CN111913202A - Distributed instant deployment three-dimensional positioning method integrating ultra-wideband and Beidou signals - Google Patents

Abstract

The invention discloses a distributed instant deployment three-dimensional positioning method fusing ultra-wideband and Beidou signals, belonging to the technical field of indoor positioning and comprising the following steps: s1: constructing a sensor network based on a Beidou module and an ultra-wideband module, and calculating any node T to be positioned in the sensor network_hThe barycentric coordinates of (a); s2: solving any node T to be positioned by parallel distributed computation_hThe positioning result is processed with iterative convergence; s3: taking the positioning result as an initial value of Taylor expansion and solving a final positioning result; s4: the final positioning result under the relative coordinate system is converted into an absolute coordinate system so as to realize distributed positioning under the relative coordinate system by using the ultra-wideband sensor network, then the relative coordinate is converted into the absolute coordinate through the Beidou module on the anchor point so as to realize positioning of the sensor network under the geodetic coordinate system, and further, indoor and outdoor integrated positioning is realizedThe purpose of the bit.

Description

Distributed instant deployment three-dimensional positioning method integrating ultra-wideband and Beidou signals

Technical Field

The invention belongs to the technical field of indoor positioning, and particularly relates to a distributed instant deployment three-dimensional positioning method integrating ultra-wideband and Beidou signals.

Background

The chinese BeiDou Navigation Satellite System (BDS for short) is a global Satellite Navigation System developed by china autonomously, and is the third mature Satellite Navigation System in the world after the american global positioning System GPS and the russian GLONASS Satellite Navigation System GLONASS. The Beidou satellite navigation system consists of an empty section, a ground section and a user section, can provide high-precision, high-reliability positioning, navigation and time service for various users all day long in the global range, has short message communication capacity, and initially has regional navigation, positioning and time service capacity. The Beidou satellite navigation and positioning system has the following characteristics:

(1) possess simultaneously location and communication function: compared with the existing GPS and GLONASS, the autonomous BDS has the greatest characteristic of simultaneously having the functions of positioning and communication, can realize two-way short message communication without the support of other communication systems, and can transmit the short message information of 120 Chinese characters at most. The short message information is combined with positioning and navigation, so that the method is a unique invention of the Beidou satellite navigation system, and brings a convenient application prospect to users and enterprises.

(2) The coverage is wide: the Beidou system space section adopts a mixed constellation consisting of three orbit satellites, has no communication blind area, has strong anti-shielding capability and particularly has more obvious performance characteristics in low latitude areas.

(3) An autonomous system: the BDS is a global satellite navigation system independently researched and developed in China, is safer, more reliable and more stable, has strong confidentiality and is suitable for key departments.

The BDS has a better performance in outdoor environments, and cannot exert its advantages in indoor environments better due to factors such as satellite signal coverage, signal quality, and complex indoor scenes in indoor environments. Therefore, a new signal is required to be introduced to complete indoor positioning, and indoor and outdoor integrated positioning is realized by combining the indoor positioning technology with the Beidou satellite positioning technology in different forms.

An Ultra Wideband (UWB) technology is a novel wireless communication technology, which does not use a carrier in a conventional communication system, but directly modulates an impulse having a steep rise time and a fall time, and transmits data by transmitting and receiving an extremely narrow pulse having a nanosecond level or less, thereby having a bandwidth of a GHz level. UWB technology has the following characteristics:

(1) the anti-interference capability is strong: due to the self frequency spectrum characteristics of the UWB signals, the frequency spectrum of the UWB signals can reach thousands of megahertz which is more than 100 times of that of a common spread spectrum system, and the anti-interference performance is very strong;

(2) strong multipath resolution capability: the UWB signal transmission utilizes extremely narrow pulse information, so that the UWB signal transmission has very low duty ratio, can realize time separation under the condition of multipath, and can fully utilize the energy of a transmitted signal;

(3) the system capacity is large: with the development of wireless communication system technology, spectrum resources become more and more tense, and the communication space capacity of the ultra-wideband technology has great advantages;

(4) strong penetrating power: UWB can penetrate media such as leaves, land, concrete, water and the like, has strong penetrability, and is very suitable for being applied in complex indoor environment;

(5) low power consumption: UWB devices have low average transmit power and therefore UWB indoor positioning systems operate without interference to other wireless communication systems, which is important for indoor environments.

In addition, UWB belongs to the communication technology in the medium and short distance range, and is very suitable for the use of constructing the indoor environment. Through research and characteristic analysis on the ultra-wideband technology, the ultra-wideband technology has irreplaceable advantages compared with other technologies when being used for indoor positioning, and is particularly suitable for indoor high-precision positioning. When UWB technology is used for indoor positioning, a ranging-based positioning algorithm is generally used. Current ranging lateral methods include time of flight signal (TOA) based, time difference of arrival (TDOA) based, angle of arrival location (AOA) based, and received signal strength location (RSS) based. Because of its very high time resolution when transmitting nanosecond narrow pulses, TOA techniques are the most common way of ranging in indoor multipath-intensive environments.

At present, indoor positioning products in the market are suitable for known indoor environments such as buildings and warehouses in application scenes, namely, the UWB anchor points need to be manually calibrated and deployed in advance. The positioning scheme has the advantages that high-precision positioning can be realized through accurate anchor point deployment, but the positioning scheme has the defects of fixed application scene, high time cost, poor maneuverability and the like, and is not suitable for positioning in unknown indoor environments such as cave and tunnel exploration. For example: when tunnel rescue is carried out, objective conditions for calibrating anchor points in advance do not exist, and a rapid positioning scheme with instant deployment and plug and play is needed.

