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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CN115290130A (en
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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

The invention discloses a distributed information estimation method based on multivariate probability quantization, which 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; s2, constructing a multivariate probability quantizer for quantizing local observation data by a sensor; s3, optimizing design parameters of multi-element quantization probability function
Figure 493582DEST_PATH_IMAGE001
(ii) a S4, designing a quantitative fusion estimator by a fusion center FC and optimizing to obtain an optimal estimation function
Figure 495036DEST_PATH_IMAGE002
(ii) a S5. Based on
Figure 910580DEST_PATH_IMAGE001
And
Figure 48300DEST_PATH_IMAGE002
the distributed information estimation is quantized with multivariate probability. The method can adapt to the situation that a quantization result has a plurality of elements and keep higher estimation performance.

Description

Distributed information estimation method based on multivariate probability quantization
Technical Field
The invention relates to distributed information estimation, in particular to a distributed information estimation method based on multivariate probability quantization.
Background
Distributed information estimation based on quantized data has been an active area of research. In a typical distributed estimation framework, local sensors send local observation data of raw information to a fusion center. The fusion center receives data sent from different local sensors and estimates unknown original information by using an estimation algorithm. However, due to bandwidth/energy limitations, the local observed data on the sensors typically needs to be quantified before transmission to the fusion center. The use of the same quantizer for all sensors is a widely adopted solution because it simplifies the design issues.
However, many conventional solutions mainly consider the problem of quantizer optimization in an environment where ideally no observation noise exists. And further research into quantizer designs that take into account observed noise conditions is lacking. Furthermore, many performance analyses and theories regarding the optimal quantizer only consider the case of binary quantization, i.e., the length of the quantized data on the sensor is limited to 1 bit. For the case of quantizing the observation data into multi-bit data on the sensor, i.e. there is a plurality of possibilities for quantization results, the corresponding quantizer design scheme is also lack of research.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a distributed information estimation method based on multivariate probability quantization, which can adapt to the situation that a quantization result has multivariate and keep higher estimation performance.
The purpose of the invention is realized by the following technical scheme: a distributed information estimation method based on multivariate probability quantization 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 100002_DEST_PATH_IMAGE001
Observing to obtain own local observation data, 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 the original information according to the quantized data sent by all the sensors；
S2, constructing a multivariate probability quantizer for quantizing local observation data by a sensor;
s3, optimizing design parameters of multi-element quantization probability function
Figure 100002_DEST_PATH_IMAGE002
；
S4, designing a quantitative fusion estimator by a fusion center FC and optimizing to obtain an optimal estimation function
Figure 100002_DEST_PATH_IMAGE003
；
S5. Based on
Figure 503964DEST_PATH_IMAGE002
And
Figure 280159DEST_PATH_IMAGE003
the distributed information estimation is quantized with multivariate probability.
The beneficial effects of the invention are: the multivariate quantization probability method still keeps the capability of approximately linearly decreasing with the total bit number under the condition that the total bit number of the network is changed, and the performance of the multivariate quantization probability method is efficiently estimated in the distributed wireless sensor network.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a distributed information estimation scenario;
FIG. 3 is a block diagram of a multivariate probability quantizer;
FIG. 4 is a diagram of a quantization function structure;
FIG. 5 is a block diagram of a quantized fusion estimator;
fig. 6 is a diagram illustrating MSE estimated by the network for the original information under the condition that the total quantization bit number of the entire network changes.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
