CN108834060B - A kind of indoor 3-D positioning method and system based on virtual subdistrict - Google Patents
A kind of indoor 3-D positioning method and system based on virtual subdistrict Download PDFInfo
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Abstract
The indoor 3-D positioning method and system, this method that the invention discloses a kind of based on virtual subdistrict include: establishing virtual subdistrict: establishing at least two virtual subdistrict according to the relative position and channel of reception terminal to be measured and node；Virtual base station is obtained to the channel matrix for receiving terminal；According to the optimizing to system and rate R, the pre-coding matrix w of virtual base station is obtainedk；Wave beam forming is carried out according to transmitting signal of the precoding to virtual base station；Reception terminal detection to be measured, with the determination position to be measured for receiving terminal.Wherein, the calculation method of pre-coding matrix includes: obtaining egoistic pre-coding matrix；Obtain his pre-coding matrix of benefit；System of homogeneous linear equations is solved, obtains the solution of equation group as his vector of benefit, according to his pre-coding matrix of benefit his vector composition benefit；According to mapping of the egoistic pre-coding matrix on his sharp pre-coding matrix, the pre-coding matrix of virtual base station k is obtained.Method and system covering of the invention is wide, anti-multipath effect is good, and indoor positioning is fast.
Description
Technical Field
The invention belongs to the technical field of space positioning, and particularly relates to an indoor three-dimensional positioning method and system based on a virtual cell.
Background
With the rapid increase of data traffic and multimedia traffic, providing services based on geographical location information has become one of the most promising services. From traditional GPS navigation, to consumer information services and social software based on geographical positions such as WeChat, the basis for realizing the functions of the system is to obtain measurement information such as distance and angle through equipment such as a terminal and convert the measurement information into coordinate information by using a positioning algorithm. Due to the particularity and complexity of the indoor environment, the GPS cannot perform positioning in the indoor environment, so that the research of a method based on mobile terminal positioning is particularly important.
Positioning is realized by using beam scanning, for example, chinese patent with application number CN201710697495.1, which 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 convergence of energy is not high enough, and the coverage range is limited.
A high-precision three-dimensional outdoor and indoor integrated positioning method and device of live-action, such as Chinese patent with application number CN201610813895.X, its method is to introduce GPS positioning result into the room, select several measurable datum points of GPS coordinate in the room, regard datum point as the origin of coordinates to set up the coordinate system of the platform; introducing a laser three-dimensional scanner at the reference point to acquire indoor three-dimensional point cloud information, and unifying the point clouds to a platform coordinate system; and further performing coordinate conversion on the coordinate system of the ultra-wideband indoor positioning system and the coordinate data to complete indoor target positioning. However, the positioning system has a complex structure, high cost and great implementation difficulty.
Disclosure of Invention
The invention aims to provide an indoor three-dimensional positioning method and system based on a virtual cell, which solve the problems of complexity and difficulty in indoor positioning in the prior art, can effectively improve the coverage of the system and perform quick positioning.
In order to achieve the above object, the present invention provides an indoor three-dimensional positioning method based on a virtual cell, the method comprising:
step 1 (S100): establishing a virtual cell: establishing at least more than two virtual cells according to the relative positions of a receiving terminal to be measured and a node and a channel, wherein the two virtual cells are respectively expressed as virtual cells k and j, and a virtual base station of the virtual cell comprises: more than 4 nodes, and at least 4 nodes are not on the same plane;
step 2 (S200): obtaining a channel matrix from the virtual base station to the receiving terminal: obtaining a channel matrix H from a virtual base station k of a virtual cell k to a receiving terminal to be testedkkAnd a channel matrix H from the virtual base station j of the virtual cell j to the receiving terminal to be testedkj；
Step 3 (S300): obtaining a precoding matrix w of the virtual base station according to the optimization of the system and the rate Rk；
Step 4 (S400): carrying out beam forming on the transmitting signals of the virtual base station according to the pre-coding;
step 5 (S500): and detecting the receiving terminal to be detected to determine the position of the receiving terminal to be detected.
