Figure 100002_DEST_PATH_IMAGE197
次迭代中，定义
Figure 100002_DEST_PATH_IMAGE198
为FC上估计的MSE，利用公式（13），
Figure 100002_DEST_PATH_IMAGE199
和第次迭代中得到的设计参数
Figure 100002_DEST_PATH_IMAGE200
，将
Figure 100002_DEST_PATH_IMAGE201
近似计算为Step 1: In the
Figure 100002_DEST_PATH_IMAGE197
In iterations, define
Figure 100002_DEST_PATH_IMAGE198
is the estimated MSE on FC, using formula (13),
Figure 100002_DEST_PATH_IMAGE199
and the design parameters obtained in the first iteration
Figure 100002_DEST_PATH_IMAGE200
,Will
Figure 100002_DEST_PATH_IMAGE201
Approximately calculated as

Figure 100002_DEST_PATH_IMAGE202
Figure 100002_DEST_PATH_IMAGE203
（16）
Figure 100002_DEST_PATH_IMAGE202
Figure 100002_DEST_PATH_IMAGE203
(16)

利用内点法和梯度下降法，解决如下最小化问题Using the interior point method and gradient descent method, the following minimization problem is solved

Figure 100002_DEST_PATH_IMAGE204
（17）
Figure 100002_DEST_PATH_IMAGE204
(17)

得到新的设计参数

Figure 100002_DEST_PATH_IMAGE205
。get new design parameters
Figure 100002_DEST_PATH_IMAGE205
.

步骤二：计算并查看收敛条件

Figure 100002_DEST_PATH_IMAGE206
是否成立；如果不成立，继续迭代，将
Figure 100002_DEST_PATH_IMAGE207
带入步骤B2进行下一次迭代，并更新迭代计数
Figure 100002_DEST_PATH_IMAGE208
；如果收敛条件成立，则输出
Figure 100002_DEST_PATH_IMAGE209
作为最优的设计参数。Step 2: Calculate and view the convergence conditions
Figure 100002_DEST_PATH_IMAGE206
Whether it is established; if not, continue to iterate, and will
Figure 100002_DEST_PATH_IMAGE207
Bring into step B2 for the next iteration and update the iteration count
Figure 100002_DEST_PATH_IMAGE208
; if the convergence condition holds, the output
Figure 100002_DEST_PATH_IMAGE209
as an optimal design parameter.

输出：最优设计参数

Figure 100002_DEST_PATH_IMAGE210
。Output: optimal design parameters
Figure 100002_DEST_PATH_IMAGE210
.

通过以上算法可以得到最优的设计参数

Figure 791940DEST_PATH_IMAGE210
，及相对应的最优估计函数
Figure 100002_DEST_PATH_IMAGE211
。The optimal design parameters can be obtained by the above algorithm
Figure 791940DEST_PATH_IMAGE210
, and the corresponding optimal estimation function
Figure 100002_DEST_PATH_IMAGE211
.

S5.基于

Figure 100002_DEST_PATH_IMAGE212
和
Figure 100002_DEST_PATH_IMAGE213
的多元概率量化分布式信息估计。S5. Based on
Figure 100002_DEST_PATH_IMAGE212
with
Figure 100002_DEST_PATH_IMAGE213
Multivariate Probability Quantification for Distributed Information Estimation.

基于上文的两个算法，我们分别得到了所有传感器上的最优多元量化概率函数

Figure 627565DEST_PATH_IMAGE212
和FC上的最优估计函数
Figure 470756DEST_PATH_IMAGE213
。接下来我们再简要描述一下整个网络对原始信息估计的全过程。其中关于传感器上的多元概率量化器和FC上的量化融合估计器，它们的功能结构在上文中已有详细描述，这里不再赘述。Based on the above two algorithms, we obtained the optimal multivariate quantization probability function on all sensors respectively
Figure 627565DEST_PATH_IMAGE212
and the optimal estimation function on FC
Figure 470756DEST_PATH_IMAGE213
. Next, we briefly describe the whole process of the entire network to estimate the original information. Regarding the multivariate probability quantizer on the sensor and the quantization fusion estimator on the FC, their functional structures have been described in detail above, and will not be repeated here.

