CN107015194B - Radio frequency identification positioning method for intelligent electric meter storage management - Google Patents
Radio frequency identification positioning method for intelligent electric meter storage management Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
Abstract
The invention relates to a radio frequency identification positioning method for intelligent electric meter storage management, which comprises the following steps: (1) collecting the energy intensity of an intelligent electric meter to be positioned in a warehouse monitoring area and the energy intensity of virtual reference labels arranged on the vertexes of the equally divided grids of the warehouse monitoring area by using a reader on the boundary of the warehouse; (2) determining a virtual reference label sample adjacent to the intelligent electric meter to be positioned; (3) determining a virtual reference label sample closest to the intelligent electric meter to be positioned according to the membership degree of the intelligent electric meter to be positioned to the energy intensity of the virtual reference label sample; (4) determining the energy density of the virtual reference label sample closest to the intelligent electric meter to be positioned; (5) determining the position of the intelligent electric meter to be positioned; the method provided by the invention has the characteristics of higher positioning precision, low complexity, low cost and low energy consumption.
Description
Technical Field
The invention relates to the technical field of radio frequency identification application, in particular to a radio frequency identification positioning method for smart electric meter storage management.
Background
With the reform of the national power industry and the planning and construction of a smart power grid, in order to guarantee the national strategic energy safety and national economy life line safety, the power asset management level is gradually improved, the power metering storage management mode is also changed greatly, the application of the smart storage management system in the power meter storage management improves the quality of the power meter storage management, and the method lays a foundation for the construction of an first-class power smart storage logistics center. The intelligent electric meter warehousing management system is a system which can more effectively manage information, resources, behaviors, inventory and distribution operation according to operation business rules and algorithms in real time. In order to improve the operation efficiency of the warehouse logistics center, acquiring the equipment position information is an indispensable link for system operation. The infrared technology enables a monitored object to be in a straight line with a reader due to the sight distance propagation characteristic, the infrared positioning precision is difficult to meet the indoor positioning requirement, the ultrasonic positioning technology needs a large number of bottom layer hardware supports and is obviously influenced by multipath effect and non-sight distance, the positioning precision of a wireless local area network is usually about 3m-30m, and the indoor positioning requirement is also difficult to meet. Radio Frequency Identification (RFID) technology, one of the core technologies of the Internet of things, meets requirements better than similar technologies. The characteristics of non-line-of-sight, contact-free and high-speed recognition of the indoor environment make the indoor environment replace the Global Positioning System (GPS) System which is slightly influenced by indoor shielding interference.
In a general radio frequency identification indoor positioning algorithm, such as a typical positioning algorithm LANDMARC, a fixed-point reader is mainly placed and an actual reference tag is laid, the reader receives a reference tag signal intensity value to reflect the physical position relation of the tag, and an indoor wireless propagation model is a circle or an ellipse with the reader as a center. In practical application, due to conditions such as temperature, humidity, barrier reflection, refraction and scattering and the like in the environment, the wireless propagation model is not a regular graph, and the actually measured received signal strength has an error in a reflection distance relation compared with an ideal situation, so that the positioning accuracy of the algorithm in practical application is reduced. A multi-reader fan-shaped overlapped model is provided for the purpose, but the requirements on the configuration and the number of the readers are high, and the cost is increased remarkably. And because the reader can simultaneously display the value of the arrival phase while receiving the signal strength of the tag, and the superposed noise of the arrival phase is additive and easy to filter, an indoor positioning algorithm utilizing the POA is provided, but when the frequency of the transmitted signal is too high, the range measurement range is limited.
Disclosure of Invention
The invention provides a radio frequency identification positioning method for intelligent electric meter storage management, and aims to provide a radio frequency identification positioning method for intelligent electric meter storage management, which has the characteristics of higher positioning precision, low complexity, low cost and low energy consumption.
The purpose of the invention is realized by adopting the following technical scheme:
the improvement of a radio frequency identification positioning method for smart meter warehousing management, which comprises the following steps:
(1) collecting the energy intensity of an intelligent electric meter to be positioned in a warehouse monitoring area and the energy intensity of virtual reference labels arranged on the vertexes of the equally divided grids of the warehouse monitoring area by using a reader on the boundary of the warehouse;
(2) determining a virtual reference label sample adjacent to the intelligent electric meter to be positioned;
(3) determining a virtual reference label sample closest to the intelligent electric meter to be positioned according to the membership degree of the intelligent electric meter to be positioned to the energy intensity of the virtual reference label sample;
(4) determining the energy density of the virtual reference label sample closest to the intelligent electric meter to be positioned;
(5) and determining the position of the intelligent electric meter to be positioned.
