CN111541988B

CN111541988B - Three-dimensional indoor positioning method based on barycentric coordinate and Taylor expansion

Info

Publication number: CN111541988B
Application number: CN202010304504.8A
Authority: CN
Inventors: 俞成浦; 何澄洋; 唐潮
Original assignee: Chongqing Innovation Center of Beijing University of Technology
Current assignee: Chongqing Innovation Center of Beijing University of Technology
Priority date: 2020-04-17
Filing date: 2020-04-17
Publication date: 2021-11-23
Anticipated expiration: 2040-04-17
Also published as: CN111541988A

Abstract

The invention discloses a three-dimensional indoor positioning method based on barycentric coordinates and Taylor expansion, which belongs to the technical field of indoor positioning and comprises the following specific steps: (1) the label T to be measured forms four tetrahedrons with the anchor point O, A, B, C in space, and the volumes V are respectively calculated_T‑ABC、V_T‑OBC、V_T‑OAC、V_T‑OABAnd volume V_O‑ABC(ii) a (2) Calculating barycentric coordinates { a ] using volume ratios_TO，a_TA，a_TB，a_TC}; (3) determination of barycentric coordinates { a }_TO，a_TA，a_TB，a_TCThe symbol pattern of { fraction }; (4) solving initial coordinates T using weighting of tetrahedral vertices₁(ii) a (5) Using initial coordinates T₁As initial values for the Taylor expansion

the method aims to calculate the initial positioning value of the label by using the characteristic that the gravity center coordinate of the tetrahedron represents any point in the space where the tetrahedron is located, and improve the indoor three-dimensional positioning precision by Taylor expansion.

Description

Three-dimensional indoor positioning method based on barycentric coordinate and Taylor expansion

Technical Field

The invention belongs to the technical field of indoor positioning, relates to a three-dimensional high-precision indoor positioning method based on ultra-wideband signals, and particularly relates to a three-dimensional indoor positioning method based on barycentric coordinates combined with Taylor expansion. According to the method, the centimeter-level high-precision three-dimensional positioning in the indoor environment is realized by utilizing the ultra-wideband ranging information between a plurality of anchor points and the labels and combining the positioning algorithm based on the tetrahedral barycentric coordinate with Taylor expansion.

Background

The Ultra Wide Band (UWB) technology is a new wireless communication technology, which makes signals have GHz-level bandwidth by directly modulating impulse with very steep rise and fall time. The UWB technology utilizes nanosecond or even picosecond ultra-narrow pulses to transmit information, and because signals with extremely low power are transmitted in a wide frequency spectrum, the UWB signals can achieve data transmission rates of hundreds of Mbps or even Gbps in a range of about 10 m. 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) the safety is high: the UWB signal has a frequency band of 7.5GHz, and the FCC limits the power spectral density to be lower than the environmental noise level, so that the UWB signal is difficult to intercept by a spectrum searching mode;

(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.

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. The UWB signal is a short-distance wireless carrier communication technology that transmits data with extremely narrow pulses, and is particularly suitable for indoor high-precision positioning because of its advantages of interference resistance, low power consumption, difficulty in interception, multipath resistance, strong penetration, and the like. When UWB technology is used for indoor positioning, a ranging-based positioning algorithm is generally used. Current ranging lateral methods include time of flight (TOA) based on signals, time difference of arrival (TDOA) based on angle of arrival location (AOA), 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.

On the premise of the traditional outdoor positioning algorithm and the pseudo requirement of position service, almost all positioning algorithms such as a Chan algorithm, a Fang algorithm, a Taylor series expansion method, a Friedlander algorithm and the like use an expansion algorithm such as a least square method or a weighted least square method to determine position information. However, the measurement error of the actual positioning system is often uncontrollable, and cannot reach zero-mean gaussian distribution required by an algorithm theory, and a multipath channel model given by IEEE cannot be completely suitable for a non-line-of-sight error in an environment with a real position service requirement. Due to the difficulties of UWB signal characteristics, wireless transmission clock synchronization and the like, in a large number of research results of traditional positioning algorithms, most of the traditional line-of-sight positioning algorithms are combined with Kalman filtering and other modes to carry out smooth filtering to eliminate non-line-of-sight errors in the ranging and positioning processes, and various algorithms are mixed for correction; in addition, some algorithms process the algorithms by data screening of statistical characteristics such as research average, rectangular correction, low bit width quantization, interchange operation and the like; there is also a small amount of research focused on the hardware characteristics of UWB signals to improve positioning accuracy.

