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CN112815947A - Indoor positioning system and method based on terminal cluster - Google Patents

Indoor positioning system and method based on terminal cluster Download PDF

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CN112815947A
CN112815947A CN202110019880.7A CN202110019880A CN112815947A CN 112815947 A CN112815947 A CN 112815947A CN 202110019880 A CN202110019880 A CN 202110019880A CN 112815947 A CN112815947 A CN 112815947A
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terminal
node
cluster
channel
outer cover
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CN112815947B (en
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王衍文
马玥
王玉
马晓璠
周锋
赵培焱
沈洲
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Xijing University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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Abstract

The invention discloses an indoor positioning system and method based on a terminal cluster, aiming at the indoor positioning system based on the terminal cluster, comprising: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1A device with read-write function; the positioning method comprises the following steps: (S100) the node transmits information in a two-level precoding manner; (S200) terminal Q1For received data from node TtDetecting the signal of (a); (S300) to the terminal Q1And carrying out three-dimensional space position estimation. The method can provide good positioning service for a plurality of terminals simultaneously, improves the positioning efficiency of the indoor positioning system, effectively overcomes inter-cluster interference and intra-cluster interference in the terminal cluster, and improves the positioning accuracy.

Description

Indoor positioning system and method based on terminal cluster
Technical Field
The invention relates to an indoor positioning method, in particular to an indoor positioning system and method based on a terminal cluster.
Background
With the rapid increase of data services and multimedia services, people's demands for positioning are increasing, and especially in complex indoor environments, such as airport halls, supermarkets, libraries, underground parking lots and the like, it is often necessary to determine the indoor position information of the mobile terminal or its holder, facilities and articles. Most current positioning algorithms are only researched for a wireless two-dimensional network, however, in practical application, a wireless network node is often in a three-dimensional environment, three-dimensional position information of a mobile terminal needs to be provided in the situations, and currently, researchers provide many indoor positioning solutions based on radio frequency identification.
For example, chinese patent CN201710697495.1, which uses beam scanning to realize positioning, uses multiple antenna tags, and combines beam scanning to realize indoor positioning. However, the downward inclination angle of the antenna in the vertical direction in the two-dimensional beam is fixed, and only the spatial domain resource in the horizontal direction is utilized, so that the energy convergence is not high enough, and the coverage range is limited.
The multi-user multi-input multi-output technology fully utilizes the space freedom degree provided by the multi-antenna and effectively improves the average throughput of the system in a time-frequency resource multiplexing mode. When the base station adopts a uniform linear array structure, the downward inclination angle of the wave beam is fixed, and the wave beam forming can be carried out only in a horizontal two-dimensional plane; it can distinguish users at different horizontal angles, but cannot distinguish two users at the same horizontal angle and different distances.
Chinese patent CN201811108110.4 discloses an indoor multi-user positioning method based on three-dimensional beams, which uses three-dimensional beam scanning for positioning, but this method uses a uniform scanning mode based on region, does not consider environmental physical characteristics of the scanning region, and its positioning accuracy is low.
Disclosure of Invention
The invention aims to provide an indoor positioning system and method based on a terminal cluster, which can provide good positioning service for a plurality of terminals simultaneously, improve the positioning efficiency of the indoor positioning system, effectively overcome inter-cluster interference and intra-cluster interference in the terminal cluster and improve the positioning accuracy.