In the step 3, the precoding matrix wkThe calculating method comprises the following steps:
step 1B (S321): obtaining a lyre precoding matrix wind(ii) a Setting matrixU eigenvalues of (a)1,λ2,...,λuThe corresponding feature vector isThen wind＝[wind1 wind2Lwindu]In the formula, the upper-corner mark H represents conjugate transposition;
step 2B (S322): obtaining a Litta precoding matrix walt(ii) a Solving a homogeneous system of linear equations Hjkwalt0, wherein HjkIs a channel matrix from a virtual base station k to a terminal j of a virtual cell k, and the solution of the equation set is obtained as a Litta vector walt1，walt2，L，waltuForming a Litta precoding matrix w from the Litta vectorsalt＝[walt1 walt2L waltu]；
Step 3B (S323): according to the Share precoding matrix windIn-his precoding matrix waltTo obtain the precoding matrix w of the virtual base station kk。
Wherein the Share precoding matrix windAnd the Litta precoding matrix waltThe dimension of the virtual base station is determined according to the number s of the transmitting antennas of the virtual base station and the number t of the receiving antennas of the receiving terminal to be tested; the number s of transmitting antennas of the virtual base station is more than or equal to the number of nodes of the virtual base station.
Preferably, in the step (5), the receiving terminal to be measured detects, a three-dimensional coordinate system xyz is established, 4 nodes which are not on the same plane are selected from all nodes as target nodes f, f is 1,2,3,4, a sphere f is respectively established by taking the distance from the receiving terminal to be measured to the target nodes as a radius and the 4 target nodes as a sphere center, a three-dimensional space spherical equation set with constraint conditions is established, and a solution of the constraint condition equation set is obtained as the position coordinate of the receiving terminal to be measured.
The constraint condition is based on the reciprocal of the target node coordinate weighting distance, and the constraint condition equation is as follows:
z＝z0+Δ·n (1)
in formula (1), N is 0, ± 1, ± 2, L, ± N; n is a step size; n is the maximum step size; delta is positioning accuracy;
in the formula (1), the reaction mixture is,wherein l1、l2、l3Estimating the distance from the receiving terminal to be measured to 3 target nodes by using a distance loss model; z is a radical of1、z2、z3Is the coordinate position of the sphere center on the z-axis.
Preferably, in the step (5), the spherical equation of the sphere f is:
in the formula (2), xf、yf、zfIs the coordinate of the sphere f in the three-dimensional coordinate system xyz, lfTo estimate using a distance loss modelAnd calculating the distance from the receiving terminal to be measured to the node.
In the step (5), when f is 1,2,3, the solution of the formula (2) is expressed as xSolution of n,ySolution of n,zSolution of nN is 0, ± 1, ± 2, L, ± N; x is to beSolution of n,ySolution of n,zSolution of nSubstituting f into 4 in formula (2), let x be xSolution of n，y＝ySolution of n，z＝zSolution of nObtaining:
the coordinate of the receiving terminal to be measured in the three-dimensional coordinate system xyz is as follows:
wherein N is 0, ± 1, ± 2, L, ± N, | represents taking absolute value,is represented by4-l4, solving for nCorresponding to (x) when the minimum value is takenSolution of n,ySolution of n,zSolution of n) And (4) taking values.
Preferably, in the step 3B, when t is 1, the precoding matrix is determinedWherein < > represents the inner product calculation, and the upper corner mark represents the conjugation; when t is more than or equal to 2, the precoding matrix wk＝[w1……wt]。
Preferably, when t is 2, the precoding matrix wk＝[wk1 wk2]Wherein
preferably, in step 3, the system and rate R are:
in the formula, HkkIs a channel matrix from a virtual base station k of a virtual cell k to a receiving terminal to be tested, HkjChannel matrix from virtual base station j of virtual cell j to receiving terminal to be tested, wkFor precoding of virtual base stations k, wjFor the pre-coding of the virtual base station j,is the variance of gaussian white noise.
Preferably, the system and the method for calculating the rate R include:
step 1A (S311): defining a rate R for a receiving terminal kkIs composed of
Step 2A (S312): according to the rate RkObtaining a system and a rate R, R being
Preferably, in step 4, the signal beam transmitted by the virtual base station k is: w is akS, where s is the signal transmitted by the virtual base station k.