Preferably, the step (2) includes:
taking the reader as a circle center, taking the sum of the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an outer diameter, taking the difference between the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an inner diameter, and constructing an energy ring of the intelligent electric meter to be positioned corresponding to the reader;
acquiring an intersection area of energy rings containing the intelligent electric meter to be positioned and the intelligent electric meter to be positioned corresponding to the reader;
and the virtual reference label contained in the intersection area is a virtual reference label sample adjacent to the intelligent electric meter to be positioned.
Preferably, in the step (3), the membership degree of the smart meter to be positioned to the energy intensity of the virtual reference tag sample is determined according to the following formula:
μ(i,j)=2×min(Ei,Ej)/(Ei+Ej) (1)
in the formula (1), mu (i, j) is the membership degree of the energy intensity of the reader receiving the ith virtual reference tag sample adjacent to the jth smart meter to be positioned to the energy intensity of the reader receiving the jth smart meter to be positioned, and EiFusion energy intensity of ith virtual reference label sample adjacent to jth smart meter to be positioned, EjThe fusion energy intensity of the jth intelligent electric meter to be positioned, i ∈ [1, k]K is the total number of virtual reference label samples adjacent to the jth smart meter to be located, j ∈ [1, l]L is the total number of the intelligent electric meters to be positioned in the warehouse monitoring area;
the fusion energy intensity E of the ith virtual reference label sample adjacent to the jth intelligent electric meter to be positionediThe calculation formula of (2) is as follows:
in the formula (2), N is the total number of readers in the warehouse monitoring area, EinReceiving the energy intensity of an ith virtual reference label sample adjacent to the jth intelligent electric meter to be positioned for the nth reader;
fusion energy intensity E of jth intelligent electric meter to be positioned in warehouse monitoring areajThe calculation formula of (2) is as follows:
in the formula (3), EjnAnd receiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader.
Further, in the descending order of membership degree of the energy intensity of the virtual reference label sample adjacent to the jth to-be-positioned intelligent electric meter received by the reader to the energy intensity of the jth to-be-positioned intelligent electric meter received by the reader, the virtual reference label samples corresponding to the first m membership degrees are selected as the nearest virtual reference label sample of the jth to-be-positioned intelligent electric meter, m is less than or equal to k, k is the total number of the virtual reference label samples adjacent to the jth to-be-positioned intelligent electric meter, and m is the total number of the virtual reference label samples nearest to the jth to-be-positioned intelligent electric meter.
Preferably, in the step (4), the energy density of the virtual reference tag sample closest to the smart meter to be positioned is determined according to the following formula:
ρ(c)=(max[d(c,j)]-d(c,j))/(max[d(c,j)]-min[d(c,j)]) (4)
in the formula (4), c belongs to [1, m ] and m is not more than k, k is the total number of virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of virtual reference label samples nearest to the jth intelligent electric meter to be positioned, ρ (c) is the energy density of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned, and d (c, j) is the energy difference between the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned;
the calculation formula of the energy difference d (c, j) between the nearest c-th virtual reference label sample of the jth intelligent meter to be positioned and the jth intelligent meter to be positioned is as follows:
in the formula (5), EjnReceiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader, EcnAnd receiving the energy intensity of the c-th virtual reference label sample nearest to the j-th intelligent electric meter to be positioned for the nth reader, wherein N is the total number of readers in the warehouse monitoring area.
Preferably, in the step (5), the position of the smart meter to be positioned is determined according to the following formula:
in formula (6), c ∈ [1, m]And m is less than or equal to k, k is the total number of the virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of the virtual reference label samples nearest to the jth intelligent electric meter to be positioned, and xjThe abscissa, y, of the jth intelligent electric meter to be positioned in the warehouse monitoring areajThe vertical coordinate, x, of the jth intelligent electric meter to be positioned in the warehouse monitoring areacThe abscissa, y, of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned in the warehouse monitoring areacThe ordinate, w, of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned in the warehouse monitoring areacA coordinate coefficient of a c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned;
the calculation formula of the coordinate coefficient of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned is as follows:
in the formula (7), ρ (c) is the energy density of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned, and μ (c, j) is the membership degree of the energy intensity of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned.