In order to achieve the above object, the present invention provides an indoor positioning method based on a terminal cluster, the method aiming at an indoor positioning system based on a terminal cluster, comprising: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1A device with read-write function; the indoor positioning method comprises the following steps:
(S100) the node transmits information in a two-stage precoding manner: any one node TtSetting the total number of terminals in the coverage area as K, and setting the node TtThe terminals in the coverage area are divided into N terminal clusters, and the number of the terminals of the q cluster is set as Kq，q∈[1,2,…,N]And is and
Figure BDA0002888264310000021
through node T1,T2,T3,T4The terminals respectively perform two-stage precoding-based transmission, and the nodes T1,T2,T3,T4The transmitted information includes: id and location information of the node;
(S200) terminal Q1For received data from node TtDetecting the signal of (a);
(S300) to the terminal Q1And (3) carrying out three-dimensional space position estimation: obtaining terminal Q through RSSI distance loss model1And T1、T2、T3And T4A distance l between1、l2、l3And l4Respectively with node T1、T2、T3And T4As the center of a circle, a distance of l1、l2、l3And l4Four balls for the radius, said terminal Q1In the space area enclosed by the four balls; re-estimating with four nodes T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Triangular pyramid circumscribed sphere center coordinate (x) as vertexOuter cover,yOuter cover,zOuter cover) The intersection points of the connecting lines of the four sphere centers and the triangular pyramid external sphere center and the sphere are determined, and the total four inner intersection points G are determinedtT is 1,2,3,4, and has the coordinate of (x)gt,ygt,zgt) And calculating the weighted mass center of the four intersection points as a terminal Q1Position coordinates of (d), mutAs a weighting factor, then terminal Q1The position coordinates of (a) are:
Figure BDA0002888264310000022
in step (S100), the method for the node to transmit information in the two-stage precoding scheme includes:
(S110) dividing the terminal clusters based on the mahalanobis distance minimum criterion: according to any two terminals QcAnd QdOf the channel covariance matrix of (a) is determined by the mahalanobis distance d (Q) between the channel covariance matrices of (a)c,Qd) And an empirical value dSetting upDetermining the division of the terminal cluster: if d (Q)c,Qd)≤dThreshold valueThen terminal QcAnd QdDivided into a same terminal cluster for use in
Figure BDA0002888264310000023
Represents;
(S120) estimating precoding from the terminal cluster: for terminal cluster
Figure BDA0002888264310000024
The estimation is based on the channel covariance matrixTwo-stage precoding of cq；
(S130) secondary precoding transmission based on terminal clustering: node TtThe original signal S is weighted by the secondary precoding and mapped to the corresponding antenna port, and the transmitted signal is: c. Cq·s。
In step (S120), the method for estimating precoding from a terminal cluster includes:
(S121) estimating outer layer precoding: according to the maximum trace of the channel covariance matrix, the outer precoding c is obtainedq, outerThe method comprises the following steps:
Figure BDA0002888264310000031
Figure BDA0002888264310000032
Figure BDA0002888264310000033
in the formulas (5), (6) and (7), the upper corner mark is used for solving the conjugation transpose; tr () represents the trace of the matrix; c. CiIs a precoding codeword; w3DIs a precoding codebook;
Figure BDA0002888264310000034
as a node TtTo the aggregate channel among all terminals in the qth cluster, where Ht,q1As a node TtChannel to 1 st terminal of qth cluster, Ht,q2As a node TtChannel to the 2 nd terminal of the qth cluster, Ht,qKqAs a node TtTo cluster q, KqA channel of each terminal;
Figure BDA0002888264310000035
for aggregating channels
Figure BDA0002888264310000036
The channel covariance matrix of (a) is determined,
Figure BDA0002888264310000037
for aggregating channels
Figure BDA0002888264310000038
The dimension(s) of (a) is,
Figure BDA0002888264310000039
is a channel covariance matrix corresponding to the terminal cluster other than the q cluster, argmax]C represents the time when the latter expression is maximizediValue selection, which means that the code word with the maximum objective function value is selected in the codebook as the outer precoding cq, outer；
(S122) estimating inner layer precoding: setting aggregated channels
Figure BDA00028882643100000310
The equivalent channel formed by the outer layer precoding of the q-th cluster terminal is as follows:
Figure BDA00028882643100000311
using equivalent channels
Figure BDA00028882643100000312
To eliminate intra-cluster interference, then:
Figure BDA00028882643100000313
(S123) obtaining a secondary precoding according to the outer layer precoding and the inner layer precoding, comprising:
cq＝cq, outer·cq, inner (9)。
Preferably, in step (S110), dividing the terminal cluster based on the mahalanobis distance minimum criterion includes:
(S111) estimating arbitrary two terminals QcAnd QdOf the channel covariance matrix of (a) is determined by the mahalanobis distance d (Q) between the channel covariance matrices of (a)c,Qd) And an empirical value dSetting upDetermining the division of the terminal cluster: if d (Q)c,Qd)≤dThreshold valueThen terminal QcAnd QdDivided into the same terminal cluster
Figure BDA0002888264310000041
Figure BDA0002888264310000042
Figure BDA0002888264310000043
In the formulae (1) and (2), RcRepresents terminal QcOf the channel covariance matrix, RdRepresents terminal QdThe upper index indicates the conjugate transpose, the upper index-1 indicates the inversion, rowqIs terminal QqChannel H ofqQ is c or d;
(S112) for
Figure BDA0002888264310000044
Representing clusters of terminals
Figure BDA0002888264310000045
Center point Y ofc+dCorresponding channel, terminal cluster
Figure BDA0002888264310000046
Is a virtual terminal, then
Figure BDA0002888264310000047
As a node TtTo the virtual terminal
Figure BDA0002888264310000048
Aggregate channels of, and
Figure BDA0002888264310000049
Ht，cas a node TtTo terminal cluster
Figure BDA00028882643100000410
Middle terminal QcChannel of (1), Ht，dAs a node TtTo terminal cluster
Figure BDA00028882643100000411
Middle terminal QdEstimating a virtual terminal
Figure BDA00028882643100000412
And QeOf the channel covariance matrix of
Figure BDA00028882643100000413
And an empirical value dSetting upDetermining the division of the terminal cluster: if it is
Figure BDA00028882643100000414
Then the terminal
Figure BDA00028882643100000415
And QeDivided into a same terminal cluster, terminal Qc、QdAnd QeBelong to the same terminal cluster;
Figure BDA00028882643100000416
Figure BDA00028882643100000417
in the formulae (3) and (4),
Figure BDA00028882643100000418
representing virtual terminals
Figure BDA00028882643100000419
The channel covariance matrix of (a); reRepresents terminal QeOf the channel covariance matrix, ReObtained by the formula (2).