The invention also provides an indoor three-dimensional positioning system based on the virtual cell, which comprises: at least more than two virtual cells and a receiving terminal to be tested; wherein any two virtual cells are represented as: a virtual cell k and a virtual cell j; the virtual base station of the virtual cell comprises: at least 4 nodes, and the 4 nodes are not on the same plane; and the receiving terminal to be tested is used for receiving signals transmitted by the nodes of the virtual base station.
Wherein, the receiving terminal to be tested comprises: the channel matrix establishing module is used for establishing a channel matrix of the node and the receiving terminal to be tested; the pre-coding module is used for acquiring the optimal system and rate R to obtain pre-coding; and the terminal position calculation module forms a signal beam transmitted by the virtual base station through the precoding and carries out space positioning so as to obtain the position of the receiving terminal to be detected.
The pre-coding module adopts the indoor three-dimensional positioning method based on the virtual cell to obtain pre-coding; the terminal position calculating module calculates the position of the receiving terminal to be measured by adopting the indoor three-dimensional positioning method based on the virtual cell.
The indoor three-dimensional positioning method and system based on the virtual cell solve the problems of complex indoor positioning and high difficulty in the prior art, and have the following advantages:
(1) the system and the method can effectively improve the coverage of the system, shorten the average access distance, reduce the path loss and also reduce the influence of the signaling overhead on interference coordination by the virtual cell based on the distributed antenna;
(2) the system and the method adopt the mapping of a Sharp precoding matrix on a Sharp precoding matrix, so that the obtained precoding is assisted by a value space tending to Sharp and mainly suppresses interference;
(3) the system and the method are based on a space coordinate estimation method of a three-dimensional spherical equation with constraint conditions, set constraint condition parameters according to the positioning precision requirement of an actual system, utilize a step traversal selection method, rapidly solve a spherical equation set, are simple to implement and are easy for engineering realization.
Drawings
Fig. 1 is a flowchart of an indoor three-dimensional positioning method based on a virtual cell according to the present invention.
Fig. 2 is a flow chart of obtaining precoding according to the present invention.
Fig. 3 is a schematic diagram of the positioning based on the establishment of a three-dimensional space ball according to the present invention.
Fig. 4 is a schematic diagram of a virtual base station k sending data to a terminal k through two transmission layers according to an embodiment of the present invention.
Fig. 5 is a flow chart of the system and method of rate calculation of the present invention.
Fig. 6 is a schematic structural diagram of an indoor three-dimensional positioning system based on a virtual cell according to the present invention.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
An indoor three-dimensional positioning method based on a virtual cell is shown in fig. 1, which is a flow chart of the indoor three-dimensional positioning method based on the virtual cell of the present invention, and the method includes:
step 1 (S100): establishing a virtual cell: establishing at least more than two virtual cells according to the relative positions of a receiving terminal to be measured and a node and a channel, wherein the two virtual cells are respectively expressed as virtual cells k and j, and a virtual base station of the virtual cell comprises: more than 4 nodes, and at least 4 nodes are not on the same plane;
step 2 (S200): obtaining a channel matrix from the virtual base station to the receiving terminal: obtaining a channel matrix H from a virtual base station k of a virtual cell k to a receiving terminal to be testedkkAnd a channel matrix H from the virtual base station j of the virtual cell j to the receiving terminal to be testedkj；
Step 3 (S300): according toOptimizing the system and the rate R to obtain a precoding matrix w of the virtual base stationk；
Step 4 (S400): carrying out beam forming on the transmitting signals of the virtual base station according to the pre-coding;
step 5 (S500): detecting a receiving terminal to be detected to determine the position of the receiving terminal to be detected;
as shown in FIG. 2, for the flow chart of obtaining precoding according to the present invention, in step 3, precoding matrix wkThe calculating method comprises the following steps:
step 1B (S321): obtaining a lyre precoding matrix wind(ii) a Setting matrixU eigenvalues of (a)1,λ2,...,λuThe corresponding feature vector isThen wind＝[wind1 wind2Lwindu]In the formula, the upper-corner mark H represents conjugate transposition;
step 2B (S322): obtaining a Litta precoding matrix walt(ii) a Solving a homogeneous system of linear equations Hjkwalt0, wherein HjkIs a channel matrix from a virtual base station k to a terminal j of a virtual cell k, and the solution of the equation set is obtained as a Litta vector walt1，walt2，L，waltuForming a Litta precoding matrix w from the Litta vectorsalt＝[walt1 walt2L waltu]；
Step 3B (S323): according to the Share precoding matrix windIn-his precoding matrix waltTo obtain the precoding matrix w of the virtual base station kk；
Sharp precoding matrix windAnd the Litta precoding matrix waltAccording to the number s of transmitting antennas of the virtual base station and the receiving terminal to be testedIs determined. The number s of transmitting antennas of the virtual base station is more than or equal to the number of nodes of the virtual base station.