Common positioning schemes at the present stage include a trilateral positioning method, a least square method, a Chan algorithm, a Fang algorithm and other positioning schemes which need to distinguish an anchor point with a known position and a label with an unknown position; meanwhile, if the anchor point is affected, the positioning result of the positioning system is seriously affected. Therefore, such systems are vulnerable to uncertain environments and are not robust and survivable. To sum up, two problems to be solved at present are: (1) real-time deployment and positioning of anchor points and labels in the sensor network are not distinguished; (2) distributed positioning that improves system survivability.

In addition, in the indoor and outdoor integrated positioning process, the coordinate systems adopted in the indoor and outdoor environments are not uniform. Indoor positioning usually uses a relatively-diagonal coordinate system, while outdoor positioning usually uses a geodetic coordinate system. Therefore, the problem of interconversion between the relative rectangular coordinate system and the absolute geodetic coordinate system is also a problem that must be solved in the task of rapidly exploring an unknown indoor environment.

Disclosure of Invention

Most indoor environments today are known environments, such as building interiors, factory warehouses, etc., where anchor points may be manually erected in advance and located on this basis. However, in an unknown indoor environment such as a cave or a tunnel where there is no artificially specified reference point, it is necessary to perform positioning while searching. Most positioning methods need to calibrate and accurately deploy a large number of anchor points in advance, and when an exploratory task is performed, the scheme is low in efficiency and cannot meet the requirement of immediate deployment. In view of the above, in order to solve the above problems in the prior art, the present invention aims to provide a distributed real-time deployment three-dimensional positioning method that integrates ultra-wideband and Beidou signals, so as to achieve distributed positioning under a relative coordinate system by using an ultra-wideband sensor network, and then convert the relative coordinate into an absolute coordinate by using a Beidou module on an anchor point, so as to achieve positioning of the sensor network under a geodetic coordinate system, thereby achieving the purpose of indoor and outdoor integrated positioning.

The technical scheme adopted by the invention is as follows: a distributed instant deployment three-dimensional positioning method fusing ultra-wideband and Beidou signals comprises the following steps:

s1: sensor network is constructed based on Beidou module and ultra wide band technology, and node T to be positioned in sensor network is calculated_hThe barycentric coordinates of (a);

s2: solving a node T to be positioned by parallel distributed computation_hThe positioning result is processed with iterative convergence;

s3: taking the positioning result as an initial value of Taylor expansion and solving a final positioning result;

s4: and converting the final positioning result in the relative coordinate system into an absolute coordinate system.

Further, calculating a node T to be positioned_hThe method of the barycentric coordinates of (1) is as follows:

s101: defining any node T to be positioned in sensor network_hSelecting a node T which can be positioned with the node T_hThe communication node is used as a neighbor node;

s102: obtaining the node T to be positioned_hRanging information with each neighbor node;

s103: calculating any node T to be positioned according to ranging information among different nodes_hCorresponding to the barycentric coordinates of its neighboring nodes.

Further, in step S101, a node T is defined_hThe neighbor nodes are respectively T_i、T_j、T_k、T_l；

In step S102, a node T to be positioned_hForming a tetrahedron with each neighbor node in space according to the node T to be positioned_hRespectively calculating the volume V of each tetrahedron according to the ranging information between each tetrahedron and each neighbor node_ijkl、V_hijk、V_hijl、V_hikl、V_hjkl；

In step S103, the absolute value { | a of the barycentric coordinates is calculated using the volume ratio_hi|，|a_hj|，|a_hk|，|a_hlL } in which

Determination of barycentric coordinates { a }_hi,a_hj,a_hk,a_hlSymbol patterns of, symbols are respectively σ_hi、σ_hj、σ_hk、σ_hlWherein: sigma_hi、σ_hj、σ_hk、σ_hlIs 1 or-1 and satisfies sigma_hi|a_hi|+σ_hj|a_hj|+σ_hk|a_hk|+σ_hl|a_hl|＝1；

Solving node T to be positioned by product of absolute value of barycentric coordinate and symbol_hCorresponding to its neighbor node T_i、T_j、T_k、T_lBarycentric coordinates of (a):

a_hi＝σ_hi|a_hi|、a_hj＝σ_hj|a_hj|

a_hk＝σ_hk|a_hk|、a_hl＝σ_hl|a_hl|。

further, the absolute value of the barycentric coordinate { | a_hi|，|a_hj|,|a_hk|，|a_hlSymbol pattern of | } σ_hi、σ_hj、σ_hk、σ_hlIs based on the node T to be positioned_hThe subspace of the position is determined.

Further, the node T to be tested_hThe spatial position comprises four spaces corresponding to four vertexes i, j, k and l, four spaces corresponding to four surfaces jkl, ijk, ijl and ikl, six spaces corresponding to six edges ij, ik, il, jk, jl and kl and a space ijkl in a tetrahedral envelope; the symbol patterns corresponding to the respective spaces are as follows:

i(1,-1,-1,-1) ij(1,1,-1,-1) jl(-1,1，-1,1) ijl(1,1,-1,1) j(-1,1,-1,-1) ik(1,-1,1,-1) kl(-1,-1,1,1) ikl(1,-1,1,1) k(-1,-1,1,-1) il(1,-1,-1,1) jkl(-1,1,1,1) ijkl(1，1，1，1) l(-1，-1，-1，1) jk(-1,1,1,-1) ijk(1,1,1，-1)。

further, the step S2 specifically includes:

s201: for a node T to be positioned_hAssigning an initial value as a current estimated position