首先，

Figure 100002_DEST_PATH_IMAGE214
个传感器对原始信息
Figure 100002_DEST_PATH_IMAGE215
分别进行观测。以第
Figure 100002_DEST_PATH_IMAGE216
个传感器举例，它对
Figure 905630DEST_PATH_IMAGE215
观测后得到自己的本地观测数据
Figure 100002_DEST_PATH_IMAGE217
，并将
Figure 605601DEST_PATH_IMAGE217
送入如图3所示的多元概率量化器中（注意此时，图3中的多元量化概率函数
Figure 100002_DEST_PATH_IMAGE218
已经被最优的
Figure 269801DEST_PATH_IMAGE212
替代），最后输出
Figure DEST_PATH_IMAGE219
bit的二进制量化数据
Figure DEST_PATH_IMAGE220
被发送给FC。所有
Figure 182262DEST_PATH_IMAGE214
个传感器一共产生了
Figure 349938DEST_PATH_IMAGE214
个量化数据
Figure DEST_PATH_IMAGE221
。FC收到来自所有传感器的
Figure 427003DEST_PATH_IMAGE214
个量化数据，并将它们送入如图5所示的量化融合估计器中（同样注意此时，图5中的估计函数
Figure DEST_PATH_IMAGE222
已经被最优的
Figure 47340DEST_PATH_IMAGE213
替代），最后输出原始信息的估计值
Figure 497913DEST_PATH_IMAGE137
。first,
Figure 100002_DEST_PATH_IMAGE214
raw information
Figure 100002_DEST_PATH_IMAGE215
observed separately. to the first
Figure 100002_DEST_PATH_IMAGE216
For example, a sensor that is
Figure 905630DEST_PATH_IMAGE215
Get your own local observation data after observation
Figure 100002_DEST_PATH_IMAGE217
, and will
Figure 605601DEST_PATH_IMAGE217
into the multivariate probability quantizer shown in Figure 3 (note that at this point, the multivariate quantization probability function in Figure 3
Figure 100002_DEST_PATH_IMAGE218
has been optimized
Figure 269801DEST_PATH_IMAGE212
alternative), and finally output
Figure DEST_PATH_IMAGE219
binary quantized data of bit
Figure DEST_PATH_IMAGE220
is sent to FC. all
Figure 182262DEST_PATH_IMAGE214
sensors produced a total of
Figure 349938DEST_PATH_IMAGE214
quantitative data
Figure DEST_PATH_IMAGE221
. FC receives from all sensors
Figure 427003DEST_PATH_IMAGE214
Quantized data, and send them to the quantized fusion estimator shown in Figure 5 (also note that at this time, the estimation function in Figure 5
Figure DEST_PATH_IMAGE222
has been optimized
Figure 47340DEST_PATH_IMAGE213
alternative), and finally output the estimated value of the original information
Figure 497913DEST_PATH_IMAGE137
.

在本申请的实施例中，考察所提出的基于多元概率量化的分布式信息估计方法在实际环境中对原始信息的估计性能，如前文所述我们在这里使用原始信息与其估计值的均方误差（MSE）作为评估准则，MSE越小表示估计性能越好。特别地，我们实验了当整个网络的总量化比特数变化的时候，网络对原始信息估计的MSE性能，并将其与目前最优的二元量化SQMLF方法和在二元量化（一比特量化）下对原始信息估计能达到的理论最小MSE下界进行比较。从图6可以看出，尽管使用二元量化的限定下，SQMLF方法已经几乎在任何时候都完全逼近对原始信息估计的MSE下界，但使用多元概率量化方法的分布式无线传感器网络对原始信息的估计MSE要远小于这两者，这意味着在不考虑对传感器上量化数据的比特数进行限制的情况下，我们提出的多元概率量化方法要优于任何一种二元量化的方法。此外，可以观察到，多元量化概率方法在网络的总比特数变化的情况下，仍然保持了随总量化比特数近似线性递减的能力。这验证了我们所提出的多元概率量化方法在分布式无线传感器网络中的高效估计性能，以及对实际环境中网络的总量化比特数动态变化的适应性和拓展性。In the embodiment of this application, we examine the estimation performance of the proposed distributed information estimation method based on multivariate probability quantification on the original information in the actual environment. As mentioned above, we use the mean square error of the original information and its estimated value here (MSE) is used as an evaluation criterion, and the smaller the MSE, the better the estimation performance. In particular, we experimented with the MSE performance of the network's estimated raw information when the total number of quantization bits of the entire network varies, and compared it with the current optimal binary quantization SQMLF method and in binary quantization (one-bit quantization ) to compare the theoretical minimum MSE lower bound that the original information estimate can achieve. It can be seen from Figure 6 that although the SQMLF method has almost completely approached the MSE lower bound of the original information estimation under the limitation of binary quantization, the distributed wireless sensor network using the multivariate probability quantization method does not The estimated MSE is much smaller than the two, which means that the proposed multivariate probability quantization method is better than any binary quantization method without considering the limitation on the number of bits of quantized data on the sensor. In addition, it can be observed that the multivariate quantization probability method still maintains the ability to approximately linearly decrease with the total number of quantized bits when the total number of bits in the network changes. This verifies the efficient estimation performance of our proposed multivariate probability quantization method in distributed wireless sensor networks, as well as its adaptability and scalability to the dynamic change of the total quantization bit number of the network in the actual environment.