The invention has the beneficial effects that:
according to the radio frequency identification positioning method for intelligent electric meter storage management, provided by the invention, the membership degree of a sample label to an electric meter to be positioned is obtained by introducing a fuzzy theory, an information fusion theory and other methods, the energy density of the sample label is calculated, and the position coordinate of the intelligent electric meter to be positioned is obtained by adopting triangular mode fusion.
Drawings
FIG. 1 is a flow chart of a radio frequency identification positioning method for smart meter warehousing management according to the present invention;
fig. 2 is a schematic view of an application scenario of a radio frequency identification positioning method for smart meter storage management according to an embodiment of the present invention;
fig. 3 is a schematic diagram of selecting a sample tag for a radio frequency identification positioning method for smart meter warehousing management according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a radio frequency identification positioning method for smart electric meter storage management, as shown in fig. 1, comprising the following steps:
(1) collecting the energy intensity of an intelligent electric meter to be positioned in a warehouse monitoring area and the energy intensity of virtual reference labels arranged on the vertexes of the equally divided grids of the warehouse monitoring area by using a reader on the boundary of the warehouse;
for example, as shown in fig. 2, the grid area is a smart meter warehouse management monitoring area, a square mark at the vertex of the grid, that is, a preset virtual reference tag, and the reader is installed at a midpoint position of a peripheral boundary of the warehouse logistics center.
(2) Determining a virtual reference tag sample adjacent to the smart meter to be positioned, comprising:
taking the reader as a circle center, taking the sum of the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an outer diameter, taking the difference between the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an inner diameter, and constructing an energy ring of the intelligent electric meter to be positioned corresponding to the reader;
wherein alpha is an energy intensity threshold value of the intelligent electric meter to be positioned;
acquiring an intersection area of energy rings containing the intelligent electric meter to be positioned and the intelligent electric meter to be positioned corresponding to the reader;
and the virtual reference label contained in the intersection area is a virtual reference label sample adjacent to the intelligent electric meter to be positioned.
For example, as shown in fig. 3, a virtual reference tag included in an intersection region of an energy ring including an intelligent electric meter i to be positioned and corresponding to readers 1, 2, and 3 respectively is a virtual reference tag sample adjacent to the intelligent electric meter to be positioned, that is, a virtual reference tag included in a shadow region is a virtual reference tag sample adjacent to the intelligent electric meter to be positioned;
(3) determining the nearest virtual reference label sample of the intelligent electric meter to be positioned according to the membership degree of the intelligent electric meter to be positioned to the energy intensity of the virtual reference label sample comprises the following steps:
determining the membership degree of the intelligent electric meter to be positioned to the energy intensity of the virtual reference label sample according to the following formula:
μ(i,j)=2×min(Ei,Ej)/(Ei+Ej) (1)
in the formula (1), mu (i, j) is the membership degree of the energy intensity of the reader receiving the ith virtual reference tag sample adjacent to the jth smart meter to be positioned to the energy intensity of the reader receiving the jth smart meter to be positioned, and EiFusion energy intensity of ith virtual reference label sample adjacent to jth smart meter to be positioned, EjThe fusion energy intensity of the jth intelligent electric meter to be positioned, i ∈ [1, k]K is the total number of virtual reference label samples adjacent to the jth smart meter to be located, j ∈ [1, l]L is the total number of the intelligent electric meters to be positioned in the warehouse monitoring area;
the fusion energy intensity E of the ith virtual reference label sample adjacent to the jth intelligent electric meter to be positionediThe calculation formula of (2) is as follows:
in the formula (2), N is the total number of readers in the warehouse monitoring area, EinReceiving the energy intensity of an ith virtual reference label sample adjacent to the jth intelligent electric meter to be positioned for the nth reader;
fusion energy intensity E of jth intelligent electric meter to be positioned in warehouse monitoring areajThe calculation formula of (2) is as follows:
in the formula (3), EjnAnd receiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader.