Aiming at the problem of information estimation based on a bandwidth/energy limited distributed wireless sensor in a future wireless communication network, the invention designs a distributed information estimation scheme based on multivariate probability quantization: the method comprises the steps of designing a multivariate probability quantizer positioned on a sensor and a corresponding multivariate quantization probability function optimization algorithm; and designing a quantitative fusion estimator positioned on the fusion center and a corresponding estimation function optimization algorithm. Consider a generalized scenario in which a distributed wireless sensor network estimates an unknown raw information, the network comprising a Fusion Center (FC) located at a hub node of the network and a plurality of sensors distributed at different locations at the edge of the network. The original information may be any kind of data required by the network, and is 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, and usually, in an actual environment, due to the influence of environmental noise on the observation, an error exists between the local observation data and the original information. For a sensor with limited bandwidth/energy, the local observation data needs to be quantized first, and the continuous observation data is converted into binary discrete data which can be used for modern digital communication, so that the own observation data can be smoothly sent to the FC. FC can only estimate the raw information using the quantized data sent from all sensors. The measurement index of the estimation performance of the original information generally uses Mean Squared Error (MSE) of the original information and the estimation value thereof, and smaller MSE means more accurate estimation and better estimation performance;
as shown in fig. 1, a distributed information estimation method based on multivariate probability quantization includes the following steps:
s1, constructing a distributed information estimation scene: as shown in fig. 2, the system comprises 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;
each sensor is responsible for the raw information required by the fusion center
Figure 100002_DEST_PATH_IMAGE004
To carry outObserving to obtain own local observation data, 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:
multiple sensors distributed at the edge of the network, together with the original information required by the fusion center
Figure 512426DEST_PATH_IMAGE004
And observing to respectively obtain own local observation. When all sensor observations are considered here, the observation noise affected by the environment is independently and identically distributed. Therefore, to reduce the difficulty in sensor design and deployment, we also consider using the exact same multivariate probability quantizer structure on all sensors, including any adjustable design parameters on the quantizer.
Since independent and identically distributed observation noise on all sensors is considered and the same multivariate quantizer is used. We take an example of any sensor (ignoring sensor numbers) herein to describe the process of observation and data quantization on the sensor, and the structure, function and design scheme of the multivariate probability quantizer. As shown in FIG. 3, the sensor observes the raw information
Figure 100002_DEST_PATH_IMAGE005
Obtaining local observations
Figure 100002_DEST_PATH_IMAGE006
By using
Figure 100002_DEST_PATH_IMAGE007
To represent the observed value
Figure 606503DEST_PATH_IMAGE006
Relative to what is observed
Figure 79597DEST_PATH_IMAGE005
To describe the randomness between them. The sensor obtains the observed value
Figure 495535DEST_PATH_IMAGE006
Then inputting the data into a multi-element probability quantizer and outputting a final quantization result
Figure 100002_DEST_PATH_IMAGE008
Quantifying the results
Figure 100002_DEST_PATH_IMAGE009
Is a one contains
Figure 100002_DEST_PATH_IMAGE010
Binary data of bits. Inside the quantizer, the observed value of the input
Figure 625819DEST_PATH_IMAGE006
Is first fed into a multivariate quantization probability control function
Figure 100002_DEST_PATH_IMAGE011
Is mapped to one
Figure 100002_DEST_PATH_IMAGE012
Probability vector of dimension
Figure 100002_DEST_PATH_IMAGE013
Probability vector
Figure 100002_DEST_PATH_IMAGE014
All of the elements in (1) are
Figure 100002_DEST_PATH_IMAGE015
The interval takes a value while satisfying the sum of 1, i.e.
Figure 100002_DEST_PATH_IMAGE016
（1）
Wherein, the first and the second end of the pipe are connected with each other,
Figure 100002_DEST_PATH_IMAGE017
is a function of design parameters
Figure 100002_DEST_PATH_IMAGE018
A variable function of control having
Figure 100002_DEST_PATH_IMAGE019
（2）
Wherein
Figure 100002_DEST_PATH_IMAGE020
Comprises a
Figure 100002_DEST_PATH_IMAGE021
All of the parameters that can be adjusted in (c),
Figure 100002_DEST_PATH_IMAGE022
is the number of design parameters. As can be seen from equation (2), by changing the design parameters
Figure 100002_DEST_PATH_IMAGE023
By changing the parameter function accordingly
Figure 602215DEST_PATH_IMAGE021
The functional expressions and structures of (1). From
Figure 333411DEST_PATH_IMAGE021
Output probability vector
Figure 100002_DEST_PATH_IMAGE024
Then fed into the quantization function
Figure 100002_DEST_PATH_IMAGE025
In (a) to (b)
Figure 985497DEST_PATH_IMAGE025
Detailed below and in fig. 4), a decimal one-dimensional discrete value is output
Figure 100002_DEST_PATH_IMAGE026
Then we go through decimal
Figure 100002_DEST_PATH_IMAGE027
Quantization result converted into binary
Figure 100002_DEST_PATH_IMAGE028
. For quantization function
Figure 100002_DEST_PATH_IMAGE029
Its output
Figure 100002_DEST_PATH_IMAGE030
A is common to
Figure 100002_DEST_PATH_IMAGE031
Different results, it is desirable to make
Figure 582569DEST_PATH_IMAGE027
Taking the probability of each result entirely from
Figure 381898DEST_PATH_IMAGE031
Probability vector of dimension
Figure 100002_DEST_PATH_IMAGE032
Control, i.e. effecting
Figure 100002_DEST_PATH_IMAGE033
（3）
Wherein
Figure 100002_DEST_PATH_IMAGE034
Representing observations at a given input multivariate probability quantizer
Figure 100002_DEST_PATH_IMAGE035
Under the premise of (1), output is quantized
Figure 100002_DEST_PATH_IMAGE036
Take a value of
Figure 100002_DEST_PATH_IMAGE037
The probability of (c).