Preferably, the weighting factor μtTaking the reciprocal of the maximum characteristic root of the channel covariance matrix as:
Figure BDA00028882643100000420
λ1as a node T1To terminal Q1Channel H of1,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA00028882643100000421
λ2as a node T2To terminal Q1Channel H of2,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA00028882643100000422
λ3as a node T3To terminal Q1Channel H of3,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA00028882643100000423
λ4as a node T4To terminal Q1Channel H of4,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA0002888264310000051
in the formula, argmax [ eig () ] represents taking the largest characteristic root in ().
Preferably, in step (S300), the terminal Q is paired1A method for performing three-dimensional spatial position estimation, comprising:
(S310) verifying four nodes T1、T2、T3And T4Are not in the same planeThe above step (1);
(S320) estimating a terminal Q using a distance loss model1To four nodes T1、T2、T3And T4A distance of l1、l2、l3And l4；
(S330) establishing a three-dimensional spherical equation set: with node T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Are the centers of the spheres and are respectively represented by1、l2、l3And l4Spherical equation for radius, is:
Figure BDA0002888264310000052
Figure BDA0002888264310000053
Figure BDA0002888264310000054
Figure BDA0002888264310000055
(S340) estimating the circumscribed spherical center coordinates of the triangular pyramid having the coordinates of the four nodes as vertexes as the decentration coordinates (x)Outer cover,yOuter cover,zOuter cover) Then, there are:
Figure BDA0002888264310000056
in the formula (I), the compound is shown in the specification,
Figure BDA0002888264310000057
| | is a determinant symbol;
(S350) 4 inner intersection points of the connecting lines of the four sphere centers and the triangular pyramid outer sphere center and the spherical surface are obtained, the reciprocal of the maximum characteristic root of the channel covariance matrix is used as a weighting factor, and the mass center of the 4 intersection points is obtained as a terminal Q1Position coordinates of (2):
centre of sphere (x)1,y1,z1) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000061
centre of sphere (x)2,y2,z2) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000062
centre of sphere (x)3,y3,z3) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000063
centre of sphere (x)4,y4,z4) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000064
the equations (10) and (14) are solved simultaneously to obtain two intersection points g1、g2Get g1、g2Middle distance of other three (x)2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000065
The equations (11) and (15) are solved simultaneously to obtain two intersection points g3、g4Get g3、g4Middle distance of other three (x)1,y1,z1)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000066
The equations (12) and (16) are solved simultaneously to obtain two intersection points g5、g6Get g5、g6Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000067
The equations (13) and (17) are solved simultaneously to obtain two intersection points g7、g8Get g7、g8Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)3,y3,z3) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000068
Another object of the present invention is to provide an indoor positioning system based on a terminal cluster, the indoor positioning system comprising: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1A device with read-write function; any terminal Q to be positioned in indoor positioning system1The positioning is carried out by the method.
The indoor positioning system and method based on the terminal cluster have the following advantages:
the method of the invention is based on the terminal cluster with the minimum Mahalanobis distance, can provide good positioning service for a plurality of terminals simultaneously, and improves the positioning efficiency of the indoor positioning system. Meanwhile, inter-cluster interference and intra-cluster interference in the terminal cluster can be effectively overcome by adopting two-stage precoding, and the positioning accuracy is improved. The space sphere weighted centroid method based on the channel covariance matrix fully utilizes channel information between each node and a terminal, and is more targeted to channel environments (including topographic features, surrounding buildings and the like), so that the service quality is improved.
Drawings
Fig. 1 is a flowchart of an indoor three-dimensional positioning method based on a terminal cluster according to the present invention.
Fig. 2 is a flowchart of a method for transmitting information by a node in a two-stage precoding manner according to the present invention.
Fig. 3 is a flowchart of a method for selecting a terminal in a terminal cluster according to the present invention.
Fig. 4 is a positioning block diagram of the method of the present invention.
Fig. 5 is a schematic diagram of terminal clusters partitioned based on mahalanobis distance minimum criterion according to the present invention.
Fig. 6 is a schematic diagram of terminal clustering-based two-stage precoding transmission.