At present, ultra-wideband positioning products actually exist in the market, and in order to accelerate the corresponding speed of equipment and reduce the price of a processor, a trilateral positioning algorithm which is a three-dimensional positioning algorithm which is relatively easy to realize is generally adopted. Although the method has certain requirements on the anchor point erecting mode, the method is different from various algorithms based on the least square method, the complex matrix operation can be avoided, the hardware operation burden is reduced, the hardware is convenient to lighten and the equipment cost is reduced. However, with the rapid development of computing device hardware, the computation workload has gradually developed into a secondary contradiction, and the primary contradiction to be solved has developed into a higher and higher requirement on the positioning accuracy. The trilateral positioning algorithm has the obvious defect that for a high-precision indoor three-dimensional positioning system, the method can calculate the coordinate positioning precision of the xOy plane, namely the requirement of general indoor two-dimensional positioning can be met; however, errors generated by the x axis and the y axis in the algorithm are accumulated to the z axis, so that the positioning error of the z axis is obviously larger than that of the x axis and the y axis, namely, the height in the three-dimensional coordinate has a larger error at present, and the problem is not solved.

Disclosure of Invention

In practical application, along with the generation of various application products, particularly unmanned aerial vehicle related products, more stringent requirements are also placed on the height in three-dimensional positioning, and in view of the above problems in the prior art, the invention aims to provide a three-dimensional indoor positioning method based on barycentric coordinates and Taylor expansion so as to achieve the purpose of comprehensively improving indoor positioning accuracy by a positioning algorithm based on distance information.

The technical scheme adopted by the invention is as follows: a three-dimensional indoor positioning method based on gravity center coordinates and Taylor expansion defines position coordinates of an anchor point O, A, B, C and a to-be-detected label T, a tetrahedron can be formed by anchor points O, A, B, C, and the distance d from anchor points O, A, B, C to the to-be-detected label T is calculated_O、d_A、d_B、d_CThe positioning method comprises the following steps:

(1) let OA length be a, OB length be b, OC length be c, AB length be c ', BC length be a ', AC length be b ', calculate volume V of tetrahedral OABC_O-ABC(ii) a And the label T to be tested and the anchor point O, A, B, C form four tetrahedrons in space, and the volumes V of the four tetrahedrons are respectively calculated_T-ABC、V_T-OBC、V_T-OAC、V_T-OAB；

(2) Calculating barycentric coordinates { a ] using volume ratios_TO,a_TA,a_TB,a_TCAre multiplied by

It should be noted that, the barycentric coordinate herein does not refer to the "barycentric" coordinate in physics, but refers to that any point in the space where the tetrahedron is located can be represented as the weighted average of the vertices, and this weight is the barycentric coordinate referred to in this scheme;

(3) determination of barycentric coordinates { a }_TO,a_TA,a_TB,a_TCSymbol patterns of, symbols are respectively σ_TO、σ_TA、σ_TB、σ_TCAnd satisfy sigma_TO|a_TO|+σ_TA|a_TA|+σ_TB|a_TB|+σ_TC|a_TC|＝1；

(4) Method for solving initial coordinate T of to-be-detected label T by using weight of tetrahedral vertex₁The following are:

T₁＝σ_TO|a_TO|O+σ_TA|a_TA|A+σ_TB|a_TB|B+σ_TC|a_TC|C；

the steps (1) to (4) are that the weighted characteristic that any point of the space where the tetrahedron is located can be represented as the vertex of the tetrahedron is utilized, and the distance measurement is carried out between the tag T to be measured and each anchor point, so that the initial positioning in the three-dimensional space is realized;