上述说明示出并描述了本发明的一个优选实施例，但如前所述，应当理解本发明并非局限于本文所披露的形式，不应看作是对其他实施例的排除，而可用于各种其他组合、修改和环境，并能够在本文所述发明构想范围内，通过上述教导或相关领域的技术或知识进行改动。而本领域人员所进行的改动和变化不脱离本发明的精神和范围，则都应在本发明所附权利要求的保护范围内。The above description shows and describes a preferred embodiment of the present invention, but as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various Various other combinations, modifications, and environments can be made within the scope of the inventive concept described herein, by the above teachings or by skill or knowledge in the relevant field. However, changes and changes made by those skilled in the art do not depart from the spirit and scope of the present invention, and should all be within the protection scope of the appended claims of the present invention.

Claims (9)

1. A distributed information estimation method based on multivariate probability quantization is characterized in that: the method comprises the following steps:
s1, constructing a distributed information estimation scene: the system comprises a fusion center FC positioned in the center of a wireless communication network and a plurality of sensors distributed at the edge of the wireless communication network;
each sensor is responsible for the raw information required by the fusion center
Figure DEST_PATH_IMAGE001
Observing to obtain local observation data of the user, performing multivariate probability quantization operation on the local observation data, converting continuous observation data into binary discrete data which can be used for digital communication, and sending the binary discrete data to a fusion center FC; the FC fusion center estimates original information according to the quantitative data sent by all the sensors;
s2, constructing a multivariate probability quantizer for quantizing local observation data by a sensor;
the step S2 includes:
s201, observing original information by a sensor
Figure DEST_PATH_IMAGE002
Obtaining local observations
Figure DEST_PATH_IMAGE003
By using
Figure DEST_PATH_IMAGE004
To express the observed value
Figure 534832DEST_PATH_IMAGE003
Relative to what is observed
Figure 248710DEST_PATH_IMAGE002
To describe randomness therebetween;
s202, obtaining an observed value by a sensor
Figure 359273DEST_PATH_IMAGE003
Then inputting the data into a multi-element probability quantizer and outputting a final quantization result
Figure DEST_PATH_IMAGE005
Quantifying the results
Figure DEST_PATH_IMAGE006
Is a one contains
Figure DEST_PATH_IMAGE007
Binary data of bits:
inside the quantizer, the observed value of the input
Figure 207012DEST_PATH_IMAGE003
Is first fed into a multivariate quantization probability function
Figure DEST_PATH_IMAGE008
Is mapped to one
Figure DEST_PATH_IMAGE009
Probability vector of dimension
Figure DEST_PATH_IMAGE010
Probability vector
Figure DEST_PATH_IMAGE011
All of the elements in (1) are
Figure DEST_PATH_IMAGE012
The interval takes a value while satisfying the sum of 1, i.e.
Figure DEST_PATH_IMAGE013
（1）
Wherein,
Figure DEST_PATH_IMAGE014
is a function of design parameters
Figure DEST_PATH_IMAGE015
A variable function of control having
Figure DEST_PATH_IMAGE016
（2）
Wherein
Figure DEST_PATH_IMAGE017
Comprises a
Figure DEST_PATH_IMAGE018
All of the parameters that can be adjusted in (c),
Figure DEST_PATH_IMAGE019
is the number of design parameters; by varying design parameters
Figure DEST_PATH_IMAGE020
By changing the parameter function accordingly
Figure 199546DEST_PATH_IMAGE018
The functional expressions and structures of (a);
from
Figure 694113DEST_PATH_IMAGE018
Output probability vector
Figure DEST_PATH_IMAGE021
Then fed into the quantization function
Figure DEST_PATH_IMAGE022
In the method, a decimal one-dimensional discrete value is output
Figure DEST_PATH_IMAGE023
Then we go through decimal
Figure DEST_PATH_IMAGE024