Fig. 7 is a schematic diagram of a spatial sphere weighted centroid method based on a channel covariance matrix.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. 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.
Example 1
An indoor positioning method based on a terminal cluster is shown in fig. 4, which is a positioning block diagram of the method of the present invention, and the indoor positioning system based on the terminal cluster aimed by the method comprises: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1The device has read-write function. As shown in fig. 1, a flowchart of an indoor three-dimensional positioning method based on a terminal cluster according to the present invention is shown, and the positioning method includes:
(S100) the node transmits information in a two-stage precoding manner: any one node TtSetting the total number of terminals in the coverage area as K, and setting the node TtThe terminals in the coverage area are divided into N terminal clusters, and the number of the terminals of the q cluster is set as Kq，q∈[1,2,…,N]And is and
Figure BDA0002888264310000081
through node T1,T2,T3,T4The terminals respectively perform two-stage precoding-based transmission, and the nodes T1,T2,T3,T4The sent information comprises the id, the position information and the like of the node;
(S200) terminal Q1For received data from node TtThe signal of (2) is detected: in actual detection, assume terminal Q1Receiving T1、T2、T3And T4Separating the signals of the four nodes from the signals of the four nodes, and then processing the signals;
(S300) to the terminal Q1And (3) carrying out three-dimensional space position estimation: obtaining terminal Q through RSSI distance loss model1And each node Tt(t is 1,2,3,4) distance lt(T is 1,2,3,4), and each node T is a node Tt(t is 1,2,3,4) as the center of circle and a distance lt(t is 1,2,3,4) four spheres are obtained as radii, and the actual terminal Q is obtained1In the space area enclosed by the four balls; re-estimating with four nodes T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Triangular pyramid circumscribed sphere center coordinate (x) as vertexOuter cover,yOuter cover,zOuter cover) (ii) a Then, the intersection points of the connecting lines of the four sphere centers and the triangular pyramid external sphere center and the sphere are calculated, and the total four inner side intersection points GtT is 1,2,3,4, and has the coordinate of (x)gt,ygt,zgt) And calculating the weighted mass center of the four intersection points as a terminal Q1Position coordinates of (d), mutAs a weighting factor, then terminal Q1The position coordinates of (a) are:
Figure BDA0002888264310000082
in step (S100), the method for transmitting information by a node in a two-stage precoding manner, referring to fig. 2, includes:
(S110) terminal clusters are divided based on the mahalanobis distance minimum criterion
FIG. 5 is a schematic diagram of a terminal cluster divided based on the Mahalanobis distance minimum criterion, T1The nodes are represented by other marks, the terminals in different clusters are distinguished by different marks, the cross is the center of a terminal cluster or the position of a virtual terminal, a dotted line represents a connecting line between the terminal and the center point of the cluster, the total number K of the terminals in the graph is 10, the number Q of the terminal clusters is 3, the number of the terminals in the 1 st cluster, the number of the terminals in the 2 nd cluster and the number of the terminals in the 3 rd cluster are respectively 3, 5 and 2, and the number is respectively marked as the terminal cluster
Figure BDA0002888264310000083
And
Figure BDA0002888264310000084
by terminal cluster
Figure BDA0002888264310000085
For an example, a method for selecting a terminal in a terminal cluster is described, with reference to fig. 3, specifically as follows:
(S111) terminal Q1Of the channel covariance matrix R1And terminal Q2Of the channel covariance matrix R2Mahalanobis distance d (Q) therebetween1,Q2) The method comprises the following steps:
Figure BDA0002888264310000091
Figure BDA0002888264310000092
in the formulas (1) and (2), the upper corner mark indicates the conjugation transpose, the upper corner mark-1 indicates the inversion, and row indicatesqIs terminal QqChannel H ofqQ is 1 or 2.
Judging the Mahalanobis distance d (Q)1,Q2) And dThreshold valueTo thereby determine whether to put the terminal Q on1And terminal Q2Divided into the same terminal cluster
Figure BDA0002888264310000093
dThreshold valueFor set empirical values (e.g. taken as 0.3 units): when d (Q)1,Q2)≤dThreshold valueThen form terminal cluster
Figure BDA0002888264310000094
(S112) for
Figure BDA0002888264310000095
Representing clusters of terminals
Figure BDA0002888264310000096
Center point Y of1+2Corresponding channel, visible terminal cluster
Figure BDA0002888264310000097
Is a virtual terminal and is a terminal with a plurality of terminals,
Figure BDA0002888264310000098
as a node T1To the virtual terminal
Figure BDA0002888264310000099
Aggregate channels of, and
Figure BDA00028882643100000910
H1，11as a node T1To terminal cluster
Figure BDA00028882643100000911
Middle terminal Q1Channel of (1), H1，12As a node T1To terminal cluster
Figure BDA00028882643100000912
Middle terminal Q2Channel of (2), then virtual terminal
Figure BDA00028882643100000913
Of the channel covariance matrix R1+2And terminal Q3Of the channel covariance matrix R3Mahalanobis distance between, is:
Figure BDA00028882643100000914
Figure BDA00028882643100000915
Figure BDA00028882643100000916
in the formula (4), row1+2As a virtual terminal
Figure BDA00028882643100000917
Of aggregated channels
Figure BDA00028882643100000918
Dimension, row of3Is terminal Q3Channel H of3Dimension (d) of (a).