To implement the above-described function of probability quantization of local observation data by the multivariate probability quantizer, we apply quantization function in the multivariate probability quantizer
Figure 72992DEST_PATH_IMAGE029
The structure shown in fig. 4 is designed.
Wherein the function is quantized
Figure 100002_DEST_PATH_IMAGE038
Is inputted by
Figure 100002_DEST_PATH_IMAGE039
Probability vector of dimension
Figure 100002_DEST_PATH_IMAGE040
The output being a one-dimensional discrete value
Figure 100002_DEST_PATH_IMAGE041
It is composed of
Figure 100002_DEST_PATH_IMAGE042
The serial sublayers with the same structure are composed, and the specific structure functions are as follows:
inputting: input device
Figure 817351DEST_PATH_IMAGE039
Probability vector of dimension
Figure 100002_DEST_PATH_IMAGE043
And an initial quantization value
Figure 100002_DEST_PATH_IMAGE044
。
Mth sublayer, M =1,2, …, M: input of mth sublayer (if M =1, its input is
Figure 449189DEST_PATH_IMAGE045
And
Figure 100002_DEST_PATH_IMAGE046
) Is output from the previous sublayer (m-1 th sublayer)
Figure 380105DEST_PATH_IMAGE047
Vector of dimensions
Figure 100002_DEST_PATH_IMAGE048
And quantized value
Figure 100002_DEST_PATH_IMAGE049
(ii) a First, in the m-th sublayer, to be inputted
Figure 100002_DEST_PATH_IMAGE050
Divided into two sub-vectors of equal length, each comprising
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
Subvectors of dimension
Figure 100002_DEST_PATH_IMAGE052
And
Figure 100002_DEST_PATH_IMAGE053
(ii) a Then, the mth sublayer utilizes
Figure 100002_DEST_PATH_IMAGE054
And
Figure 100002_DEST_PATH_IMAGE055
outputting the quantized value
Figure 100002_DEST_PATH_IMAGE056
In which
Figure 100002_DEST_PATH_IMAGE057
（4）
Figure 100002_DEST_PATH_IMAGE058
Is [0,1]Random noise, function, evenly distributed over intervals
Figure 100002_DEST_PATH_IMAGE059
An input non-negative number will output a1, whereas an input negative number will output a 0. Definition of
Figure 100002_DEST_PATH_IMAGE060
The mth sublayer output
Figure 100002_DEST_PATH_IMAGE061
Vector of dimensions
Figure 100002_DEST_PATH_IMAGE062
Wherein
Figure 100002_DEST_PATH_IMAGE063
（5）
And (3) outputting: quantization function
Figure 100002_DEST_PATH_IMAGE064
Is output quantized value
Figure 100002_DEST_PATH_IMAGE065
Is that it is
Figure 100002_DEST_PATH_IMAGE066
Quantized values output by the sub-layers
Figure 100002_DEST_PATH_IMAGE067
I.e. by
Figure 100002_DEST_PATH_IMAGE068
。
With the structure as in FIG. 4, the function is quantized
Figure 484643DEST_PATH_IMAGE064
Implements a quantized value for its output
Figure 100002_DEST_PATH_IMAGE069
Taking the probability of each possible outcome entirely from the probability vector
Figure 100002_DEST_PATH_IMAGE070
To control, the function in equation (3) is implemented.