(5) using initial coordinates T₁As initial values for the Taylor expansion

Assuming that the true coordinates of the tag T to be measured are (x, y, z), the estimated position deviation from the actual position can be expressed as (Δ x, Δ y, Δ z) as follows:

calculating deviation value delta of the estimated position and the actual position through Taylor expansion, and taking delta as [ delta x, delta y, delta z [ ]]^TAnd judging whether the conditions are met:

|Δx|+|Δy|+|Δz|≤∈；

by a Taylor unfolding method, the UWB positioning precision is improved, and the adaptive capacity of the algorithm to the environment is enhanced;

(6) if the condition in the step (5) is met, taking the coordinate of the to-be-detected label T as:

if not, taking the initial coordinate T₁Is composed of

And returning to the step (5) until the judgment condition is met to obtain T_Taylor；

Expanding the Taylor method for TDOA to TOA ranging from the step (5) to the step (6), taking an initial positioning result given by the gravity center coordinate-based method as an initial coordinate of the tag T to be detected, and realizing high-precision three-dimensional positioning through Taylor expansion calculation.

Further, the anchor points A, B, C are located in the same plane and the anchor points O are located in different planes to form a tetrahedron (the anchor points are deployed only in a preferred manner, and may be deployed in other manners on the premise that four anchor points can form a tetrahedron), and the distances d from the tag T to be detected to the four anchor points O, A, B, C are calculated by a bilateral ranging algorithm of TOA_O、d_A、d_B、d_C. Specifically, let: the position coordinates of the four anchor points O, A, B, C are (x) respectively₀,y₀,z₀)、(x₁,y₁,z₁)、(x₂,y₂,z₂) And (x)₃,y₃,z₃) Setting the three-dimensional coordinate of the tag T to be detected as (x, y, z); generally, the coordinates of the anchor point a are (0,0,0), and the deployment positions of the anchor points B, C, O are not set to be at the point (x) according to the proposed deployment manner of the anchor points₂,0,0)、(0,y₃,0)、(0,0,z₀) The four anchor points are deployed and simultaneously construct a corresponding Euclidean coordinate system, and the calculation of coordinates with the positioning points is carried out based on the coordinate system; obtaining the T to four anchor points of the label to be detected by a bilateral distance measurement method based on TOADistance d of_O、d_A、d_B、d_C(ii) a Thereby obtaining all the required input information.

Further, the volume V_O-ABCThe calculation formula of (a) is as follows:

further, the spaces separated by tetrahedrons are respectively corresponding to the symbol patterns, and the barycentric coordinates { a }_TO,a_TA,a_TB,a_TCDetermining the symbol mode according to the space of the label T to be tested, and determining the symbol sigma according to the symbol mode_TO、σ_TA、σ_TB、σ_TC。

Further, the space where the to-be-detected label T is located includes O, A, B, C four vertices, four faces ABC, OAB, OAC, OBC, six edges OA, OB, OC, AB, AC, BC, and an OABC located in an envelope in a tetrahedral envelope, and the symbol pattern corresponding to each space is as follows:

O(1,-1,-1,-1) OA(1,1,-1,-1) AC(-1,1,-1,1) OAC(1,1,-1,1)

A(-1,1,-1,-1) OB(1,-1,1,-1) BC(-1,-1,1,1) OBC(1,-1,1,1)

B(-1,-1,1,-1) OC(1,-1,-1,1) ABC(-1,1,1,1) OABC(1,1,1,1)

C(-1,-1,-1,1) AB(-1,1,1,-1) OAB(1,1,1,-1)。

further, the calculated deviation value Δ of the estimated position from the actual position is calculated by the following method:

1) setting the distance function between the label to be tested and the anchor point as d_i(x, y, z), wherein i ═ a, B, C, O, and:

2) point of the above type

Taylor expansion is performed, and the components above the second order are ignored, so that the following equation is obtained:

3) for each distance function d_i(x, y, z) is subjected to Taylor expansion, and the matrix is represented as B_Taylor＝A_TaylorΔ, wherein A_TaylorAnd B_TaylorRespectively as follows:

4) by passing

A deviation Delta of the estimated position from the actual position is calculated.