Judging the Mahalanobis distance
Figure BDA00028882643100000919
And dThreshold valueThe size of (2): when in use
Figure BDA00028882643100000920
Then form terminal cluster
Figure BDA00028882643100000921
In the same way, dividing to obtain terminal clusters
Figure BDA00028882643100000922
And
Figure BDA00028882643100000923
(S120) estimating precoding from a cluster of terminals
And aiming at the terminal cluster, estimating two-stage precoding based on a channel covariance matrix, wherein the outer-layer precoding is used for eliminating the interference among clusters, and the inner-layer precoding is used for eliminating the interference in the clusters. The method for estimating precoding according to the terminal cluster comprises the following steps:
(S121) estimating outer layer precoding: according to the maximum trace of the channel covariance matrix, the outer precoding c is obtainedq, outerThe method comprises the following steps:
Figure BDA0002888264310000101
Figure BDA0002888264310000102
Figure BDA0002888264310000103
in the formula, the upper corner mark is used for solving conjugate transpose, tr () represents the trace of solving matrix, ciFor precoding code words, W3DIn order to be a precoding codebook, a precoding codebook is selected,
Figure BDA0002888264310000104
as a node TtAggregated channels between all terminals up to the qth cluster, where Ht,q1As a node TtChannel to 1 st terminal of qth cluster, Ht,q2As a node TtChannel to qth cluster 2 nd terminal, …, Ht,qKqAs a node TtTo cluster q, KqA channel of each terminal;
Figure BDA0002888264310000105
for aggregating channels
Figure BDA0002888264310000106
The channel covariance matrix of (a) is determined,
Figure BDA0002888264310000107
for aggregating channels
Figure BDA0002888264310000108
The dimension(s) of (a) is,
Figure BDA0002888264310000109
channel covariance matrices corresponding to other terminal clusters except the qth cluster,
Figure BDA00028882643100001010
c represents the time when the latter expression is maximizediValue selection, which means that the code word with the maximum objective function value is selected in the codebook as the outer precoding cq, outer。
(S122) estimating inner layer precoding
Setting aggregated channels
Figure BDA00028882643100001011
The equivalent channel formed by the outer layer precoding of the q-th cluster terminal is as follows:
Figure BDA00028882643100001012
using equivalent channels
Figure BDA00028882643100001013
To eliminate intra-cluster interference, then:
Figure BDA00028882643100001014
(S123) obtaining a secondary precoding according to the outer layer precoding and the inner layer precoding, comprising:
cq＝cq, outer·cq, inner (9)
In the same way, the corresponding terminal cluster is obtained
Figure BDA00028882643100001015
And
Figure BDA00028882643100001016
the precoding of (c) is: c. C2And c3。
(S130) Secondary Pre-coded Transmission based on terminal clustering
FIG. 6 is a schematic diagram of two-stage precoding transmission based on terminal clustering, for a terminal cluster
Figure BDA0002888264310000111
Respectively adopting two-stage precoding mode to transmit information, i.e. adopting correspondent precoding c1、c2And c3In particular node T1The original signal S is weighted by the secondary precoding and mapped to the corresponding antenna port, i.e. the transmitted signal is: c. C1·s，c2·s，……，c3S, in which only terminal clusters are given to avoid aliasing
Figure BDA0002888264310000112
Emission legend of (1).
(S300) the terminal performs three-dimensional spatial position estimation
As shown in fig. 7, a schematic diagram of a spatial sphere weighted centroid method based on a channel covariance matrix, a method for a terminal to perform three-dimensional spatial position estimation includes:
(S310) verifying four nodes TtThe coordinates of (t ═ 1,2,3,4) are not on the same plane
Determining a unique triangular pyramid by the four coordinates, and further determining a unique mobile terminal position coordinate; in fact, four nodes T1、T2、T3And T4Are pre-arranged and not on the same plane.