S3, optimizing design parameters of multi-element quantization probability function
Figure 100002_DEST_PATH_IMAGE071
;
Probability control function is quantized by adjusting the multivariate in the multivariate probability quantizer on the sensor as shown in equations (2) and (3)
Figure 100002_DEST_PATH_IMAGE072
Design parameters of
Figure 100002_DEST_PATH_IMAGE073
Can be varied accordingly
Figure 731341DEST_PATH_IMAGE072
And further changing the probability distribution of the quantized data on the sensor relative to the local observed data and the original information. This means that we can optimize the multivariate quantization probability function for the original information subject to different random distributions and the observation noise with different random characteristics under different observation environments
Figure 872472DEST_PATH_IMAGE072
Design parameters of
Figure 698346DEST_PATH_IMAGE073
To obtain the optimal quantized data probability distribution adapted to the current environment. By using Bayesian estimation theory, we consider minimizing the channel by an algorithm
Figure 63468DEST_PATH_IMAGE073
And determining an estimated MSE lower bound which can be achieved by using quantized data in the fusion center after the sensor quantizes the local observation so as to find out the optimal design parameter suitable for the current observation environment
Figure 100002_DEST_PATH_IMAGE074
And corresponding use-optimized design parameters on the sensor
Figure 138740DEST_PATH_IMAGE074
Is optimized to a multivariate quantization probability function
Figure 83562DEST_PATH_IMAGE071
。
We assume a common
Figure 100002_DEST_PATH_IMAGE075
The individual sensors are distributed throughout the network, a multivariate probability quantizer structure as shown in FIG. 3 is used on all sensors, and we use the exact same multivariate quantization probability function in all multivariate probability quantizers
Figure 761013DEST_PATH_IMAGE072
And corresponding design parameters
Figure 562616DEST_PATH_IMAGE073
So as to reduce the design cost and difficulty of the whole network.
Figure 594025DEST_PATH_IMAGE075
Each sensor is used for respectively comparing the original information
Figure 100002_DEST_PATH_IMAGE076
Observing to obtain own local observation data with observation noise
Figure 100002_DEST_PATH_IMAGE077
. We consider the presence of independent identically distributed observation noise on each sensor and define a probability density function
Figure 100002_DEST_PATH_IMAGE078
To describe the distribution of observed noise: for the first
Figure 100002_DEST_PATH_IMAGE079
A sensor, its local observation data
Figure 100002_DEST_PATH_IMAGE080
Is quantized into a plurality of probability quantizers through a local multivariate probability quantizer
Figure 100002_DEST_PATH_IMAGE081
Binary data of bits
Figure 100002_DEST_PATH_IMAGE082
And sent to the FC at the hub. Therefore, it is not only easy to use
Figure 762445DEST_PATH_IMAGE075
A sensor jointly generates
Figure 500594DEST_PATH_IMAGE075
An
Figure 676360DEST_PATH_IMAGE081
Quantized data of bits
Figure 100002_DEST_PATH_IMAGE083
And sent to the FC, which needs to estimate the original information using all the received quantized data.