S202: the current estimated position

Sending to all nodes T to be positioned for calculation_hEach neighbor node e of the barycentric coordinates and according to the received estimated position of each neighbor node

Calculating the intermediate variable xi_hThen calculate the intermediate variable xi_hSending the information to each neighbor node;

wherein,

represents all the variables used to calculate T_hNeighbor nodes of the barycentric coordinates; a is_heRepresents T_hThe barycentric coordinates corresponding to each neighboring node,

representation collection

Coordinates of the middle node;

s203: according to the intermediate variable xi sent by each neighbor node_eCalculating a new estimate using the following equation

Wherein, 1-belongs to the weight occupied by the previous generation estimated value in the next generation estimated value in the calculation, and belongs to the weight occupied by the positioning result calculated according to the neighbor information in the current estimated value; the positioning result calculated according to the neighbor information means that:

the result of the calculation; neighbor information is a distance measurement value and a gravity center coordinate, and the distance measurement value is used for calculating T_hBarycentric coordinate a of barycentric coordinates relative to each neighbor node_he；

S205: obtaining a node T to be positioned through iterative convergence_hThe positioning result of (1).

Further, in the step S203, e is:

k represents the number of iterations performed.

Further, the step S3 specifically includes:

s301: using the positioning result as the initial value of Taylor expansion

Suppose a node T to be located_hHas real coordinates of

The estimated position deviation from the actual position can be expressed as (Δ x)_h,Δy_h,Δz_h)；

S302: setting a node T to be positioned_hThe distance function between each neighboring node is

Wherein

S303: at the point of

Performing Taylor expansion, neglecting components above the second order, and representing as B by matrix_Taylor＝A_TaylorΔ, wherein Δ ═ Δ x_h,Δy_h,Δz_h]^T；

S304: using least squares

Solving the deviation value delta of the estimated position and the actual position if the condition | delta x is satisfied_h|+|Δy_h|+|Δz_hMu is less than or equal to | in the positioning result (mu is an artificially set scalar used for controlling the precision), the output positioning result is:

if not, will

And recalculating as an initial value of Taylor expansion until a positioning result is output when a condition is met.

Further, the positioning result in the relative coordinate system is converted into an absolute coordinate system, and the method comprises the following steps:

s401: converting geodetic coordinates of anchor points in the sensor network into Web mercator coordinates;

s402: calculating a conversion relation between the Web mercator coordinates and the relative coordinates by utilizing a least square method through the known Web mercator coordinates and the relative coordinates of the anchor points;

s403: to-be-positioned node T_hThe relative coordinates of the Web-based ink card holder are converted into Web ink card holder coordinates according to the conversion relation;

s404: to-be-positioned node T_hThe Web mercator coordinates of (a) are converted to geodetic coordinates.

The invention has the beneficial effects that:

1. by adopting the distributed immediate deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals, the deployment is gradually carried out on the area to be explored from the anchor node without artificial calibration, the positioning in a completely distributed three-dimensional space is realized through the distance measurement and information interaction among sensor networks, and the error generated by random noise in the distance measurement is restrained according to the designed weight sequence of the iterative process. And the positioning precision is further improved by carrying out Taylor expansion on the distance formula.

2. By adopting the distributed immediate deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals, only a plurality of outdoor fixed anchor points are needed to be calibrated and deployed, and no artificial anchor point calibration is needed in the process of indoor exploration, all indoor nodes do not distinguish anchor points and labels for distributed positioning, so that the problem of difficulty in equipment deployment in the market is solved, the immediate deployment function is realized, and the distributed immediate deployment three-dimensional positioning method has very important significance for exploratory positioning.

3. By adopting the distributed real-time deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals, indoor relative coordinates can be converted into geodetic coordinates measured by the Beidou satellite in real time, indoor and outdoor integrated positioning can be realized, exploration of unknown areas is completed, and the distributed real-time deployment three-dimensional positioning method has stronger practical application significance compared with simple indoor positioning; in addition, in a non-sparse sensor network, individual nodes are damaged and do not influence application, and the whole positioning system has stronger robustness and survivability.

Drawings

FIG. 1 is a schematic diagram of an application scenario in a distributed instantaneous deployment three-dimensional positioning method for merging ultra-wideband and Beidou signals provided by the invention;

FIG. 2 is a schematic topological diagram of a sensor network constructed in the distributed instantaneous deployment three-dimensional positioning method for merging ultra-wideband and Beidou signals provided by the invention;

FIG. 3 is a flow chart of the operation of the distributed instantaneous deployment three-dimensional positioning method for merging UWB and Beidou signals provided by the invention;

FIG. 4 is a schematic diagram of a convergence process of a distributed instantaneous deployment three-dimensional positioning method that fuses ultra-wideband and Beidou signals in an ideal environment;

FIG. 5 is an analysis diagram of the overall positioning error of the distributed instantaneous deployment three-dimensional positioning method fusing ultra-wideband and Beidou signals under different ranging errors of 0-20 cm;

FIG. 6 is a positioning error analysis diagram of nodes with different anchor connectivity in a distributed instant deployment three-dimensional positioning method that integrates ultra-wideband and Beidou signals under different ranging errors of 0-20 cm.

Detailed Description

Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar modules or modules having the same or similar functionality throughout. The embodiments described below with reference to the drawings are exemplary only for the purpose of explaining the present application and are not to be construed as limiting the present application. On the contrary, the embodiments of the application include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.

Example 1

When unknown indoor scenes such as tunnels and caverns are rapidly explored, anchor points cannot be calibrated and deployed in advance, so that instant deployment without distinguishing node identities is of great significance to the scenes, and the application scene is shown in fig. 1.

