CN110750754A - Data processing method based on wireless sensor network in big data environment - Google Patents

Data processing method based on wireless sensor network in big data environment Download PDF

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CN110750754A
CN110750754A CN201910641858.9A CN201910641858A CN110750754A CN 110750754 A CN110750754 A CN 110750754A CN 201910641858 A CN201910641858 A CN 201910641858A CN 110750754 A CN110750754 A CN 110750754A
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filter
data
wireless sensor
sensor network
inequality
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王金玉
刘彤军
王涛
周丽丽
杨洋
甄海涛
邢娜
杨喆
杜寅甫
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Institute of Automation of Heilongjiang Academy of Sciences
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Abstract

A data processing method based on a wireless sensor network in a big data environment is provided. The existing wireless sensor network has the problems of poor accuracy and real-time performance of obtained data, node energy consumption and data post-processing capability. The invention innovatively utilizes the research of a wireless sensor network system to process the delay and loss conditions of data in the system, thereby improving the data transmission precision; a variable definition method is innovatively adopted, and the system is subjected to the amplification and dimension reduction treatment on the basis of a linear matrix inequality method, so that the method is easy to operate and improve the operation speed; the estimation algorithm proposed is more accurate than Kalman filtering.

Description

Data processing method based on wireless sensor network in big data environment
Technical Field
The invention relates to a data processing method in a big data environment based on a wireless sensor network.
Background
Big data is large-scale, particularly complex data, and statistically, the data generated in recent years accounts for 90% of the total data generated by human beings. Meanwhile, global sensing equipment collects information in real time, the data sources are countless, and various sensors such as the internet of things, the mobile internet, cloud computing, personal computers and mobile phones form a complex big data background. A great deal of research is conducted internationally and domestically, the united states uses big data technology to control world data, korea draws up a comprehensive growth plan for cloud computing, amazon introduced desktops and services, IBM introduced private cloud services, and so on. A cloud computing data platform, a Beijing cloud base, a Hangzhou cloud computing service platform, a tin-free cloud computing center and the like are built in part of provinces and cities in China. However, with the increasing amount of data, the traditional mining and storage forms are far from meeting the demand.
The research of Wireless Sensor Networks (WSNs) has just started in the late 90 s of the 20 th century, and has attracted great attention in military, academic and industrial fields in the early 21 st century. The 'national intelligent transportation system project planning' is proposed by the U.S. department of transportation in 1995, and attempts are made to integrate technologies such as information, computers, sensors and the like and preliminarily apply the integrated technologies to a ground transportation management system, so that high efficiency, omnibearing and integrated technologies are realized. The concept of wireless sensor network is firstly proposed in the united states of the seventies of the twentieth century, and then some military and civil wireless sensor network monitoring systems are developed. Since the twenty-first century, the rapid development of sensor technology, microelectronic technology, wireless communication technology, integrated circuit technology, computer technology, and the like has provided a good foundation for the development of wireless sensor networks, and wireless sensor network technology with low power consumption, low cost, and miniaturization has gained a chance of rapid development. Since the research enthusiasm has been raised worldwide, various organizations have fully realized that the wireless sensor network has huge application prospect and commercial value, and governments begin to invest a great deal of expenses for the related research of the wireless sensor network.
In the end of the twentieth century, colleges and scientific research institutions in China begin to explore and research wireless sensor networks, and countries begin to provide corresponding fund funding. In 2006, China releases a compendium for the development of the long-term science and technology in China, emphasizes the acceleration of the research and development of information technology in the compendium for the planning, and particularly proposes the acceleration of the research and application of a wireless sensor network. The intelligent perception and self-organizing network technology related to the technology is listed as the leading-edge technology of the information technology, and a plurality of national scientific research institutions are used as key points to research and develop. Although research on the technical field of WSNs starts somewhat later in China than abroad, research efforts have been increased on WSNs by countries and research institutes. Research is being conducted in the field of WSNs by some scientific research institutions and general universities. The national 863 program and the like also actively pursue and support research on various technologies of WSNs. The WSN is a brand-new information acquisition and processing technology applied to a plurality of fields, the gap between the domestic and foreign aspects of the research level and the work of the WSN is not large, the technical research of the WSN is timely and reasonably developed, the future study, life, work and the like of people are greatly influenced, and the national development, social progress and economic prosperity can be promoted.