Quantitative data on all sensors at a given time by Bayesian probability theory
Figure 100002_DEST_PATH_IMAGE084
Are independently and simultaneously distributed. Therefore, based on the probability distribution of the quantized data, first, the quantized data is calculated when the FC receives the quantized data
Figure 726225DEST_PATH_IMAGE083
For the original information
Figure 12850DEST_PATH_IMAGE084
The lower bound of the estimated MSE that the estimation can achieve, i.e. the lower bound
Figure 100002_DEST_PATH_IMAGE085
Figure 100002_DEST_PATH_IMAGE086
（6）
Wherein
Figure 100002_DEST_PATH_IMAGE087
，
Figure 100002_DEST_PATH_IMAGE088
Indicating that FC receives all the quantized data sent from the sensor,
Figure 100002_DEST_PATH_IMAGE089
representing FC utilization quantized data
Figure 100002_DEST_PATH_IMAGE090
What can be achieved is
Figure 100002_DEST_PATH_IMAGE091
Respectively, to the left of the inequality in the formula
Figure 100002_DEST_PATH_IMAGE092
Representing original information
Figure 841391DEST_PATH_IMAGE091
And itEstimated value
Figure 100002_DEST_PATH_IMAGE093
The MSE between the two is the MSE,
Figure 100002_DEST_PATH_IMAGE094
represents the operation of calculating mathematical expectation, the right side of the inequality in the formula (6) represents the lower bound of the calculated MSE,
Figure 100002_DEST_PATH_IMAGE095
is the number of combinations in the mathematical definition,
Figure 100002_DEST_PATH_IMAGE096
（7）
is formed by multi-component quantization of probability functions
Figure 100002_DEST_PATH_IMAGE097
Design parameters of
Figure 100002_DEST_PATH_IMAGE098
And original information
Figure 100002_DEST_PATH_IMAGE099
A series of intermediate calculation terms for the decision. As can be seen from equation (6), in the original information
Figure 496713DEST_PATH_IMAGE099
Probability distribution and observed noise distribution of
Figure 100002_DEST_PATH_IMAGE100
FC with both determinants utilizes quantized data pairs
Figure 502715DEST_PATH_IMAGE099
MSE estimated, i.e.
Figure 100002_DEST_PATH_IMAGE101
Whose lower bound is fully defined by the multivariate quantization probability function
Figure 124190DEST_PATH_IMAGE097
Design parameters of
Figure 571351DEST_PATH_IMAGE098
And (6) determining. Thus, the right side of the inequality in equation (6) is minimized algorithmically by
Figure 100002_DEST_PATH_IMAGE102
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 100002_DEST_PATH_IMAGE103
And corresponding optimal multivariate quantization probability function
Figure 100002_DEST_PATH_IMAGE104
。
Based on the above analysis, we consider an iterative algorithm that approximately solves the optimization problem for the design parameters in each iteration of the algorithm based on a series of samples of raw information collected from the actual observation environment and sensor local observation data, and gradually approaches the optimal design parameters during the iteration process
Figure 216484DEST_PATH_IMAGE103
。
Initialization: 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 a sample of the original information that was,
Figure 100002_DEST_PATH_IMAGE109
indicates the serial number of the sample, and
Figure 100002_DEST_PATH_IMAGE110
representing sensor versus raw information samples
Figure 490208DEST_PATH_IMAGE108
Total observations
Figure 100002_DEST_PATH_IMAGE111
Obtained secondarily
Figure 670302DEST_PATH_IMAGE111
(ii) an observation sample; setting initial design parameters
Figure 100002_DEST_PATH_IMAGE112
Setting the tolerance threshold of iteration to
Figure 100002_DEST_PATH_IMAGE113
Setting an initial iteration count to
Figure 100002_DEST_PATH_IMAGE114
。
The method comprises the following steps: in the first place
Figure 100002_DEST_PATH_IMAGE115
In the second iteration, the pairs are obtained according to the formula (7)
Figure 100002_DEST_PATH_IMAGE116
Definition of (2) to
Figure 100002_DEST_PATH_IMAGE117
Calculating from
Figure 100002_DEST_PATH_IMAGE118
Multivariate quantization probability function design parameters obtained in sub-iteration
Figure 100002_DEST_PATH_IMAGE119
A series of intermediate calculation items of the decision
Figure 100002_DEST_PATH_IMAGE120
Wherein
Figure 100002_DEST_PATH_IMAGE121
（8）
Step two: using the equation (8)
Figure 100002_DEST_PATH_IMAGE122
And sample set
Figure 100002_DEST_PATH_IMAGE123
The lower MSE 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）
Then using the interior point method and the gradient descent method, the following minimization problem is solved
Figure 100002_DEST_PATH_IMAGE126
（10）
Obtaining new design parameters after solving
Figure 100002_DEST_PATH_IMAGE127
。
Step three: calculating and viewing convergence criteria
Figure 100002_DEST_PATH_IMAGE128
Whether or not this is true.