Quantization result converted into binary
Figure DEST_PATH_IMAGE025
(ii) a For quantization function
Figure DEST_PATH_IMAGE026
Its output
Figure DEST_PATH_IMAGE027
A share of
Figure DEST_PATH_IMAGE028
Different results, it is desirable to make
Figure 321665DEST_PATH_IMAGE024
Taking each kind of knotThe probability of the fruit is totally composed of
Figure 458249DEST_PATH_IMAGE028
Probability vector of dimension
Figure DEST_PATH_IMAGE029
Control, i.e. effecting
Figure DEST_PATH_IMAGE030
（3）
Wherein
Figure DEST_PATH_IMAGE031
Representing observations at a given input multivariate probability quantizer
Figure DEST_PATH_IMAGE032
Under the premise of (1), output is quantized
Figure DEST_PATH_IMAGE033
Take a value of
Figure DEST_PATH_IMAGE034
The probability of (d);
s3, optimizing design parameters of multi-element quantization probability function
Figure DEST_PATH_IMAGE035
；
S4, designing a quantitative fusion estimator by a fusion center FC and optimizing to obtain an optimal estimation function
Figure DEST_PATH_IMAGE036
；
S5. Based on
Figure 299033DEST_PATH_IMAGE035
And
Figure 495659DEST_PATH_IMAGE036
the distributed information estimation is quantized with multivariate probability.
2. The distributed information estimation method based on multivariate probability quantization as claimed in claim 1, characterized in that: when each sensor observes the original information, the observation noises influenced by the environment are independently and identically distributed, and all the sensors use the same multivariate probability quantizer structure.
3. The distributed information estimation method based on multivariate probability quantization as claimed in claim 1, characterized in that: the quantization function
Figure DEST_PATH_IMAGE037
Is inputted by
Figure DEST_PATH_IMAGE038
Probability vector of dimension
Figure DEST_PATH_IMAGE039
The output being a one-dimensional discrete value
Figure DEST_PATH_IMAGE040
It is composed of
Figure DEST_PATH_IMAGE041
The serial sublayers with the same structure are composed, and the specific structure functions are as follows:
inputting: input device
Figure 623890DEST_PATH_IMAGE038
Probability vector of dimension
Figure DEST_PATH_IMAGE042
And an initial quantization value
Figure DEST_PATH_IMAGE043
；
The input of the mth sublayer is the output of the previous sublayer, M =1,2, …, M
Figure DEST_PATH_IMAGE044
Vector of dimensions
Figure DEST_PATH_IMAGE045
And quantized value
Figure DEST_PATH_IMAGE046
(ii) a First, in the m-th sublayer, to be inputted
Figure DEST_PATH_IMAGE047
Divided into two sub-vectors of equal length, each containing
Figure 737733DEST_PATH_IMAGE047
All elements of the first half and all elements of the second half, i.e. two
Figure DEST_PATH_IMAGE048
Subvectors of dimension
Figure DEST_PATH_IMAGE049
And
Figure DEST_PATH_IMAGE050
(ii) a Then, the m sub-layer utilizes
Figure DEST_PATH_IMAGE051
And
Figure DEST_PATH_IMAGE052
outputting the quantized value
Figure DEST_PATH_IMAGE053
In which
Figure DEST_PATH_IMAGE054
（4）
Figure DEST_PATH_IMAGE055
Is [0,1]Random noise, function, evenly distributed over intervals
Figure DEST_PATH_IMAGE056
Inputting a non-negative number and outputting 1, otherwise, inputting a negative number and outputting 0; definition of
Figure DEST_PATH_IMAGE057
The mth sublayer output
Figure DEST_PATH_IMAGE058
Vector of dimensions
Figure DEST_PATH_IMAGE059
Wherein
Figure DEST_PATH_IMAGE060
(5) And (3) outputting: quantization function
Figure DEST_PATH_IMAGE061
Output quantized value of
Figure DEST_PATH_IMAGE062
Is that it is
Figure DEST_PATH_IMAGE063
Quantized values output by the sub-layers
Figure DEST_PATH_IMAGE064
I.e. by
Figure DEST_PATH_IMAGE065
。
