CN112066996A - Virtual interpolation positioning method based on disturbance channel model - Google Patents

Virtual interpolation positioning method based on disturbance channel model Download PDF

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CN112066996A
CN112066996A CN202011160870.7A CN202011160870A CN112066996A CN 112066996 A CN112066996 A CN 112066996A CN 202011160870 A CN202011160870 A CN 202011160870A CN 112066996 A CN112066996 A CN 112066996A
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赵阳
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Civil Aviation University of China
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Abstract

A virtual interpolation positioning method based on a disturbance channel model is provided. The method comprises the steps that signal receivers are uniformly arranged in a grid shape in a space to be detected, and signal transmitters are dispersedly arranged in the space to be detected; obtaining actual signal values at each fixed node; when the signal receiver to be positioned enters a space to be detected, signal values reflected by the signal receivers at all fixed nodes under the condition are obtained; selecting four nodes with the maximum similarity to a signal value reflected by a signal receiver to be positioned, and taking a grid where the four nodes are located as a rough position of the signal receiver to be positioned; and estimating a signal value reflected by a virtual signal receiver at each node uniformly divided in the grid space based on the disturbance channel model, and estimating the position of the signal receiver to be positioned by comparing the similarity of the virtual signal value and the signal value to be positioned. The virtual interpolation of the method is closer to the actually measured data, and the method meets the application requirements of low cost and high precision.

Description

Virtual interpolation positioning method based on disturbance channel model
Technical Field
The invention belongs to the technical field of indoor wireless positioning, and particularly relates to a virtual interpolation positioning method based on a disturbance channel model.
Background
With the continuous development of the internet of things technology, the location-based service is more and more interesting, but the real-time and rapid high-precision positioning technology is still the key and difficult problem of the current research. Traditional wireless location technologies include GPS, bluetooth, ultrasound, ultra-wideband, Wi-Fi, computer vision, ultra-high frequency radio frequency identification (UHF RFID), and the like. For the positioning technology in the indoor environment, especially for the application environments such as needing to position a large number of articles and personnel, the passive UHF RFID becomes a hotspot of indoor positioning research in recent years by virtue of the advantages of non-contact, low manufacturing cost, easiness in laying, low power consumption and the like.
Because indoor wireless channels are complex and changeable, a positioning method based on scene analysis in a passive UHF RFID positioning technology is one of the key directions of current research, the scene analysis method is to introduce a fixed node, deploy a reference tag with known position information at the fixed node, select an adjacent reference tag by comparing the similarity of wireless signal information between the reference tag and a tag to be positioned, and estimate the position information of the tag to be positioned by using the adjacent reference tag. The fixed nodes are positioned at the intersection points in the uniform grid, and in order to improve the positioning accuracy, the traditional method can increase the deployment density of the fixed nodes as much as possible under the premise of budget conditions. However, since mutual coupling influence is generated between fixed nodes, the accuracy of selecting adjacent reference tags is rather reduced when the density is too high, and the positioning accuracy is further reduced, so that the improvement of the reference matching performance on the premise of not increasing the density of the reference tags becomes a key problem of research. At present, the concept of virtual reference tags has been introduced in research, and the reference matching is increased by estimating the signal value reflected by the signal receiver at the virtual node, so that the laying density of the reference tags is not increased, the coupling risk of tag antennas is reduced, and the accuracy of matching and positioning can be improved.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide a virtual interpolation positioning method based on a disturbed channel model.