The invention has the beneficial effects that:

1. by adopting the three-dimensional indoor positioning method based on the barycentric coordinate and Taylor expansion disclosed by the invention, the characteristic that any point of the space where a tetrahedron is located can be represented as the weighting of the vertex of the tetrahedron is utilized, the distance measurement is carried out between the label to be measured and the anchor point, the positioning in the three-dimensional space is realized, then the Taylor method for TDOA is expanded to TOA distance measurement, the positioning result given by the method based on the barycentric coordinate is used as the initial positioning coordinate of the label, the deviation value of the estimated position and the actual position is calculated, the high-precision three-dimensional positioning is realized, the indoor positioning precision can be comprehensively improved, and the problem of insufficient z-axis precision in a plurality of devices on the market is solved.

2. The three-dimensional indoor positioning method based on the gravity center coordinate and Taylor expansion disclosed by the invention has strong expansibility. Compared with a multi-agent system, the trilateration algorithm intelligently calculates the positions of other nodes one by one from a group of anchor points, belongs to a sequential method, and has strong limitation. The method provided by the invention belongs to a concurrent method, and can realize the parallel positioning of multiple intelligent agents after being expanded, thereby having very strong practical application significance.

Drawings

FIG. 1 is a schematic view of the disposition of anchor points in a three-dimensional indoor positioning method based on barycentric coordinates in combination with Taylor expansion provided by the present invention;

FIG. 2 is a schematic view of a tetrahedron formed between a tag to be detected and an anchor point in the three-dimensional indoor positioning method based on the barycentric coordinate and Taylor expansion provided by the present invention;

FIG. 3 is a flowchart of a three-dimensional indoor positioning method based on barycentric coordinates combined with Taylor expansion according to the present invention;

FIG. 4 is an analysis graph comparing absolute errors of a trilateral localization algorithm in the x-axis direction and a three-dimensional indoor localization method based on barycentric coordinates in combination with Taylor expansion;

FIG. 5 is an analysis graph comparing absolute errors of a trilateral localization algorithm in the y-axis direction with a three-dimensional indoor localization method based on barycentric coordinates in combination with Taylor expansion;

FIG. 6 is an analysis graph of the comparison of the trilateral localization algorithm in the z-axis direction with the three-dimensional indoor localization method based on barycentric coordinates in combination with Taylor expansion versus absolute error;

FIG. 7 is an analysis graph comparing the mean absolute error of a trilateral localization algorithm with a three-dimensional indoor localization method based on barycentric coordinates in combination with Taylor expansion;

FIG. 8 is an absolute error histogram of a trilateral localization algorithm with a three-dimensional indoor localization method based on barycentric coordinates in combination with Taylor expansion.

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

The unmanned aerial vehicle can determine a corresponding control strategy only by the current position coordinate T of the unmanned aerial vehicle, so that high-precision positioning information has very important significance to an unmanned aerial vehicle system, and an application scene schematic diagram is shown in fig. 1. The unmanned aerial vehicle system respectively carries out distance measurement through a carried label T and an anchor point when executing a task, the self position of the unmanned aerial vehicle is resolved through the obtained distance information by utilizing a related positioning algorithm, the position of the unmanned aerial vehicle is represented through a three-dimensional Euclidean space coordinate T (x, y, z) constructed by the anchor point, wherein the x, y and z respectively represent coordinate values in the directions of an x axis, a y axis and a z axis under a three-dimensional space coordinate system.

In the three-dimensional indoor positioning method based on the combination of the gravity center coordinates and the Taylor expansion provided in the embodiment, an Euclidean space coordinate system is constructed by collecting distance information between an anchor point and a tag T and position information of the anchor point as input, and then a current tag coordinate value T is obtained as output by using a proposed high-precision three-dimensional indoor algorithm based on the combination of the tetrahedral gravity center coordinates and the Taylor expansion.