When a cave is prepared to be rapidly explored, only artificial calibration anchor points at the cave mouth can be erected, as shown by star marks in fig. 1, wherein the anchor points are formed by a Beidou module and UWB nodes together. Sensor nodes in the cave only comprise UWB nodes and no longer distinguish their anchor points from their labels, so no artificial calibration of anchor points is required. Before the nodes enter deeper into the cave, the nodes are continuously arranged in the cave to construct a UWB sensor network (as shown in figure 2), the positions of the nodes in the sensor network are calculated by a distributed scheme of communicating with neighbor nodes, and the exploration of an anchor point signal area which cannot reach can be realized by continuously arranging the nodes in depth. As shown in fig. 3, the positioning method includes:

s1: calculating a node T to be positioned_hCenter of gravity coordinates of

As shown in FIG. 2, given the coordinates of four anchor points in three-dimensional space, let the anchor point coordinates be T respectively₁(x₁,y₁,z₁)、T₂(x₂,y₂,z₂)、T₃(x₃,y₃,z₃)、T₄(x₄,y₄,z₄). In this model, T is usually used₁The Euclidean coordinate system was constructed for the origin, with anchor point T for this example₁、T₂Determining the x-axis of the Euclidean coordinate system, wherein

Is the positive direction of the x axis; t is₁、T₃The anchor point determines the y-axis,

is the positive direction of the y axis; t is₁、T₄The anchor point determines the z-axis and,

is the positive direction of the z axis; four anchor points T in this example₁、T₂、T₃、T₄The relative coordinates of (A) are as follows (unit: cm):

T₁(0,0,0) T₂(400,0,0)

T₃(0,400,0) T₄(0,0,400)

any node capable of communication uses UWB signals to perform distributed ranging. In simulation, any two nodes T can be calculated through a distance formula_i、T_jThe distance between the two is used as a ranging value, and the distance function is as follows:

the distance measurement value calculated by the formula (1) is an ideal situation and does not contain noise and any disturbance, so that simulation calculation needs to be carried out under the assumption of no noise to verify the feasibility of the method provided by the invention. For the distance measurement under the actual condition, the disturbance to the distance measurement needs to be considered, and for any node T capable of communicating_i、T_jAdding additive white noise with expectation of 0 and standard deviation of v on the distance formula according to the error calibration result of UWB sensor real object

As measured distance

The anchor point T₁、T₂、T₃Located in the same plane and anchored by an anchor point T₄And the distance measurement information between the anchor points is obtained by a bilateral distance measurement algorithm of the TOA.

Specifically, let: four anchor points T₁、T₂、T₃、T₄Respectively is (x)₁,y₁,z₁)、(x₂,y₂,z₂)、(x₃,y₃,z₃) And (x)₄,y₄,z₄) Setting a label T to be tested_iHas a three-dimensional coordinate of (x)_i,y_i,z_i) Wherein i is 5,6, …, n; it is generally assumed that anchor points T₁The coordinates are (0,0,0), and the anchor point T is not enabled according to the proposed anchor point deployment mode₂、T₃、T₄Are respectively located at a point (x)₂,0,0)、(0,y₃,0)、(0,0,z₄) The four anchor points are deployed and simultaneously construct a corresponding relative Euclidean coordinate system and a to-be-detected label T_iThe coordinate calculation is also carried out based on the coordinate system; obtaining ranging information among all communicable nodes by a bilateral ranging method based on TOA, and randomly giving all tags T to be measured_iThereby obtaining all the tags T to be tested_iThe initial position information of (1).

S101: defining any node T to be positioned in sensor network_h(h is 5,6, 7 … n), node T to be positioned_hMay be a node T₅、T₆、…、T_nSelecting a node T capable of being positioned_hThe communication node is used as a neighbor node.

For a sensor network comprising n UWB nodes, an undirected graph is adopted

The composition structure thereof is shown, wherein,

representing a UWB node (i.e., a node to be located), (T)_h,T_i) E represents a node T_hAnd T_iCan utilize UWB to measure distance in communication range and for arbitrary node T to be positioned_hGet it

Representing nodes T that can and are to be positioned_hAnd (4) collecting the communicated neighbor nodes.

Defining four anchor points T₁、T₂、T₃、T₄Modeling a three-dimensional Euclidean space in which the four anchor points are positioned for a basic node of a sensor network, and acquiring input information of an algorithm; arranging an anchor point with a Beidou module at an opening, establishing an Euclidean coordinate system, and obtaining accurate position information and mutual distance information of the anchor point in an artificial calibration measurement mode.

Except for UWB nodes, the Beidou module is carried on the four anchor points simultaneously, manual calibration deployment is needed, and the rest nodes T used for exploration₅、T₆、…、T_nWithout distinguishing whether it is an anchor point or a label, the network topology formed by the nodes of the sensor network in this example is shown in fig. 2. Any node T to be positioned_h(h is 5,6, 7 … n) position by anchor point constructed three-dimensional Euclidean space coordinate T_hAnd (x, y, z), wherein x, y and z respectively represent coordinate values in the directions of an x axis, a y axis and a z axis in a three-dimensional space coordinate system.

In this embodiment, a node T to be positioned is defined_hThe neighbor nodes of (1) are respectively: t is_i、T_j、T_k、T_lTo obtain a node T to be positioned_hThe distance measurement values with each neighboring node are respectively: d_hi、d_hj、d_hk、d_hlAnd exchange the mutual current coordinate positions.