The method comprises the steps of arranging the membership degrees of the energy intensity of a virtual reference label sample adjacent to the jth intelligent electric meter to be positioned received by a reader to the energy intensity of the jth intelligent electric meter to be positioned received by the reader in a descending order, selecting a virtual reference label sample corresponding to the first m membership degrees as the nearest virtual reference label sample of the jth intelligent electric meter to be positioned, wherein m is less than or equal to k, k is the total number of the virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, and m is the total number of the virtual reference label samples nearest to the jth intelligent electric meter to be positioned.
(4) Determining the energy density of the nearest virtual reference tag sample of the smart meter to be positioned comprises:
determining the energy density of the nearest virtual reference label sample of the intelligent electric meter to be positioned according to the following formula:
ρ(c)=(max[d(c,j)]-d(c,j))/(max[d(c,j)]-min[d(c,j)]) (4)
in the formula (4), c belongs to [1, m ] and m is not more than k, k is the total number of virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of virtual reference label samples nearest to the jth intelligent electric meter to be positioned, ρ (c) is the energy density of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned, and d (c, j) is the energy difference between the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned;
the calculation formula of the energy difference d (c, j) between the nearest c-th virtual reference label sample of the jth intelligent meter to be positioned and the jth intelligent meter to be positioned is as follows:
in the formula (5), EjnReceiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader, EcnAnd receiving the energy intensity of the c-th virtual reference label sample nearest to the j-th intelligent electric meter to be positioned for the nth reader, wherein N is the total number of readers in the warehouse monitoring area.
Considering that the greater the energy density of the sample label, that is, the closer the energy intensity of the nearest virtual reference label to the energy intensity of the smart meter to be positioned, the greater the proximity, the more the distance between the plurality of reference points around the sample label and the smart meter to be positioned is, the more likely the sample label is to be close to the smart meter to be positioned. The energy difference between the nearest neighbor virtual reference label of the sample label and the intelligent electric meter to be positioned is selected, so that the influence of indoor environmental factors on the energy intensity reaction distance capability can be effectively reduced, and the accuracy of the positioning result is improved.
(5) Determining the position of the smart meter to be positioned comprises:
determining the position of the intelligent electric meter to be positioned according to the following formula:
in formula (6), c ∈ [1, m]And m is less than or equal to k, k is the total number of the virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of the virtual reference label samples nearest to the jth intelligent electric meter to be positioned, and xjThe abscissa, y, of the jth intelligent electric meter to be positioned in the warehouse monitoring areajThe vertical coordinate, x, of the jth intelligent electric meter to be positioned in the warehouse monitoring areacThe cross section of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned in the warehouse monitoring areaCoordinate, ycThe ordinate, w, of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned in the warehouse monitoring areacA coordinate coefficient of a c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned;
the calculation formula of the coordinate coefficient of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned is as follows:
in the formula (7), ρ (c) is the energy density of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned, and μ (c, j) is the membership degree of the energy intensity of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (6)
1. A radio frequency identification positioning method for smart meter warehousing management is characterized by comprising the following steps:
(1) collecting the energy intensity of an intelligent electric meter to be positioned in a warehouse monitoring area and the energy intensity of virtual reference labels arranged on the vertexes of the equally divided grids of the warehouse monitoring area by using a reader on the boundary of the warehouse;
(2) determining a virtual reference label sample adjacent to the intelligent electric meter to be positioned;
(3) determining a virtual reference label sample closest to the intelligent electric meter to be positioned according to the membership degree of the intelligent electric meter to be positioned to the energy intensity of the virtual reference label sample;
(4) determining the energy density of the virtual reference label sample closest to the intelligent electric meter to be positioned;
(5) and determining the position of the intelligent electric meter to be positioned.
2. The method of claim 1, wherein step (2) comprises:
taking the reader as a circle center, taking the sum of the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an outer diameter, taking the difference between the energy intensity and alpha of the intelligent electric meter to be positioned received by the reader as an inner diameter, and constructing an energy ring of the intelligent electric meter to be positioned corresponding to the reader;
acquiring an intersection area of energy rings containing the intelligent electric meter to be positioned and the intelligent electric meter to be positioned corresponding to the reader;
the virtual reference label contained in the intersection area is a virtual reference label sample adjacent to the intelligent electric meter to be positioned;
and alpha is an energy intensity threshold value of the intelligent electric meter to be positioned.