The high-precision three-dimensional indoor algorithm based on the combination of the gravity center coordinates of the tetrahedron and Taylor expansion is provided, the characteristics of any point in the space where the tetrahedron is located can be represented by the gravity center coordinates of the tetrahedron, the initial positioning value of the label is calculated, and the indoor three-dimensional positioning precision is improved through the Taylor expansion. The accuracy of the method is implemented and verified by using a specific example, as shown in fig. 3, the specific process is as follows:

the method comprises the following steps: modeling a three-dimensional Euclidean space where the four anchor points are located, and acquiring input information of an algorithm, wherein the modeling specifically comprises the following steps:

deploying a positioning anchor point in an indoor environment, establishing an Euclidean coordinate system, obtaining the accurate coordinate of the deployment anchor point in a manual measurement mode, and giving a three-dimensional spaceThe coordinates of the middle anchor point are (x) and the coordinates of the positions of the four anchor points O, A, B, C are (x)₀,y₀,z₀)、(x₁,y₁,z₁)、(x₂,y₂,z₂)、(x₃,y₃,z₃) In this model we use point a as the origin in space, we determine the x-axis of Euclidean space with A, B anchor points,

is the positive direction of the x axis; A. the C anchor point determines the y-axis,

is the positive direction of the y axis; A. the O anchor point determines the z-axis,

is the positive direction of the Z axis; the coordinates of the four anchor points O, A, B, C are as follows:

A(0,0,0) B(1000,0,0)

C(0,1000,0) O(0,0,1000)

in an actual application scenario, distance information from each anchor point to a tag T can be obtained through a distance measurement means, wherein the tag coordinate is assumed to be a random point in a space where four anchor points are located, and the real coordinate of the tag coordinate is T (x)_R,y_R,z_R). Since the coordinates of the four anchor points are known, by the following equation (1):

taking the true distance from each anchor point to the label as d_i(x_R,y_R,z_R) Wherein i ═ O, a, B, C.

Distance function d_i(x, y, z) are specifically as follows:

plus an additive white Gaussian noise v with an expected 0 variance of 7_i(ii) a Obtaining a measured distance

Step two: solving initial label T by using algorithm based on tetrahedral barycentric coordinates₁。

1. Respectively substituting the coordinates of the four anchor points and the ranging values from the mark T to the anchor points into the following formula (2) according to the corresponding relation so as to obtain the volume V of the tetrahedron OABC_O-ABC：

The tag T may also form four tetrahedrons with the anchor point O, A, B, C in space as shown in FIG. 2, and the distance between each node of each tetrahedron is a known quantity, using the ranging value d between the tag T and the anchor point_O、d_A、d_B、d_CAnd calculating the volume V of four tetrahedrons by combining the same principle of the formula (2)_T-ABC、V_T-OBC、V_T-OAC、V_T-OAB。

2. Substituting the determined volume into equation (3):

the barycentric coordinates { a ] are calculated by the above formula (3)_TO,a_TA,a_TB,a_TC}。

3. Determination of barycentric coordinates { a }_TO,a_TA,a_TB,a_TCSymbol pattern of, for u, v, let σ_uvE { -1,1} represents barycentric coordinate a_uvThe symbol of (2). When the label T is located within the envelope formed by the four anchor points, a can be derived from the geometrical relationship of fig. 2_TO+a_TA+a_TB+a_TC1 is ═ 1; therefore, the symbol pattern for determining the barycentric coordinates is equivalent to the following formula (4), and the symbol pattern for the barycentric coordinates is determined using the formula (4), and the formula (4) is as follows:

σ_TO|a_TO|+σ_TA|a_TA|+σ_TB|a_TB|+σ_TC|a_TC|＝1 (4)

4. from the above equation, the possible sign patterns of barycentric coordinates have 15 types, and the equation cannot be satisfied when the sign patterns are { -1, -1, -1, -1 }. The symbol pattern of the 15-class barycentric coordinates comprises four vertexes (O, A, B, C), four surfaces (ABC, OAB, OAC and OBC) and six edges (OA, OB, OC, AB, AC and BC), which respectively correspond to a symbol pattern outside an envelope, and also comprises a pattern (OABC) inside the envelope, wherein the specific patterns are as follows:

O(1,-1,-1,-1) OA(1,1,-1,-1) AC(-1,1,-1,1) OAC(1,1,-1,1)

A(-1,1,-1,-1) OB(1,-1,1,-1) BC(-1,-1,1,1) OBC(1,-1,1,1)