S102: obtaining the node T to be positioned_hRanging information with each neighbor node, the ranging information including d_ij、d_ik、d_il、d_jk、d_jl、d_kl、d_hi、d_hj、d_hk、d_hl(ii) a Node T to be positioned_hForming five tetrahedrons with each neighbor node in space according to the node T to be positioned_hRespectively calculating the volume V of each tetrahedron according to the ranging information between each tetrahedron and each neighbor node_ijkl、V_hijk、V_hijl、V_hikl、V_hjklTaking tetrahedron ijkl as an example, the volume calculation formula is as follows:

for any node T_hKnot ofThe volume V of four tetrahedrons is calculated by the close formula (3) in the same way_hijk、V_hijl、V_hikl、V_hjkl；

S103: calculating any node T to be positioned according to ranging information among different nodes_hBarycentric coordinates corresponding to its neighbor nodes, namely:

calculating absolute value { | a of barycentric coordinates by using volume ratio_hi|,|a_hj|,|a_hk|,|a_hlL } in which

It should be noted that the barycentric coordinates herein do not refer to coordinates of "barycentric" in physics, but refer to coordinates of four sides

Any point in space where a volume is located can be represented as a weighted sum of its vertices, where the weights are the barycentric coordinates referred to herein.

If node T_hAt its neighbor node T_i、T_j、T_k、T_lWithin the formed envelope, no further processing of the barycentric coordinates obtained is then necessary, however, since an exploratory work is performed, T_hPossibly outside the tetrahedron ijkl. Therefore, the symbol pattern of the current barycentric coordinates needs to be determined as follows:

determination of barycentric coordinates { a }_hi,a_hj,a_hk,a_hlSymbol patterns of which symbols are respectively σ_hi、σ_hj、σ_hk、σ_hlWherein: sigma_hi、σ_hj、σ_hk、σ_hlIs 1 or-1 and satisfies:

σ_hi|a_hi|+σ_hj|a_hj|+σ_hk|a_hk|+σ_hl|a_hl|＝1 (6)

absolute value { | a of the barycentric coordinate_hi|,|a_hj|,|a_hk|,|a_hlSymbol pattern of | } σ_hi、σ_hj、σ_hk、σ_hlIs based on the node T to be positioned_hDetermining the subspace of the position, the symbol mode and the current node T to be positioned_hThe space position is related, the tetrahedron formed by the adjacent nodes divides the space into 15 parts, and each type of symbol pattern corresponds to the divided subspace one by one as follows:

node T to be tested_hThe spatial position comprises four spaces corresponding to four vertexes i, j, k and l, four spaces corresponding to four surfaces jkl, ijk, ijl and ikl, six spaces corresponding to six edges ij, ik, il, jk, jl and kl and a space ijkl in a tetrahedral envelope; the symbol patterns corresponding to the respective spaces are as follows:

i(1,-1,-1,-1) ij(1,1,-1,-1) jl(-1,1,-1,1) ijl(1,1,-1,1) j(-1,1,-1,-1) ik(1,-1,1,-1) kl(-1,-1,1,1) ikl(1,-1,1,1) k(-1,-1,1,-1) il(1,-1,-1,1) jkl(-1,1,1,1) ijkl(1,1,1,1) l(-1,-1,-1,1) jk(-1,1,1,-1) ijk(1,1,1,-1)。

according to analysis, the formula (6) only has a solution under an ideal environment, and the formula (6) is difficult to obtain for practical application. Therefore, for practical situations with errors, fifteen symbol patterns need to be respectively substituted into formula (7):

then will obtain₁,…,₁₅Sorting from small to large, and selecting the symbol mode corresponding to the minimum value as the node T_hThe symbol mode of the barycentric coordinate absolute value is solved through the product of the barycentric coordinate absolute value and the symbol to obtain a node T to be positioned_hCorresponding to its neighbor node T_i、T_j、T_k、T_lThe barycentric coordinates of (a) are:

a_hi＝σ_hi|a_hi|、a_hj＝σ_hj|a_hj|

a_hk＝σ_hk|a_hk|、a_hl＝σ_hl|a_hl|

to be noted, the node T to be positioned_hThere may be more than four neighbor nodes, e.g. except T_i、T_j、T_k、T_lOut of four neighbor nodes, node T_gCan also be connected with a node T to be positioned_hFor communication and distance measurement, and node T_gAnd node T_i、T_j、T_kAre all neighbors of each other, then the new neighbor T can be used_g、T_i、T_j、T_kSolving a new set of barycentric coordinates

Two points need to be noted, firstly, the superscript "2" of the barycentric coordinates here does not refer to the square, but refers to the barycentric coordinates generated by the second group of neighbors, and only plays a role of referring to the group; second, the neighbor nodes of each node must be neighbors of each other to be able to be used as a group for generating barycentric coordinates, e.g. the node T to be positioned_hOf neighbor node T_gAnd node T_i、T_j、T_kAre all neighbors of each other, so they can generate a set of barycentric coordinates; if node T_gAnd node T_lCannot communicate with each other, therefore, the node T_gAnd node T_lCan not be a node T as a set of neighbors_gBarycentric coordinates are generated.