In order to achieve the above object, the virtual interpolation positioning method based on the disturbance channel model provided by the present invention comprises the following steps performed in sequence:
1) uniformly arranging a plurality of signal receivers serving as fixed nodes in a grid shape at a certain interval in a space to be detected, setting a label for each grid, and dispersedly arranging signal transmitters in the space to be detected;
2) transmitting a signal by using a signal transmitter and receiving a signal reflected by each fixed node to obtain an actual signal value reflected by each fixed node;
3) when a signal receiver t to be positioned is attached to a target to be positioned and enters a space to be detected, signal values reflected by all fixed nodes under the condition are obtained, and the similarity between the signal values reflected by the signal receiver t to be positioned and the signal values reflected by the fixed nodes is compared;
4) sorting all the similarities in a descending order, selecting a fixed node with larger similarity as an adjacent fixed node, and determining a label q of a grid where a signal receiver t to be positioned is located through the adjacent fixed node;
5) performing virtual fixed node interpolation in the grid according to the label q of the grid where the signal receiver t to be positioned is located, taking one fourth of the interval of the fixed nodes as the interval of the virtual fixed nodes, and marking labels of sub-grids divided by the virtual fixed nodes; under the condition that the positions of four fixed nodes, the positions of virtual fixed nodes and the distance between the grid and a signal transmitter, which are contained in the grid with the label q, are known, a signal value reflected by the virtual fixed nodes is estimated by using a disturbance channel model, the similarity between a signal receiver t to be positioned and the signal value reflected by the virtual fixed nodes is compared, the virtual fixed nodes with higher similarity are selected as adjacent virtual fixed nodes, the sub-grid where the signal receiver t to be positioned is located is determined by the adjacent virtual fixed nodes, and the label q is marked as1
6) Numbering q according to the method of step 5)1And then carrying out virtual fixed node interpolation on the sub-grids to obtain a final adjacent virtual fixed node, and estimating the coordinate of the signal receiver t to be positioned by the final adjacent virtual fixed node.
In step 1), the method of uniformly arranging a plurality of signal receivers as fixed nodes in a grid shape at a certain interval in a space to be detected, setting a label for each grid, and dispersedly arranging signal transmitters in the space to be detected comprises:
after num signal transmitters and n signal receivers which need to be arranged in a space to be detected are determined, the n signal receivers are uniformly arranged in the space to be detected as fixed nodes according to the g-meter interval, so that the space to be detected is uniformly divided into a plurality of grids, the fixed nodes are positioned at the intersection points of the grids, a label is set for each grid, and the num signal transmitters are dispersedly arranged in the space to be detected.
In step 2), the method for obtaining the actual signal value reflected by each fixed node by using the signal transmitter to transmit the signal and receiving the signal reflected by each fixed node is as follows:
and (3) transmitting a signal by using a signal transmitter and receiving the signal reflected by each fixed node, repeating the experiment for a plurality of times, then taking an average value, and recording the average value as an actual signal value:
Figure BDA0002744190100000031
in step 3), the method for obtaining the signal values reflected by all the fixed nodes under the condition after the signal receiver t to be positioned is attached to the target to be positioned and enters the space to be detected, and comparing the similarity between the signal values reflected by the signal receiver t to be positioned and the signal values reflected by the fixed nodes is as follows:
the signal emitter is used for emitting signals and receiving signals reflected by all the fixed nodes, the mean value of the signal values reflected by all the fixed nodes under m times of experiments is counted and recorded as:
Figure BDA0002744190100000032
then, the signal mean values under m experiments reflected by the signal receiver t to be positioned are respectively compared
Figure BDA0002744190100000033
Similarity to the mean of the signals reflected by each fixed node r 1:
Figure BDA0002744190100000041
in step 4), the method for sorting all the similarities in a descending order, selecting a fixed node with a larger similarity as an adjacent fixed node, and determining the label q of the grid where the signal receiver t to be positioned is located by the adjacent fixed node includes:
sorting all the similarities obtained in the step 3) in a descending order to obtain { S1,S2,...,SnAnd selecting the fixed nodes corresponding to the first k similarities as adjacent fixed nodes, and determining the label q of the grid where the signal receiver t to be positioned is located by using the positions of the adjacent fixed nodes.
