A high-precision indoor three-dimensional positioning method based on projection mode

Abstract

The application discloses a high-precision indoor three-dimensional positioning method based on a projection mode, which comprises the following steps: 1) setting four positioning base stations and a position label to be measured; 2) obtaining the distance from the position label to each positioning base station by a positioning measurement device; 3) projecting all the positioning base stations to a plane with a height of the height z of the position label to be measured in a projection mode; 4) calculating the distance from the position label to be measured to the projection points of the four positioning base stations; and 5) solving to obtain the coordinates of the position label to be measured. The method only needs at least four positioning base stations, and high-precision three-dimensional positioning can be realized; the method can obtain higher positioning precision and positioning stability under the same environment, the algorithm can effectively reduce the dependence on the positioning base stations, and the economic benefit is remarkable.

Description

Technical Field

[0001] This invention relates to positioning technology, and more particularly to a high-precision indoor three-dimensional positioning method based on projection patterns. Background Technology

[0002] The essence of current positioning technology is to establish equations and estimate the location of a tag using pre-positioned base stations and ranging or non-ranging positioning methods. Common test-based positioning methods include: TOA (Time of Arrival): This method measures the time difference of arrival of the signal between the positioning base station and the tag under test to obtain the distance; RSSI (Received Signal Strength Indicator): This method establishes a signal propagation path loss model based on signal attenuation data during propagation to obtain the distance; TOF (Time of Flight): This method directly measures the signal flight time between the positioning base station and the tag under test, and then obtains the distance using the distance formula (S=VT). With technological advancements, improved TOF methods include TWR (Two-Way Range): Two-way ranging, and SDS-TWR (Symmetrical Double Side-Two-Way Range): Symmetrical double-sided two-way ranging. The positioning principles of TOF and TOA are the same; the main difference is whether time synchronization is required between the positioning base station and the tag under test. TDOA (Time Difference of Arrival) works by measuring the time difference between the tag and two positioning base stations to obtain the distance difference between them. All the positioning methods described above require establishing a mathematical model after obtaining the distance or distance difference to calculate the X, Y, and Z coordinates of the tag. In practical applications, inaccurate positioning results are caused by signal propagation delays, equipment measurement errors (observation errors), calculation accuracy errors (rounding errors), and model errors. To address these issues, methods such as multiple measurements, adding positioning base stations, and using high-precision calculation libraries are generally employed to improve accuracy. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a high-precision indoor three-dimensional positioning method based on projection mode, which addresses the deficiencies in the prior art.

[0004] The technical solution adopted by this invention to solve its technical problem is: a high-precision indoor three-dimensional positioning method based on projection mode, comprising the following steps:

[0005] 1) Set up four positioning base stations and the location tag to be measured. The coordinates of the four base stations are BS1(x1,y1,z1), BS2(x2,y2,z2), BS3(x3,y3,z3), and BS4(x4,y4,z4); the coordinates of the location tag are MS(x,y,z).

[0006] 2) Using positioning measurement equipment, obtain the distance from the location tag to each positioning base station, and record the measured distances as R1, R2, R3, and R4;

[0007] 3) Using projection, all positioning base stations are projected onto a plane with a height equal to the height z of the location tag to be measured. The coordinates of the projection points of the four positioning base stations become BS1'(x1,y1,z), BS2'(x2,y2,z), BS3'(x3,y3,z), and BS4'(x4,y4,z). The distances from the projection points to the location tag are denoted as r1, r2, r3, and r4.

[0008] 4) Calculate the distances from the label to be tested to the four projection points;

[0009]

[0010] 5) Solve the system of equations from step 4);

[0011] According to equation (1), we can obtain that

[0012]

[0013] Combining equation (3) and equation (1), we can obtain

[0014]

[0015] Equation (4) can be simplified to:

[0016] AX = B (5)

[0017] in:

[0018]

[0019]

[0020] According to the least squares method, we can obtain:

[0021] X = (A T A) -1 A T B (6)

[0022] At this point, the x and y coordinates of the location label to be measured are both represented by z, that is,

[0023]

[0024] Substitution Based on prior information, the correct z value is obtained, and the MS(x,y,z) coordinates of the location label to be measured can be obtained. According to expressions (1) and (2), the system of equations is an overdetermined system, that is, by projection, redundant data can be fully utilized to improve the positioning accuracy.

[0025] The beneficial effects of this invention are:

[0026] The method of this invention requires only at least four positioning base stations to achieve high-precision three-dimensional positioning. Experimental data demonstrates that, under the same conditions, the method of this invention achieves higher positioning accuracy and stability, and the algorithm effectively reduces dependence on positioning base stations, resulting in significant economic benefits. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0028] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0029] Figure 2 This is a comparison chart of experimental results from an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0031] like Figure 1 As shown, a high-precision indoor 3D positioning method based on projection mode includes the following steps:

[0032] 1) Set up four positioning base stations and the location tag to be measured. The coordinates of the four base stations are BS1(x1,y1,z1), BS2(x2,y2,z2), BS3(x3,y3,z3), and BS4(x4,y4,z4); the coordinates of the location tag are MS(x,y,z).