The system and method of the present invention uses the mapping of the Share precoding matrix on the Share precoding matrix to make the obtained precoding mainly suppress interference.
Further, as shown in fig. 3, for the schematic diagram of the invention for performing positioning based on establishing a three-dimensional space sphere, according to an embodiment of the invention, in step (5), the receiving terminal to be measured detects, establishes a three-dimensional coordinate system xyz, selects 4 nodes not on the same plane from all nodes as target nodes f, where f is 1,2,3,4, and establishes spheres f and a three-dimensional space spherical equation set with constraint conditions by using the distance from the receiving terminal to be measured to the target nodes as a radius and the 4 target nodes as sphere centers, and obtains a solution of the constraint condition equation set as the position coordinate of the terminal to be measured. Specifically, 4 nodes P in the virtual base station of the virtual cell are selected1、P2、P3And P4，P1、P2、P3And P4Not on the same plane, respectively using a node P in a three-dimensional coordinate system xyz1、P2、P3And P4Coordinate (x) of1,y1,z1)、(x2,y2,z2)、(x3,y3,z3) And (x)4,y4,z4) For the spherical center, solving each node P of a terminal k to be positioned and a virtual base station k through an RSSI distance loss model1、P2、P3And P4Are each a distance of l1、l2、l3And l4In 1 with1、l2、l3And l4For the radius, four spheres are established, the actual terminal to be positioned being in the spatial area enclosed by these four spheres.
Adding a constraint condition equation based on the node coordinate weighted reciprocal distance:
z＝z0+Δ·n (1)
in formula (1), N is 0, ± 1, ± 2, L, ± N; n is a step size; n is the maximum step size; and delta is the positioning accuracy.
In the formula (2), wherein l1、l2、l3Estimating the distance from the receiving terminal to be measured to each node by using a distance loss model; z is a radical of1、z2、z3Is the coordinate position of the sphere center on the z-axis.
Specifically, at the above-mentioned 4 nodes P1、P2、P3And P4As the center of sphere and1、l2、l3and l4When 4 balls are established as the radius,
further, according to an embodiment of the present invention, in step (5), the spherical equation of the sphere f is:
in the formula (2), xf、yf、zfIs the coordinate of the sphere f in the three-dimensional coordinate system xyz, lfThe distance from the receiving terminal to be measured to the node is estimated by using the distance loss model.
In step (5), the solution of equation (2) when f is 1,2,3 is solved, denoted as xSolution of n,ySolution of n,zSolution of nN is 0, ± 1, ± 2, L, ± N; x is to beSolution of n,ySolution of n,zSolution of nSubstituting f into 4 in formula (2), let x be xSolution of n，y＝ySolution of n，z＝zSolution of nObtaining:
the coordinate of the receiving terminal to be measured in the three-dimensional coordinate system xyz is as follows:
in the formula (5), N ═ 0, ± 1, ± 2, L, ± N, | represents absolute values,is represented by4-l4, solution ofn is the minimum value of (x)Solution of n,ySolution of n,zSolution of n) And (4) taking values.
The method simplifies the solving process of the equation through the constraint equation, makes an assumption on the height coordinate z according to the actual positioning scene, reduces the number of equation sets (4 equation sets are changed into 3, and the rest equation is only used for verification), and enables the rapid solving to be realized.