4. A multivariate based probability mass as defined in claim 1The distributed information estimation method is characterized by comprising the following steps: in the step S3, bayesian estimation theory is used, and the method is considered
Figure DEST_PATH_IMAGE066
After the determined sensor quantifies the local observation, an estimated MSE lower bound which can be reached by using the quantified data is found in the fusion center to find the optimal design parameter suitable for the current observation environment
Figure DEST_PATH_IMAGE067
And corresponding use-optimized design parameters on the sensor
Figure 894739DEST_PATH_IMAGE067
Is optimized for the multivariate quantization probability function
Figure DEST_PATH_IMAGE068
。
5. The distributed information estimation method based on multivariate probability quantization as claimed in claim 4, wherein: the step S3 includes:
are all provided with
Figure DEST_PATH_IMAGE069
The independent sensors are distributed in the whole network, each sensor adopts the step S2 to construct a multi-element probability quantizer structure, and all the multi-element probability quantizers use the same multi-element quantization probability function
Figure DEST_PATH_IMAGE070
And corresponding design parameters
Figure DEST_PATH_IMAGE071
；
Figure 294890DEST_PATH_IMAGE069
Each sensor respectively corresponding to the original information
Figure DEST_PATH_IMAGE072
Observing to obtain own local observation data with observation noise
Figure DEST_PATH_IMAGE073
；
Considering the presence of independent and identically distributed observation noise on each sensor, and defining a probability density function
Figure DEST_PATH_IMAGE074
To describe the distribution of observed noise: for the first
Figure DEST_PATH_IMAGE075
A sensor, its local observation data
Figure DEST_PATH_IMAGE076
Is quantized into a plurality of elements by a local multivariate probability quantizer
Figure DEST_PATH_IMAGE077
Binary data of bits
Figure DEST_PATH_IMAGE078
And is sent to the FC of the network center, so
Figure 569139DEST_PATH_IMAGE069
A sensor jointly generates
Figure 765634DEST_PATH_IMAGE069
An
Figure 346788DEST_PATH_IMAGE077
Quantized data of bits
Figure DEST_PATH_IMAGE079
And sending the information to the FC, wherein the FC needs to estimate the original information by using all received quantized data;
quantitative data on all sensors at a given time by Bayesian probability theory
Figure DEST_PATH_IMAGE080
Also in the case of (2), since they are independently and identically distributed, based on the probability distribution of the quantized data, it is first calculated when the FC receives the quantized data
Figure 730889DEST_PATH_IMAGE079
For the original information
Figure 318865DEST_PATH_IMAGE080
The lower bound of the estimated MSE that the estimation can achieve, i.e. the lower bound
Figure DEST_PATH_IMAGE081
Figure DEST_PATH_IMAGE082
（6）
Wherein
Figure DEST_PATH_IMAGE083
，
Figure DEST_PATH_IMAGE084
Indicating that FC receives all the quantized data sent from the sensor,
Figure DEST_PATH_IMAGE085
representing FC utilization quantized data
Figure DEST_PATH_IMAGE086
What can be achieved is
Figure DEST_PATH_IMAGE087
Arbitrary estimation ofEvaluating the value, correspondingly to the left of the inequality in the formula
Figure DEST_PATH_IMAGE088
Representing original information
Figure 442022DEST_PATH_IMAGE087
And its estimated value
Figure DEST_PATH_IMAGE089
The MSE between the two is the MSE,
Figure DEST_PATH_IMAGE090
shows the operation of calculating mathematical expectation, the right side of the inequality in the formula (6) shows the lower bound of the MSE,
Figure DEST_PATH_IMAGE091
is the number of combinations in the mathematical definition,
Figure DEST_PATH_IMAGE092
（7）
is based on a multivariate quantization probability function
Figure DEST_PATH_IMAGE093
Design parameters of
Figure DEST_PATH_IMAGE094
And original information