In step 5), performing virtual fixed node interpolation in the grid according to the label q of the grid where the signal receiver t to be positioned is located, taking one fourth of the distance between the fixed nodes as the distance between the virtual fixed nodes, and marking the labels of the sub-grids divided by the virtual fixed nodes; under the condition that the positions of four fixed nodes, the positions of virtual fixed nodes and the distance between the grid and a signal transmitter, which are contained in the grid with the label q, are known, a signal value reflected by the virtual fixed nodes is estimated by using a disturbance channel model, the similarity between a signal receiver t to be positioned and the signal value reflected by the virtual fixed nodes is compared, the virtual fixed nodes with higher similarity are selected as adjacent virtual fixed nodes, the sub-grid where the signal receiver t to be positioned is located is determined by the adjacent virtual fixed nodes, and the label q is marked as1The method comprises the following steps:
performing virtual fixed node interpolation in a grid of a label q where a signal receiver t to be positioned is located, taking one fourth of the g-meter distance of the fixed nodes determined in the step 1) as the distance of the virtual fixed nodes, obtaining n1 virtual fixed nodes, and marking labels of sub-grids divided by the virtual fixed nodes;
the signal values reflected by the four fixed nodes contained in the grid labeled q are:
Figure BDA0002744190100000042
the distances between the n1 virtual fixed nodes and the four fixed nodes are respectively:
Figure BDA0002744190100000051
the distances between the four fixed nodes and the signal emitter are respectively as follows:
Figure BDA0002744190100000052
the distances between the n1 virtual fixed nodes and the signal emitter are respectively:
Figure BDA0002744190100000053
by using the distance between the virtual fixed node and the virtual fixed node in g/(2)wEstimating a signal value of a virtual fixed node by using fixed nodes within a meter range, wherein w represents the cycle number;
for the ith virtual fixed node, the adjacent fixed node is the jth fixed node, and the signal value thereof
Figure BDA0002744190100000054
Comprises the following steps:
Figure BDA0002744190100000055
wherein, A, a is related to the environment and the type of the signal receiver;
and then comparing the similarity of the signal receiver t to be positioned and the signal value estimated at the virtual fixed node i:
Figure BDA0002744190100000056
sequencing all the similarities in descending order to obtain { S'1,S'2,...,S'n1And selecting the first k virtual fixed nodes corresponding to the similarity as adjacent virtual fixed nodes, and further determining the sub-grid where the signal receiver to be positioned is located by the adjacent virtual fixed nodes, wherein the labels are marked asq1
In step 6), the method according to step 5) is labeled with the reference number q1The sub-grid carries out virtual fixed node interpolation to obtain a final adjacent virtual fixed node, and the method for estimating the coordinate of the signal receiver t to be positioned by the final adjacent virtual fixed node comprises the following steps:
numbering q according to the method of step 5)1And then, performing virtual fixed node interpolation on the sub-grids to obtain k final adjacent virtual fixed nodes, and determining the weight of each final adjacent virtual fixed node by utilizing the similarity between the signal value corresponding to the k final adjacent virtual fixed nodes and the signal value corresponding to the signal receiver t to be positioned:
the coordinates of the k final neighboring virtual fixed nodes are:
N(x1,y1,z1),N(x2,y2,z2),...,N(xk,yk,zk) (9)
calculating the weight of k final neighboring virtual fixed nodes using the similarity of the signal values obtained by equation (8):
Figure BDA0002744190100000061
and finally, determining the coordinates (x, y, z) of the signal receiver t to be positioned by using the coordinates and weights of the k final adjacent virtual fixed nodes:
Figure BDA0002744190100000062
compared with the prior art, the invention has the beneficial effects that:
firstly, the fixed nodes are arranged at the intersection points of the uniform grids, and the distance between the fixed nodes is set to be larger so as to weaken the negative influence of the mutual coupling of the antennas between the fixed nodes on the positioning precision. Because the fixed node and the signal receiver to be positioned are both positioned in the same propagation environment, the method has good robustness to dynamic environment factors. And finally, a disturbing signal model is provided, the signal values reflected by the virtual fixed nodes are realized based on the model, and the positioning can be completed by utilizing the similarity of the signals reflected by the virtual fixed nodes on the premise of not increasing the density of the fixed nodes. Experimental results show that the method preliminarily judges that the error of the signal receiver to be positioned is less than 10cm, so that the positioning performance is high, hardware equipment is simple and easy to realize, and the method meets the application requirements of low cost and high precision.
Drawings
Fig. 1 is a schematic diagram of a layout of reference tags in an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention are further described in detail with reference to the accompanying drawings and specific embodiments, which are merely illustrative of the present invention and are not intended to limit the present invention.
As shown in fig. 1, in this embodiment, a passive ultrahigh frequency radio frequency identification technology is taken as an example to describe the virtual interpolation positioning method based on the disturbance channel model provided by the present invention, an adopted signal transmitter is represented by a card reader including a transmitting/receiving integrated antenna, a signal receiver to be positioned is represented by a passive radio frequency tag to be positioned (tag to be positioned), a fixed node is represented by a passive radio frequency tag with a known position, which is called a reference tag, and a transmitting signal frequency is 922 MHz.