[0033] 2) Using positioning measurement equipment, obtain the distance from the location tag to each positioning base station, and record the measured distances as R1, R2, R3, and R4;

[0034] 2.1) In TOA, TOF and RSSI positioning methods, the distance from the tag to each positioning base station can be directly obtained through positioning measurement equipment. Taking four base stations as an example, the measured distances are recorded as R1, R2, R3 and R4.

[0035] 2.2) In the TDOA positioning method, the distance difference between the tag under test and the two base stations can be directly obtained through the positioning test equipment. Base station 1 is selected as the reference base station, and the distance difference can be expressed as:

[0036]

[0037] R i1 =R i -R1(i=2,3,4)

[0038] According to the formula for the distance between two points in space:

[0039]

[0040]

[0041] We can obtain:

[0042]

[0043] Substitute the pre-set base station coordinates into the formula, convert x, y, z into the expression of R1, obtain R1, substitute R1 into formula (1), and obtain R2, R3, R4.

[0044] 3) Using projection, all positioning base stations are projected onto a plane with a height equal to the height z of the location tag to be measured. The coordinates of the projection points of the four positioning base stations become BS1'(x1,y1,z), BS2'(x2,y2,z), BS3'(x3,y3,z), and BS4'(x4,y4,z). The distances from the projection points to the location tag are denoted as r1, r2, r3, and r4.

[0045] 4) Calculate the distances from the label to be tested to the four projection points;

[0046]

[0047] 5) Solve the system of equations from step 4);

[0048] According to Gaussian elimination, subtracting the first row from the second row of expression in equation (1), subtracting the first row from the third row, and subtracting the first row from the fourth row yields:

[0049]

[0050] The above equation can be rewritten in matrix form as follows:

[0051]

[0052] Combining equation (3) and equation (1), we can obtain

[0053]

[0054] Equation (4) can be simplified to:

[0055] AX = B (5)

[0056] in:

[0057]

[0058]

[0059] According to the least squares method, we can obtain:

[0060] X = (A T A) -1 A T B (6)

[0061] At this point, the x and y coordinates of the location label to be measured are both represented by z, that is,

[0062]

[0063] Substitution Based on prior information, the correct z value is obtained, and the MS(x,y,z) coordinates of the location label to be measured can be obtained. According to expressions (1) and (2), the system of equations is an overdetermined system, that is, by projection, redundant data can be fully utilized to improve the positioning accuracy.

[0064] Experiment 1

[0065] In the LOS environment, the noise was set to a mean of 0 and a standard deviation of 20 cm. Each coordinate value was calculated 1000 times. The data measured in Matlab is shown in the table below. The mean is 0 and the standard deviation is 0.2 m.

[0066] Table 1 Coordinate Data Table

[0067]

[0068] Based on the simulation results above, under the same standard deviation environment, by changing the position of the label under test, the RMSE is stable and the positioning accuracy is high.

[0069] Experiment 2

[0070] By setting different standard deviations: 0.1, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.75, 0.8, 1.0, and fixing the position of the label to be tested (1.2, 2.0, 4.8), the RMSE values ​​of the Chan algorithm, the trilateration algorithm, and the algorithm proposed in this paper are compared. Statistics are as follows: Figure 2 As shown. According to Figure 2As a result, the method of the present invention is superior to the Chan algorithm and the trilateration algorithm in terms of positioning accuracy.

[0071] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A high-precision indoor three-dimensional positioning method based on projection mode, characterized in that, Includes the following steps: 1) Set up four positioning base stations and the location tag to be measured. The coordinates of the four base stations are BS1(x1,y1,z1), BS2(x2,y2,z2), BS3(x3,y3,z3), and BS4(x4,y4,z4); the coordinates of the location tag are MS(x,y,z). 2) Using positioning measurement equipment, obtain the distance from the location tag to each positioning base station, and record the measured distances as R1, R2, R3, and R4; 3) Using projection, all positioning base stations are projected onto a plane with a height equal to the height z of the location tag to be measured. The coordinates of the projection points of the four positioning base stations become BS1'(x1,y1,z), BS2'(x2,y2,z), BS3'(x3,y3,z), and BS4'(x4,y4,z). The distances from the projection points to the location tag are denoted as r1, r2, r3, and r4. 4) Calculate the distances from the tag under test to the projection points of the four positioning base stations; ， （2） 5) Solve the system of equations in step 4) to obtain the coordinates of the label at the location to be measured; According to equation (2), we can obtain that Combining equation (3) and equation (1), we can obtain （4） Equation (4) can be simplified to: AX=B(5) in: A= ,X= , B= We can obtain: X= (6) At this point, the x and y coordinates of the location label to be measured are both represented by z, that is, (7) Substitution + Based on prior information, the correct z value is obtained, and the MS (x,y,z) coordinates of the location label to be tested can be obtained.

2. The high-precision indoor three-dimensional positioning method based on projection mode according to claim 1, characterized in that, In step 2), the distance from the tag under test to each positioning base station is obtained through TOA, TOF, and RSSI positioning methods.

3. The high-precision indoor three-dimensional positioning method based on projection mode according to claim 1, characterized in that, In step 2), the distance from the tag to each positioning base station is obtained using the TDOA positioning method.

4. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the high-precision indoor three-dimensional positioning method based on projection mode as described in any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a high-precision indoor three-dimensional positioning method based on projection mode as described in any one of claims 1 to 3.

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