Specifically, at the above-mentioned 4 nodes P1、P2、P3And P4As the center of sphere and1、l2、l3and l4When 4 spheres are established as radii, the spherical equation for the 4 spheres is:
theoretically, the intersection point of the 4 spherical surfaces in the space is solved according to the spherical equation, and the intersection point is the coordinate of the receiving terminal to be measured. However, in practical applications, due to measurement errors, the four spheres may not intersect at one point accurately, and solving the above system of equations is complicated. For this purpose, a constraint equation (1) z ═ z based on the actual environment is used0The + Δ · n constrains the spherical equation (9), thereby simplifying the solution process.
Solving the equations (6), (7), (8) and (1) to xSolution of n,ySolution of n,zSolution of nN is 0, ± 1, ± 2, L, ± N, and x isSolution of n,ySolution of n,zSolution of nSubstituting into the right side of equation (9) to obtain the corresponding estimated distance l4, solving for n：
Obtaining the coordinates of the receiving terminal k to be tested:
in actual calculation, the method may start with n being 0, set the system required positioning accuracy to be 0.3 m, that is, Δ being 0.3 m, and traverse the height interval [0, z ═ 00+Δ·n]To obtain zSolution of nThat is, when the error between the positioning coordinates and the virtual base station node distance in all the traversal processes and the distance calculated by measurement is minimum, the corresponding (x) is obtainedSolution of n,ySolution of n,zSolution of n) And as the final positioning coordinate, the three-dimensional position information of the receiving terminal k to be measured is quickly estimated under the condition of not large error.
Further, according to an embodiment of the present invention, in step 3B, when t is equal to 1, the precoding matrix is determinedWherein < > represents the inner product calculation, and the upper corner mark represents the conjugation. Specifically, when the transmitting antennas of the virtual base station k and the virtual base station j are both 4 antennas and the receiving antenna of the terminal k is 1 antenna, the virtual base station k uses a single transmission layer to send data to the terminal k (a receiving terminal to be detected), and the specific steps are as follows:
step 1B (S321): virtual base station k is according to HkkEstimating to obtain a Share precoding matrix wind4 × 1 dimension;
step 2B (S322): virtual base station k is according to HjkSolving a homogeneous linear equation set with a coefficient matrix of 4 multiplied by 1 to obtain a Litta precoding matrix walt4 × 1 dimension;
step 3B (S323): the virtual base station k obtains the precoding matrix of the virtual base station 1 according to the mapping of the Share precoding matrix on the Share precoding matrixWherein < > represents the inner product calculation, and the upper corner mark represents the conjugation.
Further, according to an embodiment of the present invention, when t is 2, the precoding matrix wk＝[wk1 wk2]Wherein
specifically, as shown in fig. 4, which is a schematic diagram of a virtual base station k sending data to a terminal k through two transmission layers according to an embodiment of the present invention, when transmitting antennas of the virtual base station k and the virtual base station j are both 4 antennas, and a receiving antenna of the terminal k is 2 antennas, the virtual base station k sends data to the terminal k through the two transmission layers, specifically, the following steps are performed:
step 1B (S321): virtual base station k is according to HkkEstimating to obtain a Share precoding matrix wind＝[wind1 wind2]Wherein w isind1、wind2All are 4 x 1 dimensional vectors;
step 2B (S322): virtual base station k is according to HjkSolving a homogeneous linear equation set with a coefficient matrix of 4 multiplied by 2 to obtain a Litta precoding matrix walt＝[walt1 walt2]Wherein w isalt1、walt2All are 4 x 1 dimensional vectors;
step 3B (S323): the virtual base station k obtains the precoding matrix w of the virtual base station 1 according to the mapping of the Share precoding matrix on the Share precoding matrixk＝[wk1 wk2]Wherein
the method according to the invention can analogize the precoding matrix when t > 2. The mapping mode of precoding is not only related to the number of receiving/transmitting antennas, but also related to the transmitted/received data stream, and the number of antennas is more than or equal to the number of streams.