In practical application, a node T to be positioned needs to be found_hAll the neighbor nodes have combinations and calculate corresponding barycentric coordinates, and supposing that the node T to be positioned has_hIf there are x neighbor combinations, then the node T to be positioned_hThe barycentric coordinates of (a) may be expressed as:

wherein e denotes an arbitrary node

S2: solving a node T to be positioned by parallel distributed computation_hAnd performing iterative convergence on the positioning result, which is specifically as follows:

s201: for all nodes T to be positioned_hGiving initial values (all of which are randomly selected) as the current estimated position

Wherein, a node T to be positioned_hN-4, are respectively: node T to be positioned₅、T₆、…、T_n(ii) a All for calculating the node T to be positioned_hThe neighbor set of barycentric coordinates is noted

S202: the current estimated position

Sending to all nodes T to be positioned for calculation_hEach neighbor node of the barycentric coordinates and according to the received estimated position of each neighbor node

Calculating the intermediate variable xi_hThe following are:

wherein,

representing all the data in the sensor network topology for calculating T_hNeighbor nodes of barycentric coordinates, e representing the set

Any one of the elements of (a);

s203: calculating the intermediate variable xi_hIs sent to each neighbor node, andaccording to the intermediate variable xi transmitted by each neighbor node_e(Here the intermediate variable ξ_eIs also equation (9), for example: intermediate variable xi of computing node e_eWhen, assume each neighbor node of node e is v, where

Then, h in equation (9) is replaced by e and e is replaced by v accordingly, i.e. the intermediate variable ξ of node e can be calculated_e) Calculating a new estimated value by using the following formula (10)

Wherein, 1-belongs to the weight occupied by the previous generation estimated value in the next generation estimated value in the calculation, and belongs to the weight occupied by the positioning result calculated according to the neighbor information in the current estimated value; the positioning result calculated according to the neighbor information means that:

the result of the calculation; the neighbor information refers to a ranging value and a barycentric coordinate, wherein the barycentric coordinate is obtained according to the ranging information between the nodes;

wherein ∈ is:

where k represents the number of iterations performed. When k → ∞ and e (k) → 0, the algorithm at this time largely depends on the past state of each node, not information from neighboring nodes. Therefore, noise generated due to a random phenomenon in ranging can be suppressed as time elapses. Meanwhile, too fast weight attenuation depends on the past state of the node too early, so that the iteration result cannot converge to a true value. Selected e (k) is different from oneIn the general form of

The weight attenuation is in a concave function form, so that divergence caused by too fast weight attenuation is avoided.

As the iteration is carried out, the former positioning result is more likely to be believed rather than the mutual information with the neighbor, so that the aims of suppressing noise and improving the system robustness are fulfilled.

S205: obtaining a node T to be positioned through iterative convergence_hThe positioning result of (1).

S3: taking the positioning result as an initial value of Taylor expansion and solving a final positioning result, wherein the method specifically comprises the following steps:

s301: using the positioning result as the initial value of Taylor expansion

Suppose a node T to be located_hHas real coordinates of

The estimated position deviation from the actual position can be expressed as (Δ x)_h,Δy_h,Δz_h) The following relationship exists:

s302: setting a node T to be positioned_hThe distance function between each neighboring node is

Wherein

And:

s303: at the point of

Performing Taylor expansion, neglecting components above the second order, and representing as B by matrix_Taylor＝A_TaylorΔ, wherein:

Δ＝[Δx_h,Δy_h,Δz_h]^T

s304: using least squares

Solving the deviation value delta of the estimated position and the actual position if the condition | delta x is satisfied_h|+|Δy_h|+|Δz_hMu is less than or equal to | in the positioning result (mu is an artificially set scalar used for controlling the precision), the output positioning result is:

if not, will

And recalculating as an initial value of Taylor expansion until a positioning result is output when a condition is met. In the Taylor expansion part, each node only needs to obtain the ranging information of the neighbor nodes and the current position information of the neighbor nodes, so the scheme is still completely distributed.

Examples are as follows: taking node 5 as an example, the ranging formula of its neighbor nodes is:

taylor expansion is carried out on the four formulas, the formulas are expressed in a matrix form, the deviation value delta of the estimated position and the actual position is calculated through a least square method, and if the condition | delta x is met₅|+|Δy₅|+|Δz₅If the | is less than or equal to mu, outputting a positioning result; if not, the deviation value is added with the initial value to be used as the initial value of the next Taylor expansion to continue the operation until the condition is met.

S4: the method takes Web mercator coordinates as a medium, and the final positioning result under a relative coordinate system is converted into an absolute coordinate system, and comprises the following steps:

s401: anchoring point (T) in sensor network₁、T₂、T₃、T₄) Converting the geodetic coordinates into Web mercator coordinates; assuming that the coordinates of the four anchor points in the relative coordinate system are T₁(x₁,y₁,z₁)、T₂(x₂,y₂,z₂)、T₃(x₃,y₃,z₃)、T₄(x₄,y₄,z₄) And the geodetic coordinate measured by the Beidou module is T₁(L₁,B₁,H₁)、T₂(L₂,B₂,H₂)、T₃(L₃,B₃,H₃)、T₄(L₄,B₄,H₄) Where L, B, H denotes the geodetic longitude, the geodetic latitude and the geodetic height, respectively. In the positioning system, the corresponding relation of the heights is fixed and can be directly converted.

Anchor pointBig dipper geodetic coordinate is converted into Web mercator coordinate T₁(X₁,Y₁)、T₂(X₂,Y₂)、T₃(X₃,Y₃)、T₄(X₄,Y₄) The following formula (16):

s402: calculating a conversion relation between the Web mercator coordinates and the relative coordinates by utilizing a least square method through the known Web mercator coordinates and the relative coordinates of the anchor points; get

According to the relation:

by using the least square method, we can get:

s403: to-be-positioned node T_h(e.g., node T in relative coordinate system₅、T₆、…、T_n) The relative coordinates of the Web-based ink card holder are converted into Web ink card holder coordinates according to the conversion relation; namely: according to the calculated conversion relation

And converting the relative coordinates into Web mercator coordinates.