The application technology of big data is combined with a wireless sensor network, and is already in logistics, retail sale, communication, medical treatment and electric power
And the like, are widely used and play an important role. Because the wireless sensor is the core part of the Internet of things, a large number of sensor nodes continuously transmit acquired data to the data center to form a mass data stream. The processing and storage of mass data is a great problem to be faced by the wireless sensor network, but currently, related technical research on the management and processing of mass data of the application layer of the wireless sensor network is still relatively few, and there is a great research and development space. In a wireless sensor network, the performance of a data sensing/acquisition technology directly affects the accuracy and real-time performance of acquired data, node energy consumption and data post-processing, such as data transmission. In addition, in a wireless sensor network environment, when a large amount of sensing data is required, each wireless sensor may cause a rapid increase in power consumption in the process of data sensing, data acquisition, data transmission, and the like. The management technology of the wireless sensor network data indicates a new direction for the research of the wireless sensor network application layer software system, and provides a new opportunity.
Disclosure of Invention
The invention aims to solve the problems of poor accuracy and real-time performance of obtained data, node energy consumption and data post-processing capability of the conventional wireless sensor network, and provides a data processing method based on a wireless sensor network in a big data environment.
In the present invention, a linear matrix inequality is used to perform matrix processing, which is introduced as follows, and in recent years, the linear matrix inequality is widely used to solve a series of problems in systems and control. With the popularization of the LMI control tool box in Matlab, the LMI tool has received attention. In practical applications, it is found that many control problems in engineering can be converted into a linear matrix inequality form, a feasibility problem or an optimization problem with various constraints is solved through the linear inequality, and the application of the LMI to solve the control problem of the system has become a great research focus in these fields. The LMI toolset provides tools for solving linear matrix inequalities, and the matrix inequalities can be described by matrix blocks through programming tools; information that can fully describe the inequality; the existing matrix inequality can be corrected; a fixed solving function is used for realizing a specific solving function; the solution results of the system can be examined.
Three linear matrix inequalities are given below. The solver is given in the LMI toolbox, wherein x represents the vector formed by the decision variables, namely the matrix variable x1,…,xkDirection of independent argument in (1)Amount of the compound (A).
1. Problem of feasibility
One x ∈ RnSuch that the LMI system: a (x) < B (x) is true,
the solver for this problem is feasp. The feasp solver is an assisted convex optimization problem by solving:
s.t.A(x)-B(x)≤tI
to solve the feasibility problem of the linear matrix inequality.
Mincx solver
The problem is the minimization of a linear objective function with linear matrix inequality constraints
Figure BDA0002132140810000031
s.t.A(x)＜B(x)
3. Problem of minimization of generalized eigenvalues
Figure BDA0002132140810000032
s.t.C(x)＜D(x)
0＜B(x)
A(x)＜λB(x)
The corresponding solver is gevp. In practical application, a suitable solver is selected according to the actual condition of the system so as to obtain the required parameters.
Definition 1: given γ > 0, if the system satisfies both of the following conditions:
(i) (mean square stability) external disturbance wkAt 0, there is a constant φ > 0 and τ ∈ (0,1), such that
Figure BDA0002132140810000033
This is true.
(ii)(H∞Performance) at zero initial conditions, for all non-zero wk∈l2[0, ∞) and given H∞Performance index gamma > 0, filtering error ekSatisfies the following conditions
The filter error system is then said to be exponential stable in the mean square sense and to have H∞The property γ.