If not, the explanation needs to continue iteration, and needs to be
Figure 100002_DEST_PATH_IMAGE129
Step A2 is carried out to carry out the next iteration, and the iteration count is updated
Figure 100002_DEST_PATH_IMAGE130
(ii) a If the convergence condition is established, outputting
Figure 100002_DEST_PATH_IMAGE131
As an optimal design parameter.
And (3) outputting: optimum design parameters
Figure 828095DEST_PATH_IMAGE103
The optimal design parameters can be obtained through the algorithm
Figure 250986DEST_PATH_IMAGE103
And corresponding to the optimal multivariate quantization probability function
Figure 100002_DEST_PATH_IMAGE132
。
S4, designing a quantitative fusion estimator by a fusion center FC and optimizing to obtain an optimal estimation function
Figure 100002_DEST_PATH_IMAGE133
；
As mentioned in the foregoing description,
Figure 293897DEST_PATH_IMAGE075
a sensor jointly generates
Figure 991595DEST_PATH_IMAGE075
An
Figure 147770DEST_PATH_IMAGE081
Of bits
Figure 275650DEST_PATH_IMAGE083
And sent to the FC, and the FC needs to utilize all received quantized data to correct the original informationThe information is estimated. Therefore, we first present a quantitative fusion estimator design on FC.
As shown in fig. 5, the FC receives a slave
Figure 100002_DEST_PATH_IMAGE134
Transmitted from a sensor
Figure 681224DEST_PATH_IMAGE134
Quantized data
Figure 100002_DEST_PATH_IMAGE135
And inputting it into the quantization fusion estimator, and outputting the original information
Figure 100002_DEST_PATH_IMAGE136
Is estimated value of
Figure 100002_DEST_PATH_IMAGE137
. In the quantitative fusion estimator, of the input
Figure 100002_DEST_PATH_IMAGE138
An
Figure 100002_DEST_PATH_IMAGE139
Binary quantized data of bits
Figure DEST_PATH_IMAGE140
Is first converted into
Figure 819163DEST_PATH_IMAGE138
Is arranged at
Figure 100002_DEST_PATH_IMAGE141
Mean decimal discrete data
Figure 100002_DEST_PATH_IMAGE142
；
Figure 16795DEST_PATH_IMAGE138
Decimal data
Figure 100002_DEST_PATH_IMAGE143
Then the data is sent to an Onehot function for carrying out one-hot coding operation to obtain the corresponding data
Figure 578227DEST_PATH_IMAGE138
One-hot coded vector
Figure 100002_DEST_PATH_IMAGE144
. To a first order
Figure 100002_DEST_PATH_IMAGE145
Decimal data
Figure 100002_DEST_PATH_IMAGE146
By way of example only, it is possible to use,
Figure 100002_DEST_PATH_IMAGE147
is its corresponding one-hot coded vector,
Figure 100002_DEST_PATH_IMAGE148
is composed of
Figure 100002_DEST_PATH_IMAGE149
binary data of bit length to
Figure 100002_DEST_PATH_IMAGE150
In total of
Figure 379086DEST_PATH_IMAGE149
The bits bit are numbered in sequence as
Figure 100002_DEST_PATH_IMAGE151
Bit, decimal data
Figure 100002_DEST_PATH_IMAGE152
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 100002_DEST_PATH_IMAGE153
To (1)
Figure 100002_DEST_PATH_IMAGE154
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 100002_DEST_PATH_IMAGE155
，
Figure 100002_DEST_PATH_IMAGE156
（11）
Then, the process of the present invention is carried out,
Figure 100002_DEST_PATH_IMAGE157
one-hot coded vector
Figure 100002_DEST_PATH_IMAGE158
Is fed into an averager to obtain their mean vectors
Figure 100002_DEST_PATH_IMAGE159
；
After that
Figure 100002_DEST_PATH_IMAGE160
Is then fed into the estimation function
Figure 100002_DEST_PATH_IMAGE161
In the method, an estimated value of the original information is output
Figure 100002_DEST_PATH_IMAGE162
，
Figure 100002_DEST_PATH_IMAGE163
Is also a design parameter
Figure 100002_DEST_PATH_IMAGE164
A function of control, i.e.