(S320) estimating a terminal Q using a distance loss model1Distance to each node
Let terminal Q1Has coordinates of (x, y, z), four nodes T1、T2、T3And T4Respectively is (x)1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Then, the terminal Q is estimated by using the distance loss model1To each node T1、T2、T3And T4Are each a distance of1、l2、l3And l4；
(S330) establishing a three-dimensional spherical equation set
Three-dimensional space with nodes T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Are the centers of the spheres and are respectively represented by1、l2、l3And l4Spherical equation for radius, is:
Figure BDA0002888264310000113
Figure BDA0002888264310000114
Figure BDA0002888264310000115
Figure BDA0002888264310000116
theoretically, the terminal Q to be positioned is obtained according to the estimation1And four nodes T1、T2、T3And T4Is a Euclidean distance l1、l2、l3And l4And solving to obtain a terminal Q to be positioned1The solution of the above equation system can be regarded as solving the intersection point of 4 spherical surfaces in space. In practical applications, the four spheres may not intersect at exactly one point due to measurement errors. For this purpose, a weighted centroid algorithm based on the intersection of the connecting line of the sphere center and the outer center and the sphere surface is used for estimation.
(S340) estimating coordinates of the center of the circumscribed sphere of the triangular pyramid having the coordinates of the four nodes as vertexes
Estimate with four nodes T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) The circumscribed spherical center coordinate of a triangular pyramid having a vertex, i.e. the outer center coordinate (x)Outer cover,yOuter cover,zOuter cover) Then, there are:
Figure BDA0002888264310000121
in the formula (I), the compound is shown in the specification,
Figure BDA0002888264310000122
and | is a determinant symbol.
(S350) determining the intersection point of the connecting line of the four sphere centers and the triangular pyramid external sphere center and the sphere4 inner intersection points are totally calculated, the reciprocal of the maximum characteristic root of the channel covariance matrix is used as a weighting factor, and the centroid of the 4 intersection points is obtained as a terminal Q1The position coordinates of (a).
Centre of sphere (x)1,y1,z1) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000123
centre of sphere (x)2,y2,z2) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000124
centre of sphere (x)3,y3,z3) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000125
centre of sphere (x)4,y4,z4) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure BDA0002888264310000126
the equations (10) and (14) are solved simultaneously to obtain two intersection points g1、g2Get g1、g2Middle distance of other three (x)2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000127
The equations (11) and (15) are solved simultaneously to obtain two intersection points g3、g4Get g3、g4Middle distance of other three (x)1,y1,z1)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000137
The equations (12) and (16) are solved simultaneously to obtain two intersection points g5、g6Get g5、g6Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000138
The equations (13) and (17) are solved simultaneously to obtain two intersection points g7、g8Get g7、g8Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)3,y3,z3) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure BDA0002888264310000139
The three-dimensional weighted centroid method based on the space sphere is adopted for estimation, and the weighting factor mu1,μ2,μ3,μ4Taking the reciprocal of the maximum characteristic root of the channel covariance matrix as:
Figure BDA0002888264310000131
λ1as a node T1To terminal Q1Channel H of1,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA0002888264310000132
λ2as a node T2To terminal Q1Channel H of2,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA0002888264310000133
λ3as a node T3To terminal Q1Channel H of3,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA0002888264310000134
λ4as a node T4To terminal Q1Channel H of4,1The maximum characteristic root of the covariance matrix of (a) is:
Figure BDA0002888264310000135
in the formula, argmax [ eig () ] represents taking the largest characteristic root in ().
Then terminal Q1The estimated value of the three-dimensional coordinates of (a) is:
Figure BDA0002888264310000136
while the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (5)

1. An indoor positioning method based on a terminal cluster is characterized in that the indoor positioning system based on the terminal cluster aimed by the method comprises the following steps: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1A device with read-write function; the indoor positioning method comprises the following steps:
(S100) the node transmits information in a two-stage precoding manner: any one node TtSetting the total number of terminals in the coverage area as K, and setting the node TtThe terminals in the coverage area are divided into N terminal clusters, and the number of the terminals of the q cluster is set as Kq，q∈[1,2,…,N]And is and
Figure FDA0002888264300000011
through node T1,T2,T3,T4The terminals respectively perform two-stage precoding-based transmission, and the nodes T1,T2,T3,T4The transmitted information includes: id and location information of the node;
(S200) terminal Q1For received data from node TtDetecting the signal of (a);