Lesion 1: V (η)k) Is the Lyapunov function. If rho is more than or equal to 0, mu is more than 0, upsilon is more than 0 and 0 is more than phi and less than 1, so that
μ||ηk||2≤Vk(ηk)≤υ||ηk||2
E{Vk+1(ηk+1)|ηk}-Vk(ηk)≤ρ-φVk(ηk)
Then there are
Figure BDA0002132140810000041
Theorem 2(Schurcomplement) giving a matrix of constants S1,S2,S3Here, the
Figure BDA0002132140810000042
And
Figure BDA0002132140810000043
when in useWhen true, if and only if
Figure BDA0002132140810000045
Or
Figure BDA0002132140810000046
Theorem 3 let x be in the range of Rn,y∈RnThe sum matrix Q > 0, then
xTQy+yTQx≤xTQx+yTQy
A data processing method in a big data environment based on a wireless sensor network, the method comprising:
step one, converting a plurality of control problems in engineering into a form of a linear matrix inequality, solving a feasibility problem or an optimization problem with a plurality of constraint conditions through the linear inequality, and describing a matrix processing problem as a discrete time linear system;
step two, defining variables to obtain a dimension reduction and augmentation system;
step three, designing filter parameters of the dimensionality reduction and augmentation system obtained in the step two to obtain a filter;
step four, the filter parameters are obtained by reverse deduction of the designed filter, so that the filter of the filter parameters is used for processing the big data
The signals are processed, so that the data is restored to the maximum extent, and the effectiveness of the data is ensured.
The invention has the beneficial effects that:
the discrete-time model of the system is given as:
Figure BDA0002132140810000047
C1＝[18.99720.7440]C2＝0.6，
D1＝[-0.300.6]D2＝0.4.
in the simulation, it is assumed that
Figure BDA0002132140810000051
Namely, the probability that the observation data can be received on time in the transmission process is 0.6, and the probability of one-step random time delay is 0.112. When w iskUsing a mean of zero and a variance QwThe simulation results are shown in fig. 3 for 1 white noise. Figure 4 gives a standard Kalman filter estimation curve under the same conditions. It is obvious from the simulation result that the estimation algorithm provided by the invention has higher estimation precision than Kalman filtering. It follows that in a network environment, i.e. when observing numbersThe filter of the present invention is more efficient than a standard Kalman filter in the presence of random time delays.
Drawings
FIG. 1 is a block diagram of a wireless sensor network system according to the present invention;
FIG. 2 is a flow chart of an algorithm involved in the present invention;
FIG. 3 shows the true values and H according to the invention∞Filtering the value;
fig. 4 shows the real values and Kalman filtered values to which the present invention relates.
Detailed Description
The first embodiment is as follows:
in this embodiment, a data processing method in a big data environment based on a wireless sensor network is implemented by the following steps for a wireless sensor network system structure shown in fig. 1, as shown in fig. 2:
step one, converting a plurality of control problems in engineering into a form of a linear matrix inequality, solving a feasibility problem or an optimization problem with a plurality of constraint conditions through the linear inequality, and describing a matrix processing problem as a discrete time linear system;
step two, defining variables to obtain a dimension reduction and augmentation system;
step three, designing filter parameters of the dimensionality reduction and augmentation system obtained in the step two to obtain a filter;
and step four, the filter parameters are obtained by reverse-deducing the designed filter, so that the filter of the filter parameters processes the large data signals, the data is restored to the maximum extent, and the effectiveness of the data is ensured.