Further, as shown in fig. 5, which is a flowchart of the system and the method for calculating the rate of the present invention, according to an embodiment of the present invention, in step 3, the method for calculating the system and the rate R includes:
step 1A (S311): defining a rate R for a receiving terminal kkIs composed of
Step 2A (S312): according to the rate RkObtaining a system and a rate R, R being
In the above formula, HkkIs a channel matrix from a virtual base station k of a virtual cell k to a receiving terminal to be tested, HkjChannel matrix from virtual base station j of virtual cell j to receiving terminal to be tested, wkFor precoding of virtual base stations k, wjFor the pre-coding of the virtual base station j,is the variance of gaussian white noise.
Further, according to an embodiment of the present invention, in step 4, the signal beam transmitted by the virtual base station k is: w is akS, where s is the signal transmitted by the virtual base station k.
An indoor three-dimensional positioning system based on a virtual cell is shown in fig. 6, which is a schematic structural diagram of the indoor three-dimensional positioning system based on a virtual cell of the present invention, and the system includes: at least more than two virtual cells and a receiving terminal to be tested; wherein any two virtual cells are represented as: a virtual cell k and a virtual cell j; the virtual base station of the virtual cell comprises: at least 4 nodes, and the 4 nodes are not on the same plane; the receiving terminal to be tested is used for receiving signals transmitted by the nodes of the virtual base station.
The receiving terminal to be tested includes: the channel matrix establishing module is used for establishing a channel matrix of the node and the receiving terminal to be detected; the pre-coding module is used for acquiring the optimal system and rate R to obtain pre-coding; and the terminal position calculation module is used for forming a signal beam transmitted by the virtual base station through precoding and carrying out space positioning so as to obtain the position of the receiving terminal to be detected.
The pre-coding module obtains pre-coding by adopting the indoor three-dimensional positioning method based on the virtual cell; the terminal position calculating module calculates the position of the receiving terminal to be measured by adopting the indoor three-dimensional positioning method based on the virtual cell.
In summary, the indoor three-dimensional positioning method and system based on the virtual cell of the present invention overcome the problems of complexity, low positioning accuracy, etc. of the existing indoor positioning method, have the characteristics of wide coverage, good anti-multipath effect, strong expandability, etc., and can realize indoor rapid three-dimensional positioning.
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 (2)
1. An indoor three-dimensional positioning method based on a virtual cell is characterized by comprising the following steps:
step 1 (S100): establishing a virtual cell: establishing at least more than two virtual cells according to the relative positions of a receiving terminal to be measured and a node and a channel, wherein the two virtual cells are respectively expressed as virtual cells k and j, and a virtual base station of the virtual cell comprises: more than 4 nodes, and at least 4 nodes are not on the same plane;
step 2 (S200): obtaining a channel matrix from the virtual base station to the receiving terminal:obtaining a channel matrix H from a virtual base station k of a virtual cell k to a receiving terminal to be testedkkAnd a channel matrix H from the virtual base station j of the virtual cell j to the receiving terminal to be testedkj；
Step 3 (S300): obtaining a precoding matrix w of the virtual base station according to the optimization of the system and the rate Rk；
Step 4 (S400): carrying out beam forming on the transmitting signals of the virtual base station according to the pre-coding;
step 5 (S500): detecting a receiving terminal to be detected to determine the position of the receiving terminal to be detected;
in the step 3, the precoding matrix wkThe calculating method comprises the following steps:
step 1B (S321): obtaining a lyre precoding matrix wind(ii) a Setting matrixU eigenvalues of (a)1,λ2,...,λuThe corresponding feature vector isThen wind＝[wind1wind2Lwindu]In the formula, the upper-corner mark H represents conjugate transposition;
step 2B (S322): obtaining a Litta precoding matrix walt(ii) a Solving a homogeneous system of linear equations Hjkwalt0, wherein HjkIs a channel matrix from a virtual base station k to a terminal j of a virtual cell k, and the solution of the equation set is obtained as a Litta vector walt1，walt2，L，waltuForming a Litta precoding matrix w from the Litta vectorsalt＝[walt1 walt2 L waltu]；
Step 3B (S323): according to the Share precoding matrix windIn-his precoding matrix waltTo obtain the precoding matrix w of the virtual base station kk；