B(-1,-1,1,-1) OC(1,-1,-1,1) ABC(-1,1,1,1) OABC(1,1,1,1)

C(-1,-1,-1,1) AB(-1,1,1,-1) OAB(1,1,1,-1)；

when determining the sign pattern of barycentric coordinates, the sign pattern of selecting barycentric coordinates is determined according to the position of the tag T, for example: the tag T is in a space corresponding to the OA ridge, the tetrahedron divides the space into 15 parts, and OA {1,1, -1, -1} is selected as a symbol pattern when the T is in the part corresponding to the OA ridge;

respectively corresponding to the symbols sigma_TO＝1、σ_TA＝1、σ_TB＝-1、σ_TCIs-1 and substituted into equation (5) for solving for the tag position as follows.

5. Solving initial coordinates T of label T by using weighting of tetrahedral vertexes₁Substituting the obtained barycentric coordinate, the sign mode and the coordinates of the four anchor points into formula (5):

T₁＝σ_TO|a_TO|O+σ_TA|a_TA|A+σ_TB|a_TB|B+σ_TC|a_TC|C (5)

wherein O, A, B, C, T in the formula₁Refers to the four vertices and the initial label coordinates.

Step three: calculating initial coordinate T₁As initial values for the Taylor expansion

Will measure the distance

Corresponding to d in formula (6)_O、d_A、d_B、d_CAt the same time handle

And coordinates of four anchor points are substituted into the formula (6), and Δ ═ Δ x, Δ y, Δ z are calculated]^TEquation (6) is as follows:

taking Δ ═ Δ x, Δ y, Δ z]^TBy passing

Calculating estimated position and realityDeviation value of the position.

if not, taking:

Step five: by the above numerical example, the accuracy of the positioning method using the tetrahedron-based barycentric coordinate combined with the Taylor expansion is verified.

Directly using the coordinates T (x) of the true position of the tag_R,y_R,z_R) And the location coordinate T_Taylor(x_f,y_f,x_f) The distance between them represents the absolute error E of the distance, and the difference value of the z-axis represents the absolute error in the z-axis direction as E_z；

E_z＝|z_f-z_T|；

3000 groups of numerical experiments under the influence of additive white Gaussian noise are carried out on the numerical example, and the accuracy of the proposed three-dimensional indoor positioning method is verified through numerical simulation. Compared with the trilateration algorithm, the obtained absolute error map and absolute error distribution histogram show that, as shown in fig. 4-7: white Gaussian noise v at a standard deviation of 7cm_iUnder the interference, as shown in fig. 4, the average absolute error of the trilateration algorithm in the x-axis direction is 4.8304cm, and the average absolute error of the method proposed in this embodiment in the x-axis direction is 4.3968 cm;

as shown in fig. 5, the average absolute error in the y-axis direction of the trilateration algorithm is 5.4000cm, and the average absolute error in the y-axis direction of the method proposed in this embodiment is 4.9118 cm;

as shown in fig. 6, the average absolute error in the z-axis direction of the trilateral localization algorithm is 16.8676cm, and the average absolute error in the z-axis direction of the method provided by the embodiment is 6.0818cm, which is 63.94% higher than that of the trilateral localization algorithm;

as shown in fig. 7, the average absolute error of the trilateral location algorithm is 19.7790cm, and the average absolute error of the method provided by the embodiment is 10.2728cm, which is 48.06% higher than the accuracy of the trilateral location algorithm;

through simulation, compared with a trilateral positioning algorithm generally applied in the market, the high-precision three-dimensional indoor positioning method based on the tetrahedral barycentric coordinate algorithm and the Taylor expansion, which is provided by the embodiment, can realize more accurate positioning under the noise interference condition, and the precision in the directions of the x axis, the y axis and the z axis is improved to different degrees, particularly the precision in the direction of the z axis is greatly improved.