The second embodiment is as follows:
different from the first embodiment, in the first embodiment, a data processing method in a big data environment based on a wireless sensor network is described, where the first step is to describe a problem as a discrete-time linear system:
Figure BDA0002132140810000052
wherein x isk∈RnIs a vector of the states of the system,is the observed output, wk∈RpIs a disturbance input, zk∈RmIs the estimated state, A, B, C1,C2,D1,D2Is a matrix of known constants; the observed data received by the filter may have random time lag or even data loss, and the case with one-step random time lag is described as follows:
Figure BDA0002132140810000062
wherein, yk∈RrIs an observation received by the filter, ξi,k(i ═ 1,2) are mutually uncorrelated random sequences that satisfy the Bernoulli distribution, and satisfy the statistical probability
Figure BDA0002132140810000063
Wherein
When ξ1,kWhen 1, it means that the data is received on time, and the probability is
Figure BDA0002132140810000065
When ξ1,k＝0,ξ1,k-1＝0,ξ2,kWhen the time is 1, the time indicates that one step of random time delay exists in the data transmission process, and the probability is
Figure BDA0002132140810000066
From ξi,kCan be distributed to
Figure BDA0002132140810000067
The third concrete implementation mode:
different from the first or second embodiment, the data processing method in the big data environment based on the wireless sensor network of the embodiment,
in the second step, the process of defining the variables to obtain the dimension reduction and augmentation system is as follows,
definition of
Figure BDA0002132140810000068
Thus, can obtain
Order to
Figure BDA00021321408100000610
The dimension reduction and augmentation system comprises:
Figure BDA0002132140810000071
wherein the content of the first and second substances,
Figure BDA0002132140810000072
and phii,Γi,i＝0,1,2,HiI is 0,1 and
Figure BDA0002132140810000073
the definition is as follows:
Figure BDA0002132140810000074
Figure BDA0002132140810000075
Figure BDA00021321408100000712
the amplification system containing a random variable thetai,k(i ═ 1,2), giving the following statistical properties:
the fourth concrete implementation mode:
different from the third specific embodiment, in the third step, the dimension reduction and amplification system obtained in the second step designs the filter parameters, and the process of obtaining the filter is that the filter parameter a is performed on the systemf,Bf,Cf,DfThe filter is of the following formula:
Figure BDA0002132140810000077
here, the
Figure BDA0002132140810000078
Is an estimate of the state of the dimension-expansion,
Figure BDA0002132140810000079
is the state z to be estimatedkFilter of Af,Bf,Cf,DfIs the filter parameter to be designed; defining a filtering error asThis results in a filter error system
Figure BDA00021321408100000711
Wherein
Figure BDA0002132140810000081
Figure BDA0002132140810000082
Figure BDA0002132140810000083
Figure BDA0002132140810000084
Figure BDA0002132140810000085
Figure BDA0002132140810000086
F0＝D2,F1＝-DfC2
For convenience of the following description, the following notation is introduced:
Figure BDA0002132140810000087
when an external disturbance wkWhen 0, for filtering error system definition
Figure BDA0002132140810000088
Then there are:
Figure BDA0002132140810000089
where A is1,2＝A1-A2,
Figure BDA00021321408100000810
Then another Ψ < 0 is equivalent to the inequalityIt is true that the first and second sensors,
namely, it isWherein the lambda is more than 0 and less than or equal to αmax(Ψ) there must be 0 < α ≦ ν, where λ ═ λmax(P) then have
Figure BDA0002132140810000093
The system obtained according to definition 1 and lemma 1 is stable in mean square index;
when w iskWhen the signal is not equal to 0, the signal is transmitted,
Figure BDA0002132140810000094
Figure BDA0002132140810000095
wherein
Figure BDA0002132140810000096
Figure BDA0002132140810000097
Figure BDA0002132140810000098
According to introduction 2
Figure BDA0002132140810000099
Thus, can obtain
Adding K from 0 to ∞ can obtain
Figure BDA0002132140810000101
At zero initial conditions V0(η0) When being equal to 0, then there is
Figure BDA0002132140810000102
The system has a given H∞And (4) performance.
The fifth concrete implementation mode:
different from the fourth embodiment, the data processing method in the big data environment based on the wireless sensor network of the present embodiment,
in the fourth step, the process of obtaining the filter parameters by the reverse-deducing of the designed filter is as follows,
assuming the inequality of the following equation holds:
wherein the content of the first and second substances,
Figure BDA0002132140810000104
Figure BDA0002132140810000105
Figure BDA0002132140810000106
Figure BDA0002132140810000107
Figure BDA0002132140810000108
then there isFrom the lemma 2, X-Z > 0, and the presence of the non-singular matrices R and S makes the formula true. Order to
Figure BDA0002132140810000112
Then there is
Figure BDA0002132140810000113
Wherein Q is-RTYS-T＝S-1Y(X-Y-1)YS-TIs greater than 0. And X-RQ-1RT＝(I-XY)(X-Y-1) (I-YX) > 0 from 2, P > 0.