The Sharp precoding matrix windAnd the Litta precoding matrix waltIs according toThe number s of transmitting antennas of the virtual base station and the number t of receiving antennas of the receiving terminal to be tested are determined; the number s of transmitting antennas of the virtual base station is more than or equal to the number of nodes of the virtual base station;
in the step 5, the receiving terminal to be tested detects, establishes a three-dimensional coordinate system xyz, selects 4 nodes not on the same plane from all nodes as target nodes f, where f is 1,2,3,4, respectively establishes a sphere f with the distance from the receiving terminal to be tested to the target nodes as a radius and the 4 target nodes as sphere centers, establishes a three-dimensional space spherical equation set with constraint conditions, and solves the solution of the constraint equation set as the position coordinates of the terminal to be tested;
the constraint condition is based on the reciprocal of the target node coordinate weighting distance, and the constraint condition equation is as follows:
z＝z0+Δ·n (1)
in formula (1), N is 0, ± 1, ± 2, L, ± N; n is a step size; n is the maximum step size; delta is positioning accuracy;
in the formula (1), the reaction mixture is,wherein l1、l2、l3Estimating the distance from the receiving terminal to be measured to 3 target nodes by using a distance loss model; z is a radical of1、z2、z3The coordinate position of the sphere center on the z axis is taken;
in step 5, the spherical equation of the sphere f is:
in the formula (2), xf、yf、zfIs the coordinate of the sphere f in the three-dimensional coordinate system xyz, lfEstimating the distance from the receiving terminal to be measured to the node by using a distance loss model;
in step 5, when f is 1,2,3, the solution of the formula (2) is expressed as xSolution of n,ySolution of n,zSolution of n，n＝0，Plus or minus 1, plus or minus 2, L, plus or minus N; x is to beSolution of n,ySolution of n,zSolution of nSubstituting f into 4 in formula (2), let x be xSolution of n，y＝ySolution (II)n，z＝zSolution of nObtaining:
the coordinate of the receiving terminal to be measured in the three-dimensional coordinate system xyz is as follows:
wherein N is 0, ± 1, ± 2, L, ± N, | represents taking absolute value,is represented by4-l4, solving for nCorresponding to (x) when the minimum value is takenSolution of n,ySolution of n,zSolution of n) Taking values;
in step 3B, when t is 1, the precoding matrix is determinedWherein,<>representing inner product calculation, and representing conjugation by using an upper corner mark;
when t is more than or equal to 2, the precoding matrix wk＝[w1……wt]；
When t is 2, the precoding matrix wk＝[wk1wk2]Wherein
in step 3, the system and rate R are:
in the formula, HkkIs a channel matrix from a virtual base station k of a virtual cell k to a receiving terminal to be tested, HkjChannel matrix from virtual base station j of virtual cell j to receiving terminal to be tested, wkFor precoding of virtual base stations k, wjFor the pre-coding of the virtual base station j,is the variance of Gaussian white noise;
the system and the calculation method of the rate R comprise the following steps:
step 1A (S311): defining a rate R for a receiving terminal kkIs composed of
Step 2A (S312): according to the rate RkObtaining a system and a rate R, R being
In step 4, the signal beam transmitted by the virtual base station k is: w is akS, where s is the signal transmitted by the virtual base station k.
2. An indoor three-dimensional positioning system based on virtual cells, the system comprising: at least more than two virtual cells and a receiving terminal to be tested; wherein any two virtual cells are represented as: a virtual cell k and a virtual cell j; the virtual base station of the virtual cell comprises: at least 4 nodes, and the 4 nodes are not on the same plane; the receiving terminal to be tested is used for receiving signals transmitted by the nodes of the virtual base station;
the receiving terminal to be tested comprises:
the channel matrix establishing module is used for establishing a channel matrix of the node and the receiving terminal to be tested;
the pre-coding module is used for acquiring the optimal system and rate R to obtain pre-coding; and
the terminal position calculation module forms a signal beam transmitted by the virtual base station through the precoding and carries out space positioning to obtain the position of the receiving terminal to be detected;
the pre-coding module adopts the indoor three-dimensional positioning method based on the virtual cell according to claim 1 to obtain pre-coding;
the terminal position calculating module calculates the position of the receiving terminal to be measured by using the indoor three-dimensional positioning method based on the virtual cell according to claim 1.
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