S404: the node T to be positioned is determined according to the formula (19)_hConverting the Web mercator coordinates to geodetic coordinates (L_i,B_i) The formula (19) is as follows:

in the embodiment, the distributed real-time deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals is applied, and the node to be positioned performs distance measurement and communication with the neighbor node, so that the distributed positioning effect is realized. Meanwhile, because the nodes in the cave do not distinguish the labels and the anchor points, all the nodes can realize positioning, calibration is not needed, and the function of immediate deployment can be realized.

In addition, the distributed real-time deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals, which is provided by the embodiment, is relatively light in calculation burden, and the whole positioning network has stronger robustness and survivability.

Based on the positioning method, the accuracy degree of the positioning method based on the combination of the gravity center coordinates of the tetrahedron and Taylor expansion is verified as follows:

the real coordinates of the node to be located selected in this example are as follows (unit: cm):

T_5,real(-400,200,21)、T_6,real(-730,120,300)、T_7,real(-800,500,10)

directly using the coordinates T of the real position of the tag_h,real(x_h,real,y_h,real,z_h,real) And the location coordinate T_h(x_h,y_h,z_h) The distance therebetween represents the absolute error of the distance E:

the numerical example carries out a plurality of groups of experiments, and the effectiveness of the method provided by the invention in an actual scene is observed by adding an error of 0-20cm in a distance measurement stage.

In the present example, the distance measurement errors are added to all the connection line portions in fig. 2, and the influence of different distance measurement errors on the positioning result is observed by performing 20 sets of simulations respectively.

Fig. 4 shows that, in an ideal environment with a range error of 0, a circle "o" indicates a true position of a node, and a solid line indicates a convergence process of the node from an initial point given at random to the true position through iterative computation, and it can be seen that each solid line finally converges to the true position accurately. It can be illustrated that the method proposed in this embodiment is adopted to perform positioning of the sensor network, and a convergence process is shown in the figure, which illustrates the feasibility of this solution.

Fig. 5 shows the overall error of the proposed method of the present invention, and it can be seen from the figure that the ranging error has an influence on the proposed method of the present embodiment, and as the ranging error increases from 0cm to 20cm, the overall positioning error of the sensor network shows an increasing trend. At present, the distance measurement error of the actual device can be generally controlled to be about 10cm, and at this time, the total positioning error of the method proposed by the present embodiment is 17.2938cm, which can illustrate the total performance of the present solution.

Fig. 6 shows the positioning results of the nodes 5,6, and 7 respectively affected by the measurement distance error, and the relationship between the nodes to be positioned with different hop counts and the relationship between the nodes to be positioned and the error can be seen from fig. 6, as follows:

the positioning errors of the three nodes show the following trend: the positioning error of the 1-hop node is less than that of the 2-hop node, and the positioning error of the 2-hop node is less than that of the 3-hop node. In addition, their positioning errors all increase as the ranging error increases. When the ranging error is 10cm, the 1-hop node error, the 2-hop node positioning error and the 3-hop node error in the simulation are 3.4578cm, 22.2216cm and 26.2020cm respectively. (note: in this example node 5 is capable of communicating with anchors 1, 2, 3, 4, defined herein as 1 hop; node 6 is capable of communicating with nodes 1, 3, 4, 5, defined herein as 2 hops since there are only three anchors in the nodes capable of communicating; node 7 is capable of communicating with nodes 3, 4, 5,6, defined herein as 3 hops, including only two anchors in its neighbors.)

Simulation can show that compared with the anchor point-label positioning scheme commonly used in the market, the distributed immediate deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals can perform distributed three-dimensional positioning indoors without distinguishing the anchor points and the labels of the sensor nodes, and due to the characteristic, the immediate deployment function can be realized, and the rapid exploration of the unknown indoor environment can be realized; meanwhile, when the sensor network is not sparse, due to the characteristic of distributed computation, the overall positioning effect cannot be influenced under the condition that part of nodes are dead or damaged.

It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present application, the meaning of "a plurality" means at least two unless otherwise specified.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.

It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.

It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.

In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.

The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.

In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (9)

1. A distributed instant deployment three-dimensional positioning method fusing ultra-wideband and Beidou signals is characterized by comprising the following steps:

s1: a sensor network is constructed based on the Beidou module and the ultra-wideband technology, andcalculating node T to be positioned in sensor network_hThe barycentric coordinates of (a);

s2: solving a node T to be positioned by parallel distributed computation_hThe positioning result is processed with iterative convergence;

s3: taking the positioning result as an initial value of Taylor expansion and solving a final positioning result;

s4: and converting the final positioning result in the relative coordinate system into an absolute coordinate system.

2. The method of claim 1, wherein a node T to be positioned is calculated_hThe method of the barycentric coordinates of (1) is as follows:

s101: defining any node T to be positioned in sensor network_hSelecting a node T which can be positioned with the node T_hThe communication node is used as a neighbor node;

s102: acquiring the node T to be positioned through UWB signals_hRanging information with each neighbor node;

s103: calculating any node T to be positioned according to ranging information among different nodes_hCorresponding to the barycentric coordinates of its neighboring nodes.