Respectively multiplying inequalities left and right by the following matrix
diag{I,Y,I,I,Y,I,Y,I,Y,I,Y,I,I}
To obtain
Figure BDA0002132140810000114
Wherein
Figure BDA0002132140810000115
Figure BDA0002132140810000116
Π1＝diag{-Π,-Π,-Π,-Π},Π2＝diag{-I,-I}
And is
Figure BDA0002132140810000117
Figure BDA0002132140810000118
Figure BDA0002132140810000119
Figure BDA0002132140810000121
Figure BDA0002132140810000122
Figure BDA0002132140810000123
The calculation results are that:
Figure BDA0002132140810000125
Figure BDA0002132140810000126
Figure BDA0002132140810000127
Figure BDA0002132140810000128
Figure BDA0002132140810000129
thus, the inequality can be rewritten as follows:
Figure BDA00021321408100001210
on both sides of the inequality, respectively, to the left
Figure BDA0002132140810000131
Right passenger
Inequality equivalent to can be obtained
Figure BDA0002132140810000133
The above discussion has been demonstrated, and thus assuming the inequality holds, it will be assumed that the inequality is identical
Figure BDA0002132140810000134
Comparing to obtain the parameters of the filter to be designed
Figure BDA0002132140810000135
The large data signals are processed through the filter with the designed filter parameters, so that the data is restored to the maximum extent, and the effectiveness of the data is guaranteed.
Example 1:
the problem is described as a discrete-time linear system as follows:
Figure BDA0002132140810000136
wherein x isk∈RnIs a vector of the states of the system,
Figure BDA0002132140810000137
is the observed output, wk∈RpIs an interference input and belongs to the square integrable2[0, ∞) space, zk∈RmIs the estimated state, A, B, C1,C2,D1,D2Is a matrix of known constants. Observed output
Figure BDA0002132140810000138
The observation data received by the filter may have a step of random time delay or even data loss, and the corresponding mathematical model may be described as follows:
Figure BDA0002132140810000139
wherein, yk∈RrIs an observation received by the filter, ξi,k(i ═ 1,2) are mutually uncorrelated random sequences that satisfy the Bernoulli distribution, and satisfy the statistical probability:
Figure BDA00021321408100001310
wherein
Figure BDA00021321408100001311
Since the sensor and the filter communicate with each other via the network, the data transmission inevitably causes delay and packet loss, and the delay and packet loss occur randomly, here ξi,k(i ═ 1, 2).
When ξ1,kWhen 1, it means that the data is received on time, and the probability is
Figure BDA0002132140810000141
When ξ1,k＝0,ξ1,k-1＝0,ξ2,kWhen the time is 1, the time indicates that one step of random time delay exists in the data transmission process, and the probability is
Figure BDA0002132140810000142
When ξ1,k＝0,ξ 1,k-11 or ξ1,k＝0,ξ1,k-1＝0,ξ2,kWhen 0, it means that the packet is lost, and its probability is:
Figure BDA0002132140810000143
from ξi,kThe distribution of (c) can be found in:
Figure BDA0002132140810000144
Figure BDA0002132140810000145
Figure BDA0002132140810000146
E{ξi,k(1-ξi,k)}＝0,
Figure BDA0002132140810000147
introducing a new variable definition method, and enabling:
θ1,k＝ξ1,k,θ2,k＝(1-ξ1,k)ξ2,k+1.
note ξi，k(1-ξi，k)＝0，ξi，kAndare equivalent, so there are
θ1,kθ2,k＝ξ1,k(1-ξ1,k)ξ2,k+1＝0
From the formula:
Figure BDA0002132140810000149
defining:
then there are:
Figure BDA00021321408100001411
thus, there are obtained:
Yk＝(θ1,k+θ2,k)C1xk+(θ1,k+θ2,k)C2wk+(1-θ1，k-θ2,k)Yk-1
yk＝θ1,kC1xk+θ1,kC2wk+(1-θ1,k)Yk-1
order to
Figure BDA00021321408100001412
The following augmentation system:
wherein
Figure BDA0002132140810000152
And
Figure BDA0002132140810000153
the following can be written:
Figure BDA0002132140810000154
and phii,Γi,i＝0,1,2,HiI is 0,1 and
Figure BDA0002132140810000155
the definition is as follows:
Figure BDA0002132140810000156
Figure BDA0002132140810000157
Figure BDA0002132140810000158
the system is a system containing a random variable thetai,k(i ═ 1,2), giving the following statistical properties:
Figure BDA0002132140810000159
Figure BDA00021321408100001510
Figure BDA00021321408100001511
Figure BDA00021321408100001512
Figure BDA00021321408100001513
the filter is designed in the following form
Figure BDA00021321408100001514
Here, the
Figure BDA00021321408100001515
Is an estimate of the state of the dimension-expansion,
Figure BDA00021321408100001516
is the state z to be estimatedkFilter of Af,Bf,Cf,DfAre the filter parameters to be designed. Defining a filtering error as
Figure BDA00021321408100001517
The following two conditions are satisfied:
(i) (mean square stability) external disturbance wkWhen 0, the constants Φ > 0 and τ ∈ (0,1) exist, so that the following expression holds.