(S300) to the terminal Q1And (3) carrying out three-dimensional space position estimation: obtaining terminal Q through RSSI distance loss model1And T1、T2、T3And T4A distance l between1、l2、l3And l4Respectively with node T1、T2、T3And T4As the center of a circle, a distance of l1、l2、l3And l4Four balls for the radius, said terminal Q1In the space area enclosed by the four balls; re-estimating with four nodes T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Triangular pyramid circumscribed sphere center coordinate (x) as vertexOuter cover,yOuter cover,zOuter cover) The intersection points of the connecting lines of the four sphere centers and the triangular pyramid external sphere center and the sphere are determined, and the total four inner intersection points G are determinedtT is 1,2,3,4, and has the coordinate of (x)gt,ygt,zgt) And calculating the weighted mass center of the four intersection points as a terminal Q1Position coordinates of (d), mutAs a weighting factor, then terminal Q1The position coordinates of (a) are:
Figure FDA0002888264300000012
in step (S100), the method for the node to transmit information in the two-stage precoding scheme includes:
(S110) dividing the terminal clusters based on the mahalanobis distance minimum criterion: according to any two terminals QcAnd QdOf the channel covariance matrix of (a) is determined by the mahalanobis distance d (Q) between the channel covariance matrices of (a)c,Qd) And an empirical value dSetting upDetermining the division of the terminal cluster: if d (Q)c,Qd)≤dThreshold valueThen terminal QcAnd QdDivided into a same terminal cluster for use in
Figure FDA0002888264300000021
Represents;
(S120) estimating precoding from the terminal cluster: for terminal cluster
Figure FDA0002888264300000022
Estimating two-stage precoding c based on channel covariance matrixq；
(S130) secondary precoding transmission based on terminal clustering: node TtThe original signal S is weighted by the secondary precoding and mapped to the corresponding antenna port, and the transmitted signal is: c. Cq·s；
In step (S120), the method for estimating precoding from a terminal cluster includes:
(S121) estimating outer layer precoding: according to the maximum trace of the channel covariance matrix, the outer precoding c is obtainedqAnd, in addition, is:
Figure FDA0002888264300000023
Figure FDA0002888264300000024
Figure FDA0002888264300000025
in the formulas (5), (6) and (7), the upper corner mark is used for solving the conjugation transpose; tr () represents the trace of the matrix; c. CiIs a precoding codeword; w3DIs a precoding codebook;
Figure FDA0002888264300000026
as a node TtTo the aggregate channel among all terminals in the qth cluster, where Ht,q1As a node TtChannel to 1 st terminal of qth cluster, Ht,q2As a node TtChannel to the 2 nd terminal of the qth cluster, Ht,qKqAs a node TtTo cluster q, KqA channel of each terminal;
Figure FDA0002888264300000027
for aggregating channels
Figure FDA0002888264300000028
The channel covariance matrix of (a) is determined,
Figure FDA0002888264300000029
for aggregating channels
Figure FDA00028882643000000210
The dimension(s) of (a) is,
Figure FDA00028882643000000211
is a channel covariance matrix corresponding to the terminal cluster other than the q cluster, argmax]C represents the time when the latter expression is maximizediValue selection, which means that the code word with the maximum objective function value is selected in the codebook as the outer precoding cqAnd, externally;
(S122) estimating inner layer precoding: setting aggregated channels
Figure FDA00028882643000000212
The equivalent channel formed by the outer layer precoding of the q-th cluster terminal is as follows:
Figure FDA00028882643000000213
using equivalent channels
Figure FDA00028882643000000214
To eliminate intra-cluster interference, then:
Figure FDA00028882643000000215
(S123) obtaining a secondary precoding according to the outer layer precoding and the inner layer precoding, comprising:
cq＝cqouter, cqInner (9).
2. The indoor positioning method based on terminal cluster as claimed in claim 1, wherein in the step (S110), dividing the terminal cluster based on mahalanobis distance minimum criterion comprises:
(S111) estimating arbitrary two terminals QcAnd QdOf the channel covariance matrix of (a) is determined by the mahalanobis distance d (Q) between the channel covariance matrices of (a)c,Qd) And an empirical value dSetting upDetermining the division of the terminal cluster: if d (Q)c,Qd)≤dThreshold valueThen terminal QcAnd QdDivided into the same terminal cluster
Figure FDA0002888264300000031
Figure FDA0002888264300000032
Figure FDA0002888264300000033
In the formulae (1) and (2), RcRepresents terminal QcOf the channel covariance matrix, RdRepresents terminal QdThe upper index indicates the conjugate transpose, the upper index-1 indicates the inversion, rowqIs terminal QqChannel H ofqQ is c or d;
(S112) for
Figure FDA0002888264300000034
Representing clusters of terminals
Figure FDA0002888264300000035
Center point Y ofc+dCorresponding channel, terminal cluster
Figure FDA0002888264300000036
Is a virtual terminal, then
Figure FDA0002888264300000037
As a node TtTo the virtual terminal
Figure FDA0002888264300000038
Aggregate channels of, and
Figure FDA0002888264300000039
Ht，cas a node TtTo terminal cluster
Figure FDA00028882643000000310
Middle terminal QcChannel of (1), Ht，dAs a node TtTo terminal cluster
Figure FDA00028882643000000311
Middle terminal QdEstimating a virtual terminal
Figure FDA00028882643000000312
And QeOf the channel covariance matrix of
Figure FDA00028882643000000313
And an empirical value dSetting upDetermining the division of the terminal cluster: if it is
Figure FDA00028882643000000314
Then the terminal
Figure FDA00028882643000000315
And QeDivided into a same terminal cluster, terminal Qc、QdAnd QeBelong to the same terminal cluster;
Figure FDA00028882643000000316
Figure FDA00028882643000000317
in the formulae (3) and (4),
Figure FDA00028882643000000318
representing virtual terminals
Figure FDA00028882643000000319
The channel covariance matrix of (a); reRepresents terminal QeOf the channel covariance matrix, ReObtained by the formula (2).