Figure 100002_DEST_PATH_IMAGE165
Figure 100002_DEST_PATH_IMAGE166
（12）
Wherein
Figure 100002_DEST_PATH_IMAGE167
Comprises a
Figure 100002_DEST_PATH_IMAGE168
All adjustable parameters in (1).
When the same multivariate probability quantizer as shown in FIG. 3 is used on all sensors, and with the same optimal design parameters
Figure 100002_DEST_PATH_IMAGE169
Of the multivariate quantization probability function
Figure 100002_DEST_PATH_IMAGE170
The quantized data sent by all sensors to the FC is compared to the original information
Figure 100002_DEST_PATH_IMAGE171
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 100002_DEST_PATH_IMAGE172
With the original information
Figure 100002_DEST_PATH_IMAGE173
MSE between
Figure 100002_DEST_PATH_IMAGE174
Figure 100002_DEST_PATH_IMAGE175
（13）
Figure 100002_DEST_PATH_IMAGE176
In order to estimate the MSE,
Figure 100002_DEST_PATH_IMAGE177
（14）
following the pair in equation (7)
Figure 100002_DEST_PATH_IMAGE178
By quantifying the optimal design parameters of the probability function
Figure 100002_DEST_PATH_IMAGE179
And original information
Figure 100002_DEST_PATH_IMAGE180
A determined series of intermediate calculation terms;
the optimal design parameters of the probability function in the multivariate quantization are obtained from the formula (13)
Figure 452476DEST_PATH_IMAGE179
The MSE estimated on FC for the original information is determined entirely by the estimation function
Figure 100002_DEST_PATH_IMAGE181
Variable design parameters of
Figure 100002_DEST_PATH_IMAGE182
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 100002_DEST_PATH_IMAGE183
Solving the optimum estimation function design parameters that minimize the estimated MSE on FC
Figure 100002_DEST_PATH_IMAGE184
。
Initialization: total number of input sensors
Figure 100002_DEST_PATH_IMAGE185
Optimal multivariate quantization probability function on sensor
Figure 16531DEST_PATH_IMAGE183
And corresponding optimum design parameters
Figure 100002_DEST_PATH_IMAGE186
Sample set
Figure 100002_DEST_PATH_IMAGE187
Following the pair in equation (14)
Figure 100002_DEST_PATH_IMAGE188
For any of
Figure 100002_DEST_PATH_IMAGE189
Will be composed of
Figure 100002_DEST_PATH_IMAGE190
And original information samples
Figure 100002_DEST_PATH_IMAGE191
Intermediate item of decision
Figure 100002_DEST_PATH_IMAGE192
Is approximately calculated as
Figure 100002_DEST_PATH_IMAGE193
（15）
Setting initial design parameters
Figure 100002_DEST_PATH_IMAGE194
Setting the tolerance threshold of iteration to
Figure 100002_DEST_PATH_IMAGE195
Setting an initial iteration count to
Figure 100002_DEST_PATH_IMAGE196
。
The method comprises the following steps: in the first place
Figure 100002_DEST_PATH_IMAGE197
In the second iteration, define
Figure 100002_DEST_PATH_IMAGE198
For the estimated MSE at FC, using equation (13),
Figure 100002_DEST_PATH_IMAGE199
and the design parameters obtained in the first iteration
Figure 100002_DEST_PATH_IMAGE200
Will be
Figure 100002_DEST_PATH_IMAGE201
Is approximately calculated as
Figure 100002_DEST_PATH_IMAGE202
Figure 100002_DEST_PATH_IMAGE203
（16）
Using the interior point method and the gradient descent method, the following minimization problem is solved
Figure 100002_DEST_PATH_IMAGE204
（17）
Obtaining new design parameters
Figure 100002_DEST_PATH_IMAGE205
。
Step two: calculating and viewing convergence criteria
Figure 100002_DEST_PATH_IMAGE206
Whether the result is true or not; if not, continue iteration, will
Figure 100002_DEST_PATH_IMAGE207
Step B2 is carried out to carry out the next iteration and the iteration count is updated
Figure 100002_DEST_PATH_IMAGE208
(ii) a If the convergence condition is established, outputting
Figure 100002_DEST_PATH_IMAGE209
As an optimal design parameter.