Figure BDA0002132140810000161
(ii)(H∞Performance) at zero initial conditions, for all non-zero wk∈l2[0, ∞) and given H∞Performance index gamma > 0, filtering error ekThe following are satisfied:
the filter error system is then said to be exponential stable in the mean square sense and to have H∞The property γ.

Claims (5)

1. A data processing method based on a wireless sensor network under a big data environment is characterized in that: the method is realized by the following steps:
converting a control problem in engineering into a form of a linear matrix inequality, solving a feasibility problem or an optimization problem with multiple constraint conditions through the linear inequality, and describing a matrix processing problem as a discrete time linear system;
step two, defining variables to obtain a dimension reduction and augmentation system;
step three, designing filter parameters of the dimensionality reduction and augmentation system obtained in the step two to obtain a filter;
and step four, the filter parameters are obtained by reverse-deducing the designed filter, so that the filter of the filter parameters processes the large data signals, the data is restored to the maximum extent, and the effectiveness of the data is ensured.
2. The data processing method in the big data environment based on the wireless sensor network according to claim 1, wherein: the first step is to describe the problem as a discrete-time linear system:
Figure FDA0002132140800000011
wherein x isk∈RnIs a vector of the states of the system,
Figure FDA0002132140800000012
is the observed output, wk∈RpIs a disturbance input, zk∈RmIs the estimated state, A, B, C1,C2,D1,D2Is a matrix of known constants; the observed data received by the filter may have random time lag or even data loss, and the case with one-step random time lag is described as follows:
Figure FDA0002132140800000013
wherein, yk∈RrIs an observation received by the filter, ξi,k(i ═ 1,2) are mutually uncorrelated random sequences that satisfy the Bernoulli distribution, and satisfy the statistical probability
Wherein
Figure FDA0002132140800000015
When ξ1,kWhen 1, it means that the data is received on time, and the probability is
Figure FDA0002132140800000016
When ξ1,k＝0,ξ1,k-1＝0,ξ2,kWhen the time is 1, the time indicates that one step of random time delay exists in the data transmission process, and the probability is
Figure FDA0002132140800000017
From ξi,kCan be distributed to
Figure FDA0002132140800000021
3. The data processing method in the big data environment based on the wireless sensor network according to claim 2, characterized in that: in the second step, the process of defining the variables to obtain the dimension reduction and augmentation system is as follows,
definition of theta1,k＝ξ1,k,
Figure FDA0002132140800000022
Thus, can obtain
Figure FDA0002132140800000023
Order to
Figure FDA0002132140800000024
The dimension reduction and augmentation system comprises:
Figure FDA0002132140800000025
wherein the content of the first and second substances,
Figure FDA0002132140800000026
and phii,Γi,i＝0,1,2,HiI is 0,1 and
Figure FDA0002132140800000027
the definition is as follows:
Figure FDA0002132140800000028
H0＝[0 I 0]，H1＝[C1-I 0]，
Figure FDA00021321408000000210
the amplification system containing a random variable thetai,k(i ═ 1,2), giving the following statistical properties:
4. the data processing method in the big data environment based on the wireless sensor network according to claim 3, wherein: in the third step, the dimension reduction and amplification system obtained in the second step designs filter parameters, and the process of obtaining the filter is that the filter parameter A is carried out on the systemf,Bf,Cf,DfThe filter is of the following formula:
Figure FDA0002132140800000031
here, the
Figure FDA0002132140800000032
Is an estimate of the state of the dimension-expansion,