Figure DEST_PATH_IMAGE095
The determined series of intermediate calculation terms, as can be seen from equation (6), are in the original information
Figure 441464DEST_PATH_IMAGE095
Probability distribution and observed noise distribution of
Figure DEST_PATH_IMAGE096
Are all determinedFC utilizes quantized data pairs
Figure 337745DEST_PATH_IMAGE095
MSE estimated, i.e.
Figure DEST_PATH_IMAGE097
Whose lower bound is fully defined by the multivariate quantization probability function
Figure 147438DEST_PATH_IMAGE093
Design parameters of
Figure 233205DEST_PATH_IMAGE094
Determining;
minimizing the right side of the inequality in equation (6) by an algorithm
Figure DEST_PATH_IMAGE098
The determined FC uses the lower bound of the MSE estimated by the quantized data on the original information to find the optimal design parameter adapted to the current observation environment
Figure DEST_PATH_IMAGE099
And corresponding optimal multivariate quantization probability function
Figure DEST_PATH_IMAGE100
。
6. The distributed information estimation method based on multivariate probability quantization as claimed in claim 5, wherein: in the step S3, optimal design parameters suitable for the current observation environment are obtained
Figure 900203DEST_PATH_IMAGE099
And corresponding optimal multivariate quantization probability function
Figure 436227DEST_PATH_IMAGE100
The process comprises the following steps:
a1, setting the total number of sensors as
Figure DEST_PATH_IMAGE101
Sample set
Figure DEST_PATH_IMAGE102
,
Figure DEST_PATH_IMAGE103
Is the total number of samples contained in the sample set,
Figure DEST_PATH_IMAGE104
is a sample of the original information that was,
Figure DEST_PATH_IMAGE105
indicates the serial number of the sample, and
Figure DEST_PATH_IMAGE106
representing sensor versus raw information samples
Figure 47730DEST_PATH_IMAGE104
Total observations
Figure DEST_PATH_IMAGE107
Obtained by
Figure 452036DEST_PATH_IMAGE107
(ii) an observation sample; setting initial design parameters
Figure DEST_PATH_IMAGE108
Setting the tolerance threshold of iteration to
Figure DEST_PATH_IMAGE109
Setting an initial iteration count to
Figure DEST_PATH_IMAGE110
；
A2 is atFirst, the
Figure DEST_PATH_IMAGE111
In the second iteration, the pairs are shown in formula (7)
Figure DEST_PATH_IMAGE112
Definition of (2) to
Figure DEST_PATH_IMAGE113
Is calculated by
Figure DEST_PATH_IMAGE114
Multivariate quantization probability function design parameters obtained in sub-iteration
Figure DEST_PATH_IMAGE115
A determined series of intermediate calculation terms
Figure DEST_PATH_IMAGE116
Wherein
Figure DEST_PATH_IMAGE117
（8）
A3, using the formula (8)
Figure DEST_PATH_IMAGE118
And sample set
Figure DEST_PATH_IMAGE119
The lower MSE bound on the right side of the inequality in equation (6) is approximately calculated as
Figure DEST_PATH_IMAGE120
Figure DEST_PATH_IMAGE121
（9）
Then using the interior point method and the gradient descent method, the following minimization problem is solved
Figure DEST_PATH_IMAGE122
（10）
Obtaining new design parameters after solving
Figure DEST_PATH_IMAGE123
；
A4, calculating and checking convergence conditions
Figure DEST_PATH_IMAGE124
Whether or not:
if not, the explanation needs to continue iteration, and needs to be
Figure DEST_PATH_IMAGE125
Step A2 is carried out to carry out the next iteration, and the iteration count is updated
Figure DEST_PATH_IMAGE126
(ii) a If the convergence condition is established, outputting
Figure DEST_PATH_IMAGE127
As an optimal design parameter, and determining a corresponding optimal multivariate quantization probability function
Figure DEST_PATH_IMAGE128
。
7. The distributed information estimation method based on multivariate probability quantization as claimed in claim 5, wherein: the step S4 includes:
s401.FC reception from
Figure DEST_PATH_IMAGE129
Transmitted from a sensor
Figure 748107DEST_PATH_IMAGE129
Quantized data
Figure DEST_PATH_IMAGE130
And inputting it into the quantization fusion estimator, and outputting the original information
Figure DEST_PATH_IMAGE131
Is estimated value of
Figure DEST_PATH_IMAGE132
；
In the quantitative fusion estimator, of the input
Figure DEST_PATH_IMAGE133
An
Figure DEST_PATH_IMAGE134
Binary quantized data of bits
Figure DEST_PATH_IMAGE135
Is first converted into
Figure 171478DEST_PATH_IMAGE133
Is arranged at
Figure DEST_PATH_IMAGE136
Mean decimal discrete data
Figure DEST_PATH_IMAGE137
；
Figure 486921DEST_PATH_IMAGE133
Decimal data
Figure DEST_PATH_IMAGE138
Then the data is sent to an Onehot function for carrying out one-hot coding operation to obtain the corresponding data
Figure 976809DEST_PATH_IMAGE133
One-hot coded vector
Figure DEST_PATH_IMAGE139
；
S402, with the first
Figure DEST_PATH_IMAGE141
Decimal data
Figure DEST_PATH_IMAGE142
By way of example only, it is possible to use,
Figure DEST_PATH_IMAGE143
is its corresponding one-hot coded vector,
Figure DEST_PATH_IMAGE144
is composed of
Figure DEST_PATH_IMAGE145
binary data of bit length, to
Figure DEST_PATH_IMAGE146
In total of
Figure 867666DEST_PATH_IMAGE145
The bits bit are numbered in sequence as
Figure DEST_PATH_IMAGE147
Bit, decimal data
Figure DEST_PATH_IMAGE148
The value range of (1) is just the serial number of all bits, and the one-hot coding means that only one bit is coded
Figure DEST_PATH_IMAGE149
To
Figure DEST_PATH_IMAGE150
The bit will be set to 1 and all the rest of the bit bits will be set to 0, i.e. the bit is set to 1
Figure DEST_PATH_IMAGE151
，
Figure DEST_PATH_IMAGE152
（11）
Then, the process of the present invention is carried out,
Figure DEST_PATH_IMAGE153
one-hot coded vector
Figure DEST_PATH_IMAGE154
Is sent to an averager to obtain their mean vectors
Figure DEST_PATH_IMAGE155
；
After that
Figure DEST_PATH_IMAGE156
Is then fed into the estimation function
Figure DEST_PATH_IMAGE157
In the method, an estimated value of the original information is output
Figure DEST_PATH_IMAGE158
，
Figure DEST_PATH_IMAGE159
Is also a design parameter
Figure DEST_PATH_IMAGE160
A function of control, i.e.
Figure DEST_PATH_IMAGE161
Figure DEST_PATH_IMAGE162
（12）
Wherein
Figure DEST_PATH_IMAGE163
Comprises a
Figure DEST_PATH_IMAGE164
All of the adjustable parameters;
s403. When the same multivariate probability quantizer is used on all the sensors, and the multivariate probability quantizer with the same optimal design parameters is used
Figure DEST_PATH_IMAGE165
Of the multivariate quantization probability function
Figure DEST_PATH_IMAGE166
The quantized data sent by all sensors to the FC is compared to the original information
Figure DEST_PATH_IMAGE167
Are conditionally independent and identically distributed;
at the moment, based on Bayesian estimation theory and probability model, the estimation value of FC to the original information is calculated
Figure DEST_PATH_IMAGE168
With the original information
Figure DEST_PATH_IMAGE169
MSE between
Figure DEST_PATH_IMAGE170
Figure DEST_PATH_IMAGE171
（13）
Figure DEST_PATH_IMAGE172
In order to estimate the MSE,
Figure DEST_PATH_IMAGE173
（14）
following the pair in equation (7)
Figure DEST_PATH_IMAGE174
By quantifying the optimal design parameters of the probability function
Figure DEST_PATH_IMAGE175
And original information
Figure DEST_PATH_IMAGE176
A determined series of intermediate calculation terms;
the optimal design parameters in the multivariate quantization probability function obtained from the formula (13)
Figure 929514DEST_PATH_IMAGE175
The MSE estimated on FC for the original information is determined entirely by the estimation function
Figure DEST_PATH_IMAGE177