3. The method of claim 1, wherein in step (3), the degree of membership of the smart meter to be positioned to the energy intensity of the virtual reference tag sample is determined as follows:
μ(i,j)=2×min(Ei,Ej)/(Ei+Ej) (1)
in the formula (1), mu (i, j) is the membership degree of the energy intensity of the reader receiving the ith virtual reference tag sample adjacent to the jth smart meter to be positioned to the energy intensity of the reader receiving the jth smart meter to be positioned, and EiFusion energy intensity of ith virtual reference label sample adjacent to jth smart meter to be positioned, EjThe fusion energy intensity of the jth intelligent electric meter to be positioned, i ∈ [1, k]K is the total number of virtual reference label samples adjacent to the jth smart meter to be located, j ∈ [1, l]L is the total number of the intelligent electric meters to be positioned in the warehouse monitoring area;
the fusion energy intensity E of the ith virtual reference label sample adjacent to the jth intelligent electric meter to be positionediThe calculation formula of (2) is as follows:
in the formula (2), N is the total number of readers in the warehouse monitoring area, EinReceiving the energy intensity of an ith virtual reference label sample adjacent to the jth intelligent electric meter to be positioned for the nth reader;
fusion energy intensity E of jth intelligent electric meter to be positioned in warehouse monitoring areajThe calculation formula of (2) is as follows:
in the formula (3), EjnAnd receiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader.
4. The method of claim 3, wherein in a descending membership ranking of the energy intensity of the virtual reference tag sample adjacent to the jth smart meter to be positioned received by the reader versus the energy intensity of the jth smart meter to be positioned received by the reader, the virtual reference tag sample corresponding to the first m membership degrees is selected as the nearest virtual reference tag sample of the jth smart meter to be positioned, m is less than or equal to k, k is the total number of virtual reference tag samples adjacent to the jth smart meter to be positioned, and m is the total number of virtual reference tag samples nearest to the jth smart meter to be positioned.
5. The method of claim 1, wherein in step (4), the energy density of the nearest virtual reference tag sample of the smart meter to be located is determined according to the following formula:
ρ(c)=(max[d(c,j)]-d(c,j))/(max[d(c,j)]-min[d(c,j)]) (4)
in the formula (4), c belongs to [1, m ] and m is not more than k, k is the total number of virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of virtual reference label samples nearest to the jth intelligent electric meter to be positioned, ρ (c) is the energy density of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned, and d (c, j) is the energy difference between the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned and the jth intelligent electric meter to be positioned;
the calculation formula of the energy difference d (c, j) between the nearest c-th virtual reference label sample of the jth intelligent meter to be positioned and the jth intelligent meter to be positioned is as follows:
in the formula (5), EjnReceiving the energy intensity of the jth intelligent electric meter to be positioned for the nth reader, EcnAnd receiving the energy intensity of the c-th virtual reference label sample nearest to the j-th intelligent electric meter to be positioned for the nth reader, wherein N is the total number of readers in the warehouse monitoring area.
6. The method of claim 1, wherein in step (5), the location of the smart meter to be located is determined according to the following formula:
in formula (6), c ∈ [1, m]And m is less than or equal to k, k is the total number of the virtual reference label samples adjacent to the jth intelligent electric meter to be positioned, m is the total number of the virtual reference label samples nearest to the jth intelligent electric meter to be positioned, and xjThe abscissa, y, of the jth intelligent electric meter to be positioned in the warehouse monitoring areajThe vertical coordinate, x, of the jth intelligent electric meter to be positioned in the warehouse monitoring areacThe abscissa, y, of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned in the warehouse monitoring areacThe ordinate of the c-th virtual reference label sample nearest to the jth smart meter to be positioned in the warehouse monitoring area,wca coordinate coefficient of a c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned;
the calculation formula of the coordinate coefficient of the c-th virtual reference label sample nearest to the jth intelligent electric meter to be positioned is as follows:
in the formula (7), ρ (c) is the energy density of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned, and μ (c, j) is the membership degree of the energy intensity of the c-th virtual reference tag sample nearest to the jth intelligent meter to be positioned and the jth intelligent meter to be positioned.
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