Step 1, deploying a reference label:
the size of the space to be detected is a two-dimensional space of 4 x 4 meters, the card readers are connected with a computer for uploading data, and four card readers are deployed at four corners of the space to be detected and face the space to be detected, as shown in fig. 1.
Reference tags are deployed at the intersection points of the grids, 16 grids are planned according to the interval distance of 1 meter, and the planned grids are assumed to contain 25 fixed nodes, and each fixed node is called a reference tag.
Step 2, counting the signal value reflected by the reference label:
the card reader is used for transmitting signals and receiving signals reflected from all the reference labels, the average value is obtained after repeated experiments, and the theoretical signal value corresponding to all the reference labels is recorded as:
Figure BDA0002744190100000071
and 3, screening adjacent reference labels:
when a label t to be positioned is attached to a target to be positioned and enters a space to be detected, signal values reflected by all reference labels under the condition are obtained, and the similarity between the signal value reflected by the label t to be positioned and the signal value reflected by the reference labels is compared;
the mean value of the signal values corresponding to the reference labels in the m experiments is counted and recorded as
Figure BDA0002744190100000081
Then, the signal mean values of m times of experiments reflected by the labels t to be positioned are respectively compared
Figure BDA0002744190100000082
Similarity to the mean of the signals reflected by each reference label r 1:
Figure BDA0002744190100000083
step 4, preliminarily determining the label q of the grid where the label to be positioned is located:
sorting all the similarities in descending order to obtain { S1,S2,...,S25And selecting reference labels corresponding to the first 6 similarities as adjacent reference labels, and determining the label q of the grid where the label to be positioned is located by using the positions of the adjacent reference labels. For example, the first grid has a corresponding reference label of {1,2,6,7 }.
Step 5, estimating a signal value corresponding to the virtual reference label:
further dividing the mesh at intervals of 25cm within the mesh of reference sign q to obtain 21 virtual reference labels, and marking the reference signs of the sub-meshes divided by the virtual fixed nodes;
the four reference tags contained in the grid labeled q reflect the following signal values:
Figure BDA0002744190100000084
the distances between the 21 virtual reference tags and the four reference tags are respectively as follows:
Figure BDA0002744190100000085
the distances from the four reference tags to the four readers are respectively as follows:
Figure BDA0002744190100000086
the distances from the 21 virtual reference tags to the four readers are respectively as follows:
Figure BDA0002744190100000087
with a spacing of 1/(2) from the virtual reference labelwEstimating a signal value of the virtual reference tag by the reference tags within the range of meters, wherein w represents the cycle number; taking the 1 st virtual reference tag as an example, assume that its neighboring reference tag is the first reference tag, and its signal value
Figure BDA0002744190100000088
Comprises the following steps:
Figure BDA0002744190100000091
where a, a is related to the environment and the type of signal receiver.
And then comparing the similarity of the signal values of the tag t to be positioned and the virtual reference tag i:
Figure BDA0002744190100000092
sorting the similarity in descending order to obtain { S'1,S'2,...,S'21}. Selecting the virtual reference labels corresponding to the first 6 similarities as adjacent virtual reference labels, determining the submesh of the label t to be positioned by the adjacent virtual reference labels, and marking as q1
Step 6, estimating the position of the label to be positioned:
numbering q according to the method of step 5)1And then, performing virtual reference label interpolation on the sub-grids to obtain k final adjacent virtual reference labels, and determining the weight of each final adjacent virtual reference label by utilizing the similarity between the signal value corresponding to the k final adjacent virtual reference labels and the signal value corresponding to the label t to be positioned:
the coordinates of the 6 final adjacent virtual reference tags are:
N(x1,y1,z1),N(x2,y2,z2),...,N(x6,y6,z6) (20)
using the similarity of the signal values obtained by equation (19), the weights of the 6 final neighboring virtual reference tags are calculated:
Figure BDA0002744190100000093
and finally, determining the coordinates (x, y, z) of the tag t to be positioned by utilizing the coordinates and the weights of the 6 final adjacent virtual reference tags:
Figure BDA0002744190100000101
assuming that the tag to be located enters the first grid, the actual location is (25,35) (cm), the location of the tag to be located is estimated by equation (22) in step 4 (which can be determined to be within the first grid.) to be about: (21,40) (cm), the position estimation error is about: 6.40 cm. The label used in this test is about 5cm x 5cm, and the size of the article to which the label is attached is generally larger than the size of the label, and it can be seen that this error is in the order of magnitude of the article's own size, so this error can be considered to be within an acceptable range.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.