3. The method of claim 1, wherein the weighting factor μ istTaking the reciprocal of the maximum characteristic root of the channel covariance matrix as:
Figure FDA00028882643000000320
λ1as a node T1To terminal Q1Channel H of1,1The maximum characteristic root of the covariance matrix of (a) is:
Figure FDA00028882643000000321
λ2as a node T2To terminal Q1Channel H of2,1The maximum characteristic root of the covariance matrix of (a) is:
Figure FDA0002888264300000041
λ3as a node T3To terminal Q1Channel H of3,1The maximum characteristic root of the covariance matrix of (a) is:
Figure FDA0002888264300000042
λ4as a node T4To terminal Q1Channel H of4,1The maximum characteristic root of the covariance matrix of (a) is:
Figure FDA0002888264300000043
in the formula, argmax [ eig () ] represents taking the largest characteristic root in ().
4. The method for indoor positioning based on terminal cluster according to any one of claims 1-3, characterized in that in step (S300), Q is applied to terminal1A method for performing three-dimensional spatial position estimation, comprising:
(S310) verifying four nodes T1、T2、T3And T4Are not on the same plane;
(S320) estimating a terminal Q using a distance loss model1To four nodes T1、T2、T3And T4A distance of l1、l2、l3And l4；
(S330) establishing a three-dimensional spherical equation set: with node T1、T2、T3And T4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) Are the centers of the spheres and are respectively represented by1、l2、l3And l4Spherical equation for radius, is:
Figure FDA0002888264300000044
Figure FDA0002888264300000045
Figure FDA0002888264300000046
Figure FDA0002888264300000047
(S340) estimating the circumscribed spherical center coordinates of the triangular pyramid having the coordinates of the four nodes as vertexes as the decentration coordinates (x)Outer cover,yOuter cover,zOuter cover) Then, there are:
Figure FDA0002888264300000051
in the formula (I), the compound is shown in the specification,
Figure FDA0002888264300000052
| | is a determinant symbol;
(S350) 4 inner intersection points of the connecting lines of the four sphere centers and the triangular pyramid outer sphere center and the spherical surface are obtained, the reciprocal of the maximum characteristic root of the channel covariance matrix is used as a weighting factor, and the mass center of the 4 intersection points is obtained as a terminal Q1Position coordinates of (2):
centre of sphere (x)1,y1,z1) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure FDA0002888264300000053
centre of sphere (x)2,y2,z2) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure FDA0002888264300000054
centre of sphere (x)3,y3,z3) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure FDA0002888264300000055
centre of sphere (x)4,y4,z4) To the heart (x)Outer cover,yOuter cover,zOuter cover) Equation of the connecting line:
Figure FDA0002888264300000056
the equations (10) and (14) are solved simultaneously to obtain two intersection points g1、g2Get g1、g2Middle distance of other three (x)2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure FDA0002888264300000057
The equations (11) and (15) are solved simultaneously to obtain two intersection points g3、g4Get g3、g4Middle distance of other three (x)1,y1,z1)、(x3,y3,z3) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure FDA0002888264300000058
The equations (12) and (16) are solved simultaneously to obtain two intersection points g5、g6Get g5、g6Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)4,y4,z4) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure FDA0002888264300000061
The equations (13) and (17) are solved simultaneously to obtain two intersection points g7、g8Get g7、g8Middle distance of other three (x)1,y1,z1)、(x2,y2,z2) And (x)3,y3,z3) The intersection point of the sphere centers is the inner intersection point and is marked as
Figure FDA0002888264300000062
5. An indoor positioning system based on a terminal cluster, the indoor positioning system comprising: indoor access node TtAnd a plurality of terminals QpP is terminal number, T is node number, and at least four nodes T not on the same plane1、T2、T3And T4The node is a base station around the environment to be positioned and uses a terminal Q1Any terminal to be positioned in a plurality of terminals in the representation area, namely a terminal Q1A device with read-write function; any terminal Q to be positioned in indoor positioning system1Localization is performed by the method according to any of claims 1-4.
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