Variable design parameters of
Figure DEST_PATH_IMAGE178
Controlling;
s404, a series of samples based on the original information collected from the actual observation environment and the local observation data of the sensor, and an optimal multivariate quantization probability function on the sensor
Figure DEST_PATH_IMAGE179
Solving the optimum estimation function design parameters that minimize the estimated MSE on FC
Figure DEST_PATH_IMAGE180
。
8. The distributed information estimation method based on multivariate probability quantization as claimed in claim 7, wherein: the step S404 includes:
b1, total number of input sensors
Figure DEST_PATH_IMAGE181
Optimal multivariate quantization probability function on sensor
Figure 122466DEST_PATH_IMAGE179
And their corresponding optimum design parameters
Figure DEST_PATH_IMAGE182
Sample set
Figure DEST_PATH_IMAGE183
Following the pair in equation (14)
Figure DEST_PATH_IMAGE184
Definition of (2) to arbitrary
Figure DEST_PATH_IMAGE185
Will be composed of
Figure DEST_PATH_IMAGE186
And original information samples
Figure DEST_PATH_IMAGE187
Intermediate item of decision
Figure DEST_PATH_IMAGE188
Is approximately calculated as
Figure DEST_PATH_IMAGE189
（15）
Setting initial settingsMetering parameters
Figure DEST_PATH_IMAGE190
Setting the tolerance threshold of iteration to
Figure DEST_PATH_IMAGE191
Setting an initial iteration count to
Figure DEST_PATH_IMAGE192
；
B2 in the first
Figure DEST_PATH_IMAGE193
In the second iteration, define
Figure DEST_PATH_IMAGE194
For the estimated MSE at FC, using equation (13),
Figure DEST_PATH_IMAGE195
and the design parameters obtained in the first iteration
Figure DEST_PATH_IMAGE196
Will be
Figure DEST_PATH_IMAGE197
Is approximately calculated as
Figure DEST_PATH_IMAGE198
Figure DEST_PATH_IMAGE199
（16）
Using the interior point method and the gradient descent method, the following minimization problem is solved
Figure DEST_PATH_IMAGE200
（17）
Obtaining new design parameters
Figure DEST_PATH_IMAGE201
；
B3, calculating and checking convergence conditions
Figure DEST_PATH_IMAGE202
Whether the result is true or not; if not, continue iteration, will
Figure DEST_PATH_IMAGE203
Step B2 is carried out for the next iteration, and the iteration count is updated
Figure DEST_PATH_IMAGE204
(ii) a If the convergence condition is established, outputting
Figure DEST_PATH_IMAGE205
As optimal design parameters and determining corresponding optimal estimation functions
Figure DEST_PATH_IMAGE206
。
9. The distributed information estimation method based on multivariate probability quantization as claimed in claim 1, characterized in that: the step S5 includes:
Figure DEST_PATH_IMAGE207
individual sensor pair raw information
Figure DEST_PATH_IMAGE208
And (3) respectively observing:
for the first
Figure DEST_PATH_IMAGE209
A sensor, it is to
Figure 561186DEST_PATH_IMAGE208
Obtaining own local observation data after observation
Figure DEST_PATH_IMAGE210
And will be
Figure 601823DEST_PATH_IMAGE210
Fed into a multivariate probability quantizer, multivariate quantization probability functions
Figure DEST_PATH_IMAGE211
Get the best
Figure DEST_PATH_IMAGE212
And finally output
Figure DEST_PATH_IMAGE213
binary quantization data of bit
Figure DEST_PATH_IMAGE214
Is sent to the FC; all of
Figure 218925DEST_PATH_IMAGE207
A sensor jointly generates
Figure 508961DEST_PATH_IMAGE207
Quantized data
Figure DEST_PATH_IMAGE215
；
FC receiving signals from all sensors
Figure 871809DEST_PATH_IMAGE207
Quantizing the data and feeding them into a quantization fusion estimator, estimating the function
Figure DEST_PATH_IMAGE216
Get the best
Figure DEST_PATH_IMAGE217
Finally, the estimated value of the original information is output
Figure DEST_PATH_IMAGE218
。
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