Claims (7)

1. A virtual interpolation positioning method based on a disturbance channel model is characterized in that: the virtual interpolation positioning method based on the disturbance channel model comprises the following steps in sequence:
1) uniformly arranging a plurality of signal receivers serving as fixed nodes in a grid shape at a certain interval in a space to be detected, setting a label for each grid, and dispersedly arranging signal transmitters in the space to be detected;
2) transmitting a signal by using a signal transmitter and receiving a signal reflected by each fixed node to obtain an actual signal value reflected by each fixed node;
3) when a signal receiver t to be positioned is attached to a target to be positioned and enters a space to be detected, signal values reflected by all fixed nodes under the condition are obtained, and the similarity between the signal values reflected by the signal receiver t to be positioned and the signal values reflected by the fixed nodes is compared;
4) sorting all the similarities in a descending order, selecting a fixed node with larger similarity as an adjacent fixed node, and determining a label q of a grid where a signal receiver t to be positioned is located through the adjacent fixed node;
5) according to the mark q of the grid where the signal receiver t to be positioned is located, the mark q is positionedCarrying out virtual fixed node interpolation in the grids, taking one fourth of the distance between the fixed nodes as the distance between the virtual fixed nodes, and marking the labels of the sub-grids divided by the virtual fixed nodes; under the condition that the positions of four fixed nodes, the positions of virtual fixed nodes and the distance between the grid and a signal transmitter, which are contained in the grid with the label q, are known, a signal value reflected by the virtual fixed nodes is estimated by using a disturbance channel model, the similarity between a signal receiver t to be positioned and the signal value reflected by the virtual fixed nodes is compared, the virtual fixed nodes with higher similarity are selected as adjacent virtual fixed nodes, the sub-grid where the signal receiver t to be positioned is located is determined by the adjacent virtual fixed nodes, and the label q is marked as1
6) Numbering q according to the method of step 5)1And then carrying out virtual fixed node interpolation on the sub-grids to obtain a final adjacent virtual fixed node, and estimating the coordinate of the signal receiver t to be positioned by the final adjacent virtual fixed node.
2. The method according to claim 1, wherein the virtual interpolation positioning method based on the perturbation channel model comprises: in step 1), the method of uniformly arranging a plurality of signal receivers as fixed nodes in a grid shape at a certain interval in a space to be detected, setting a label for each grid, and dispersedly arranging signal transmitters in the space to be detected comprises:
after num signal transmitters and n signal receivers which need to be arranged in a space to be detected are determined, the n signal receivers are uniformly arranged in the space to be detected as fixed nodes according to the g-meter interval, so that the space to be detected is uniformly divided into a plurality of grids, the fixed nodes are positioned at the intersection points of the grids, a label is set for each grid, and the num signal transmitters are dispersedly arranged in the space to be detected.
3. The method according to claim 1, wherein the virtual interpolation positioning method based on the perturbation channel model comprises: in step 2), the method for obtaining the actual signal value reflected by each fixed node by using the signal transmitter to transmit the signal and receiving the signal reflected by each fixed node is as follows:
and (3) transmitting a signal by using a signal transmitter and receiving the signal reflected by each fixed node, repeating the experiment for a plurality of times, then taking an average value, and recording the average value as an actual signal value:
Figure FDA0002744190090000021
4. the method according to claim 1, wherein the virtual interpolation positioning method based on the perturbation channel model comprises: in step 3), the method for obtaining the signal values reflected by all the fixed nodes under the condition after the signal receiver t to be positioned is attached to the target to be positioned and enters the space to be detected, and comparing the similarity between the signal values reflected by the signal receiver t to be positioned and the signal values reflected by the fixed nodes is as follows:
the signal emitter is used for emitting signals and receiving signals reflected by all the fixed nodes, the mean value of the signal values reflected by all the fixed nodes under m times of experiments is counted and recorded as:
Figure FDA0002744190090000022
then, the signal mean values under m experiments reflected by the signal receiver t to be positioned are respectively compared
Figure FDA0002744190090000031
Similarity to the mean of the signals reflected by each fixed node r 1:
Figure FDA0002744190090000032
5. the method according to claim 1, wherein the virtual interpolation positioning method based on the perturbation channel model comprises: in step 4), the method for sorting all the similarities in a descending order, selecting a fixed node with a larger similarity as an adjacent fixed node, and determining the label q of the grid where the signal receiver t to be positioned is located by the adjacent fixed node includes:
sorting all the similarities obtained in the step 3) in a descending order to obtain { S1,S2,...,SnAnd selecting the fixed nodes corresponding to the first k similarities as adjacent fixed nodes, and determining the label q of the grid where the signal receiver t to be positioned is located by using the positions of the adjacent fixed nodes.