Figure FDA0002132140800000033
is the state z to be estimatedkFilter of Af,Bf,Cf,DfIs the filter parameter to be designed; defining a filtering error as
Figure FDA0002132140800000034
This results in a filter error system
Figure FDA0002132140800000035
Wherein
Figure FDA0002132140800000036
Figure FDA0002132140800000037
Figure FDA0002132140800000038
Figure FDA0002132140800000039
Figure FDA00021321408000000310
Figure FDA00021321408000000311
F0＝D2,F1＝-DfC2
For convenience of the following description, the following notation is introduced:
when an external disturbance wkWhen 0, for filtering error system definitionThen there are:
Figure FDA00021321408000000314
Figure FDA0002132140800000041
where A is1,2＝A1-A2,
Figure FDA0002132140800000042
Then another Ψ < 0 is equivalent to the inequality
Figure FDA0002132140800000043
It is true that the first and second sensors,
namely, it is
Figure FDA0002132140800000044
Wherein the lambda is more than 0 and less than or equal to αmax(Ψ) there must be 0 < α ≦ ν, where λ ═ λmax(P) then have
Figure FDA0002132140800000045
The obtained system is stable in mean square index;
when w iskWhen the signal is not equal to 0, the signal is transmitted,
Figure FDA0002132140800000046
Figure FDA0002132140800000047
wherein
Figure FDA0002132140800000051
Figure FDA0002132140800000052
Figure FDA0002132140800000053
It can be known that
Figure FDA0002132140800000054
Thus, can obtain
Figure FDA0002132140800000055
Adding K from 0 to ∞ can obtain
Figure FDA0002132140800000056
At zero initial conditions V0(η0) When being equal to 0, then there is
Figure FDA0002132140800000057
The system has a given H∞And (4) performance.
5. The data processing method in the big data environment based on the wireless sensor network according to claim 4, wherein: in the fourth step, the process of obtaining the filter parameters by the reverse-deducing of the designed filter is as follows,
assuming the inequality of the following equation holds:
Figure FDA0002132140800000058
wherein the content of the first and second substances,
Figure FDA0002132140800000059
Figure FDA00021321408000000510
Figure FDA00021321408000000511
Figure FDA0002132140800000061
then there is
Figure FDA0002132140800000063
The expression is established by X-Z > 0 and the presence of non-singular matrices R and S; order to
Y＝Z-1，
Figure FDA0002132140800000065
Then there is
Figure FDA0002132140800000066
Wherein Q is-RTYS-T＝S-1Y(X-Y-1)YS-TIs greater than 0; and X-RQ-1RT＝(I-XY)(X-Y-1) (I-YX) > 0 indicates that P > 0;
respectively multiplying inequalities left and right by the following matrix
diag{I,Y,I,I,Y,I,Y,I,Y,I,Y,I,I}
To obtain
Wherein
Figure FDA0002132140800000068
Figure FDA0002132140800000069
Π1＝diag{-Π,-Π,-Π,-Π},Π2＝diag{-I,-I}
And is
Figure FDA0002132140800000071
Figure FDA0002132140800000072
Figure FDA0002132140800000073
Figure FDA0002132140800000075
Figure FDA0002132140800000076
The calculation results are that:
Figure FDA0002132140800000077
Figure FDA0002132140800000078
Figure FDA0002132140800000079
Figure FDA00021321408000000710
Figure FDA00021321408000000711
Figure FDA00021321408000000712
G1Σ2＝[-DfH1-DfH1Y].
thus, the inequality can be rewritten as follows:
on both sides of the inequality, respectively, to the left
Figure FDA0002132140800000082
Right passenger
Figure FDA0002132140800000083
Inequality equivalent to can be obtained
Figure FDA0002132140800000084
The above discussion has been demonstrated, and thus assuming the inequality holds, it will be assumed that the inequality is identical
Figure FDA0002132140800000085
Comparing to obtain the parameters of the filter to be designed
Figure FDA0002132140800000086
The large data signals are processed through the filter with the designed filter parameters, so that the data is restored to the maximum extent, and the effectiveness of the data is guaranteed.
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