As shown in fig. 8, a positioning absolute error histogram obtained by 3000 simulations is shown, and it can be seen that the probabilities of the absolute error of the trilateration algorithm within 5 cm, 5 to 10 cm, 10 to 15 cm, 15 to 20 cm, 20 to 25 cm, 25 to 30 cm, and 30 cm or more are 3.97%, 17.37%, 21.93%, 17.67%, 12.03%, 9.37%, and 17.30%, respectively. The probabilities that the absolute error of the method proposed by the embodiment is within 5 cm, 5 to 10 cm, 10 to 15 cm, 15 to 20 cm, 20 to 25 cm, 25 to 30 cm and more than 30 cm are 11.00%, 40.60%, 33.00%, 12.76%, 2.3%, 0.30% and 0% respectively; the simulation result shows that under the condition that the standard deviation of the noise is 7cm, the probability that the indoor positioning error is less than 20 cm under the three-dimensional space is as high as 97.36 percent.

Through the analysis of statistical simulation results, it can be seen that the method provided by the embodiment is greatly improved in precision compared with a common trilateral positioning method, the probability that the error exceeds 30 centimeters for 3000 times of simulation is 0%, and the probability that the error is less than 20 centimeters is 97.36%, so that the method is greatly improved compared with the trilateral positioning method.

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

1. A three-dimensional indoor positioning method based on barycentric coordinates and Taylor expansion defines position coordinates of anchor point O, A, B, C and a to-be-detected label T, and calculates a distance d from anchor point O, A, B, C to the to-be-detected label T_O、d_A、d_B、d_CThe method is characterized by comprising the following steps:

(2) Calculating barycentric coordinates { a ] using volume ratios_TO，a_TA，a_TB，a_TCAre multiplied by

(3) Determination of barycentric coordinates { a }_TO，a_TA，a_TB，a_TCSymbol patterns of, symbols are respectively σ_To、σ_TA、σ_TB、σ_TCAnd satisfy sigma_TO|a_TO|+σ_TA|a_TA|+σ_TB|a_TB|+σ_TC|a_TC|＝1；

T₁＝σ_TO|a_TO|O+σ_TA|a_TA|A+σ_TB|a_TB|B+σ_TC|a_TC|C；

wherein O, A, B, C refers to the coordinates of four vertices, respectively;

(5) using initial coordinates T₁As initial values for the Taylor expansion

|Δx|+|Δy|+|Δz|≤∈；

wherein epsilon is a preset threshold value;

if not, taking the initial coordinate T₁Is composed of

And returning to the step (5) until the judgment condition is met to obtain T_Taylor。

2. The three-dimensional indoor positioning method based on barycentric coordinate and Taylor expansion of claim 1, wherein the anchor points A, B, C are located in the same plane and the anchor points O are located in different planes to form a tetrahedron, and the distances d from the tag T to be detected to the four anchor points O, A, B, C are calculated by a bilateral ranging algorithm of TOA_O、d_A、d_B、d_C。

3. The method as claimed in claim 1, wherein the volume V is a volume V based on the centroid coordinates and Taylor expansion_O-ABCThe calculation formula of (a) is as follows:

4. the method as claimed in claim 1, wherein the space divided by tetrahedron is corresponding to each symbol pattern, and the barycentric coordinates { a } are determined by combining Taylor expansion_TO，a_TA，a_TB，a_TCDetermining the symbol mode according to the space position of the tag T to be tested, wherein the symbol mode corresponds to the symbols sigma respectively_TO、σ_TA、σ_TB、σ_TC。

5. The method as claimed in claim 4, wherein the spatial position of the tag T to be detected includes O, A, B, C four vertices, four faces ABC, OAB, OAC and OBC, six edges OA, OB, OC, AB, AC and BC, and OABC located in a tetrahedral envelope, and the symbol pattern corresponding to each spatial position is as follows:

6. the method as claimed in claim 1, wherein the calculated deviation Δ between the estimated position and the actual position is determined by the following method:

2) point of the above type

3) for each distance function d_i(x, y, z) is subjected to Taylor expansion, and the matrix is expressed asB_Taylor＝A_TaylorΔ, wherein A_TaylorAnd B_TaylorRespectively as follows:

wherein (x)₀，y₀，z₀)、(x₁，y₁，z₁)、(x₂，y₂，z₂) And (x)₃，y₃，z₃) Position coordinates of four anchor points O, A, B, C, respectively;

4) by passing