6. The method according to claim 1, wherein the virtual interpolation positioning method based on the perturbation channel model comprises: in step 5), performing virtual fixed node interpolation in the grid according to the label q of the grid where the signal receiver t to be positioned is located, taking one fourth of the distance between the fixed nodes as the distance between the virtual fixed nodes, and marking the labels of the sub-grids divided by the virtual fixed nodes; under the condition that the positions of four fixed nodes, the positions of virtual fixed nodes and the distance between the grid and a signal transmitter, which are contained in the grid with the label q, are known, a signal value reflected by the virtual fixed nodes is estimated by using a disturbance channel model, the similarity between a signal receiver t to be positioned and the signal value reflected by the virtual fixed nodes is compared, the virtual fixed nodes with higher similarity are selected as adjacent virtual fixed nodes, the sub-grid where the signal receiver t to be positioned is located is determined by the adjacent virtual fixed nodes, and the label q is marked as1The method comprises the following steps:
performing virtual fixed node interpolation in a grid of a label q where a signal receiver t to be positioned is located, taking one fourth of the g-meter distance of the fixed nodes determined in the step 1) as the distance of the virtual fixed nodes, obtaining n1 virtual fixed nodes, and marking labels of sub-grids divided by the virtual fixed nodes;
the signal values reflected by the four fixed nodes contained in the grid labeled q are:
Figure FDA0002744190090000041
the distances between the n1 virtual fixed nodes and the four fixed nodes are respectively:
Figure FDA0002744190090000042
the distances between the four fixed nodes and the signal emitter are respectively as follows:
Figure FDA0002744190090000043
the distances between the n1 virtual fixed nodes and the signal emitter are respectively:
Figure FDA0002744190090000044
by using the distance between the virtual fixed node and the virtual fixed node in g/(2)wEstimating a signal value of a virtual fixed node by using fixed nodes within a meter range, wherein w represents the cycle number;
for the ith virtual fixed node, the adjacent fixed node is the jth fixed node, and the signal value thereof
Figure FDA0002744190090000045
Comprises the following steps:
Figure FDA0002744190090000046
wherein, A, a is related to the environment and the type of the signal receiver;
and then comparing the similarity of the signal receiver t to be positioned and the signal value estimated at the virtual fixed node i:
Figure FDA0002744190090000047
sorting all the similarities in descending order to obtain { S1',S2',...,Sn1' }, selecting the virtual fixed nodes corresponding to the former k similarities as adjacent virtual fixed nodes, and further determining the sub-grid where the signal receiver to be positioned is located by the adjacent virtual fixed nodes, wherein the label is marked as q1
7. The method according to claim 1 or 8, wherein: in step 6), the method according to step 5) is labeled with the reference number q1The sub-grid carries out virtual fixed node interpolation to obtain a final adjacent virtual fixed node, and the method for estimating the coordinate of the signal receiver t to be positioned by the final adjacent virtual fixed node comprises the following steps:
numbering q according to the method of step 5)1And then, performing virtual fixed node interpolation on the sub-grids to obtain k final adjacent virtual fixed nodes, and determining the weight of each final adjacent virtual fixed node by utilizing the similarity between the signal value corresponding to the k final adjacent virtual fixed nodes and the signal value corresponding to the signal receiver t to be positioned:
the coordinates of the k final neighboring virtual fixed nodes are:
N(x1,y1,z1),N(x2,y2,z2),...,N(xk,yk,zk) (9)
calculating the weight of k final neighboring virtual fixed nodes using the similarity of the signal values obtained by equation (8):
Figure FDA0002744190090000051
and finally, determining the coordinates (x, y, z) of the signal receiver t to be positioned by using the coordinates and weights of the k final adjacent virtual fixed nodes:
Figure FDA0002744190090000052
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