3. The method for distributed instantaneous deployment three-dimensional positioning fusing ultra-wideband and Beidou signals according to claim 2, characterized in that in step S101, a node T is defined_hThe neighbor nodes are respectively T_i、T_j、T_k、T_l；

In step S102, a node T to be positioned_hForming a tetrahedron with each neighbor node in space according to the node T to be positioned_hRespectively calculating the volume V of each tetrahedron according to the ranging information between each tetrahedron and each neighbor node_ijkl、V_hijk、V_hijl、V_hikl、V_hjkl；

In step S103, the absolute value { | a of the barycentric coordinates is calculated using the volume ratio_hi|，|a_hj|，|a_hk|，|a_hlL } wherein:

determination of barycentric coordinates { a }_hi，a_hj，a_hk，a_hlSymbol patterns of, symbols are respectively σ_hi、σ_hj、σ_hk、σ_hlWherein: sigma_hi、σ_hj、σ_hk、σ_hlIs 1 or-1 and satisfies sigma_hi|a_hi|+σ_hj|a_hj|+σ_hk|a_hk|+σ_hl|a_hl|＝1；

Solving node T to be positioned by product of absolute value of barycentric coordinate and symbol_hCorresponding to its neighbor node T_i、T_j、T_k、T_lBarycentric coordinates of (a):

a_hi＝σ_hi|a_hi|、a_hj＝σ_hj|a_hj|

a_hk＝σ_hk|a_hk|、a_hl＝σ_hl|a_hl|。

4. the method of claim 3, wherein the absolute value of the barycentric coordinate { | a { [ a ]) is determined by a method of distributed instantaneous deployment of fused UWB and Beidou signals_hi|，|a_hj|，|a_hk|，|a_hlSymbol pattern of | } σ_hi、σ_hj、σ_hk、σ_hlIs based on the node T to be positioned_hThe subspace of the position is determined.

5. The distributed immediate deployment three-dimensional positioning method integrating ultra-wideband and Beidou signals according to claim 4, characterized in that the node T to be detected_hThe space position includes four spaces corresponding to four vertexes i, j, k and l, four spaces corresponding to four surfaces jkl, ijk, ijl and ikl, six edges ij,ik. Six spaces corresponding to il, jk, jl, kl and a space ijkl in a tetrahedral envelope; the symbol patterns corresponding to the respective spaces are as follows:

i(1,-1，-1，-1) ij(1,1,-1,-1) jl(-1，1,-1，1) ijl(1，1,-1，1)

j(-1,1，-1，-1) ik(1,-1,1,-1) kl(-1，-1,1,1) ikl(1,-1，1,1)

k(-1，-1，1，-1) il(1，-1，-1,1) jkl(-1,1,1，1) ijkl(1，1，1，1)

l(-1,-1,-1，1) jk(-1,1,1,-1) ijk(1，1,1,-1)。

6. the method for distributed instantaneous deployment three-dimensional positioning fusing ultra-wideband and Beidou signals according to claim 1, wherein the step S2 specifically comprises:

s201: for a node T to be positioned_hAssigning an initial value as a current estimated position

S202: the current estimated position

Sending to all nodes T to be positioned for calculation_hEach neighbor node of the barycentric coordinates and according to the received estimated position of each neighbor node

Calculating the intermediate variable xi_hThen calculate the intermediate variable xi_hSending the information to each neighbor node;

wherein,

represents all the variables used to calculate T_hOf coordinates of center of gravityA neighbor node; a is_heRepresents T_hThe barycentric coordinates corresponding to each neighboring node,

representation collection

Coordinates of the middle node;

s203: according to the intermediate variable xi sent by each neighbor node_eCalculating a new estimate using the following equation

Wherein, 1 represents the weight occupied by the previous generation estimated value in the next generation estimated value in the calculation, and the epsilon represents the weight occupied by the positioning result calculated according to the neighbor information in the current estimated value;

s205: obtaining a node T to be positioned through iterative convergence_hThe positioning result of (1).

7. The method for distributed instantaneous deployment three-dimensional positioning fusing ultra-wideband and Beidou signals according to claim 6, wherein in the step S203, e is as follows:

k represents the number of iterations performed.

8. The method for distributed instantaneous deployment three-dimensional positioning fusing ultra-wideband and Beidou signals according to claim 1, wherein the step S3 specifically comprises:

s301: expanding the positioning result as TaylorInitial value

Suppose a node T to be located_hHas real coordinates of

The estimated position deviation from the actual position can be expressed as (Δ x)_h，Δy_h，Δz_h)；

S302: setting a node T to be positioned_hThe distance function between each neighboring node is

Wherein

S303: at the point of

Performing Taylor expansion, neglecting components above the second order, and representing as B by matrix_Taylor＝A_TaylorΔ, wherein Δ ═ Δ x_h，Δy_h，Δz_h]^T；

S304: using least squares

Solving the deviation value delta of the estimated position and the actual position if the condition | delta x is satisfied_h|+|Δy_h|+|Δz_hIf the | is less than or equal to mu, the output positioning result is as follows:

if not, will

As the initial value of the Taylor expansionAnd newly calculating until the positioning result is output when the condition is met.

9. The distributed instantaneous deployment three-dimensional positioning method fusing the ultra-wideband and the Beidou signals according to claim 1, characterized in that the positioning result under the relative coordinate system is converted into an absolute coordinate system, and the method comprises the following steps:

s401: converting geodetic coordinates of anchor points in the sensor network into Web mercator coordinates;

s402: calculating a conversion relation between the Web mercator coordinates and the relative coordinates by utilizing a least square method through the known Web mercator coordinates and the relative coordinates of the anchor points;

s403: to-be-positioned node T_hThe relative coordinates of the Web-based ink card holder are converted into Web ink card holder coordinates according to the conversion relation;

s404: to-be-positioned node T_hThe Web mercator coordinates of (a) are converted to geodetic coordinates.

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