And (3) outputting: optimum design parameters
Figure 100002_DEST_PATH_IMAGE210
。
The optimal design parameters can be obtained through the algorithm
Figure 791940DEST_PATH_IMAGE210
And corresponding optimal estimation function
Figure 100002_DEST_PATH_IMAGE211
。
S5. Based on
Figure 100002_DEST_PATH_IMAGE212
And
Figure 100002_DEST_PATH_IMAGE213
the distributed information estimation is quantized with multivariate probability.
Based on the two algorithms, the optimal multivariate quantization probability functions on all the sensors are obtained respectively
Figure 627565DEST_PATH_IMAGE212
And the best estimation function on FC
Figure 470756DEST_PATH_IMAGE213
. Next, we will briefly describeThe whole process of estimating the original information by the whole network. The functional structures of the multivariate probability quantizer on the sensor and the quantized fusion estimator on the FC are described in detail above, and are not described herein again.
First of all, the first step is to,
Figure 100002_DEST_PATH_IMAGE214
individual sensor pair raw information
Figure 100002_DEST_PATH_IMAGE215
The observation was performed separately. To a first order
Figure 100002_DEST_PATH_IMAGE216
An example of a sensor, it
Figure 905630DEST_PATH_IMAGE215
Obtaining own local observation data after observation
Figure 100002_DEST_PATH_IMAGE217
And will be
Figure 605601DEST_PATH_IMAGE217
Into a multivariate probability quantizer as shown in FIG. 3 (note that at this time, the multivariate quantization probability function in FIG. 3
Figure 100002_DEST_PATH_IMAGE218
Has been optimized
Figure 269801DEST_PATH_IMAGE212
Replacement), and finally output
Figure DEST_PATH_IMAGE219
binary quantization data of bit
Figure DEST_PATH_IMAGE220
Is sent to the FC. All of
Figure 182262DEST_PATH_IMAGE214
All sensors shareGenerate a
Figure 349938DEST_PATH_IMAGE214
Quantized data
Figure DEST_PATH_IMAGE221
. FC receiving signals from all sensors
Figure 427003DEST_PATH_IMAGE214
Quantizes the data and feeds them into the quantized fusion estimator shown in fig. 5 (note also that at this point, the estimation function in fig. 5
Figure DEST_PATH_IMAGE222
Has been optimized
Figure 47340DEST_PATH_IMAGE213
Replacement), and finally outputs an estimate of the original information
Figure 497913DEST_PATH_IMAGE137
。
In the embodiment of the present application, considering the estimation performance of the proposed distributed information estimation method based on multivariate probability quantization on original information in a practical environment, as described above, we use the Mean Square Error (MSE) of the original information and its estimation value as an evaluation criterion, and a smaller MSE indicates better estimation performance. Specifically, we have tested the MSE performance of the network on the original information estimate when the total quantized bit number of the entire network changes and compared it with the current optimal binary quantization SQMLF method and the lower bound of the theoretical minimum MSE that can be reached on the original information estimate under binary quantization (one-bit quantization). As can be seen from fig. 6, although the SQMLF method has almost completely approximated the lower MSE bound for the original information at any time with the constraint of binary quantization, the estimated MSE for the original information by the distributed wireless sensor network using the multivariate probability quantization method is much smaller than both, which means that the multivariate probability quantization method we propose is superior to any binary quantization method without considering the constraint on the number of bits of quantized data on the sensor. Furthermore, it can be observed that the multivariate quantization probability approach still maintains the ability to decrease approximately linearly with the total number of quantized bits, as the total number of bits of the network changes. The method verifies the efficient estimation performance of the multivariate probability quantification method in the distributed wireless sensor network and the adaptability and the expansibility of the total quantification bit number dynamic change of the network in the actual environment.
While the foregoing description shows and describes a preferred embodiment of the invention, it is to be understood, as noted above, that the invention is not limited to the form disclosed herein, but is not intended to be exhaustive or to exclude other embodiments and may be used in various other combinations, modifications, and environments and may be modified within the scope of the inventive concept described herein by the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

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 the content of the first and second substances,
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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