A visible light communication-assisted single-source perspective circular line indoor positioning method

Abstract

This invention discloses a single-source perspective circular line indoor positioning method assisted by visible light communication, belonging to the field of communication networks. First, a single circular LED is used as the transmitter. By modulating the LED's flashing frequency and combining it with the LED's coordinates, four coordinate systems are established. The receiver uses a mobile phone camera to simultaneously capture visible light information, LED and ceiling outline information, and extracts visual information of the circle and parallel lines. Then, based on spatial geometry theorems, the normal vector of the ceiling under the CCS is calculated. Next, by establishing an auxiliary coordinate system, the coordinates of the LED center and the four vertices of the ceiling under the CCS are solved using the circular visual information. Finally, based on single-view geometry theory, the position and orientation of the receiver are estimated according to the transformation relationship between WCS and CCS and the known positioning information. This invention can achieve high-precision 3D positioning in single-source positioning scenarios without the need for auxiliary equipment such as IMUs. Simulation results show that the sample point positioning error is within 10cm.

Description

Technical Field

[0001] This invention belongs to the field of communication networks and relates to a single-source perspective circular line indoor positioning method assisted by visible light communication. Background Technology

[0002] In recent years, the emergence of various mobile terminal devices has provided people with comprehensive and convenient services in their daily lives. Among them, location-based services (LBS) play a fundamental role in many fields such as the Internet of Things.

[0003] Positioning technology is one of the core technologies of LBS (Location-Based Services). Full-coverage, high-precision seamless indoor and outdoor positioning technology plays a crucial role in people's future lives. Outdoor positioning typically only requires meter-level accuracy, while indoor positioning requires decimeter or even centimeter-level accuracy, and the indoor environment is more complex and variable than the outdoor environment.

[0004] Currently, the mainstream indoor positioning technologies include Bluetooth, Wi-Fi, Ultra Wideband (UWB), and Radio Frequency Identification (RFID). However, these technologies all suffer from the problem of balancing positioning cost and positioning performance. For example, Bluetooth and Wi-Fi technologies have low construction costs, but their positioning accuracy is only at the meter level, which is difficult to meet the needs of high-precision indoor positioning. UWB technology can achieve positioning accuracy at the centimeter level, but it requires specialized equipment for deployment, resulting in high construction costs.

[0005] Compared to the technologies mentioned above, LED-based VLP technology can reuse existing lighting equipment while offering advantages in high precision and low cost. Furthermore, VLP technology is highly portable; the receiver only requires a photodiode (PD) or image sensor (IS) to operate on existing mobile devices. In recent years, with the widespread adoption of smartphones and the development of microelectromechanical systems (MEMS) technology, VLP technology based on high-resolution complementary metal-oxide-semiconductor (CMOS) cameras built into smartphones has gradually become a new research focus. Existing research typically relies on the unique rolling shutter effect of CMOS cameras to transmit visible light information, combined with various positioning algorithms for localization.

[0006] IS-based localization algorithms are generally referred to as image sensor methods. These methods utilize the geometric relationship between the position of an LED in the world coordinate system and its projection on the image plane for localization. However, these methods usually require multiple LEDs. For example, [1] proposed a perspective tri-point localization algorithm based on the received signal strength, which requires the use of three LEDs to achieve 3D localization. [2] proposed an IS-based VLP algorithm for localization using two LEDs. It describes the horizontal distance between the LED and the receiver through dense SIFT image features, and then achieves localization through the positional relationship between the two LEDs on the image. [3] also proposed a dual-LED localization algorithm based on machine learning.

[0007] However, the sparse light source density and the FOV of the receiver in real-world scenarios often limit the application of these multi-light source-based positioning algorithms. In addition, although [4][5] proposed algorithms for positioning using a single light source, they require auxiliary equipment such as inertial measurement units (IMUs) to achieve positioning, which to some extent also limits the practicality of visible light positioning.

[0008] Therefore, it is necessary to study an indoor positioning method that is suitable for single-light source scenarios and does not require other auxiliary equipment, so as to overcome the scene limitations of visible light positioning.

[0009] [1]Bai L,Yang Y,Feng C,et al.Received signal strength assistedperspective-three-point algorithm for indoor visible light positioning[J].Optics Express,2020,28(19):28045-28059.

[0010] [2]Zhang B, Zhang M, Ghassemlooy Z, et al.A Visible Light PositioningSystem with aNovel Positioning Algorithm and Two LEDs[C] / / 2019 24thOptoElectronics and Communications Conference(OECC)and 2019InternationalConference on Photonics in Switching and Computing(PSC).2019.

[0011] [3]Guan W, Zhang X, Wu Y, et al. High precision indoor visible lightpositioning algorithm based on double LEDs using CMOS image sensor [J]. AppliedSciences, 2019, 9(6): 1238.

[0012] [4]Zhang R, Zhong WD, Kemao Q, et al.A single LED positioning systembased on circle projection[J]. IEEE Photonics Journal, 2017, 9(4):1-9.

[0013] [5]Cheng H, Xiao C, Ji Y, et al.A Single LED Visible Light PositioningSystem Based on Geometric Features and CMOS Camera[J]. IEEE PhotonicsTechnology Letters, 2020, 32(17):1097-1100. Summary of the Invention

[0014] To address the aforementioned problems, this invention proposes a single-source perspective circular line indoor positioning method assisted by visible light communication. This method utilizes a single light source as the transmitter and common linear features found on ceilings as auxiliary geometric information. Furthermore, a monocular camera captures visible light information along with visual information about circles and lines to estimate the pose of the receiver. This invention achieves high-precision 3D positioning in single-light source scenarios without the need for auxiliary equipment, and it is not limited by receiver pose, effectively improving the practicality of visible light positioning.

[0015] The visible light communication-assisted single-source perspective circular line indoor positioning method comprises the following specific steps:

[0016] Step 1: Set up an indoor positioning scene. The transmitting end is a single circular LED placed on the ceiling, and the receiving end is a camera. The camera and the circular LED form an elliptical cone Γ, and the camera and the ceiling form a square pyramid Γ1.

[0017] In the elliptical cone Γ, the circular LED light fixture is the base, and the optical center of the camera is the vertex;

[0018] In the quadrangular pyramid Γ1, the rectangular ceiling is the base, and the optical center of the camera is the vertex.

[0019] Step 2: By modulating the LED flashing frequency, and combining the LED's world coordinates, LED radius, and ceiling side length, establish four coordinate systems for the visible light positioning system model;

[0020] The four coordinate systems include: World Coordinate System (WCS), Camera Coordinate System (CCS), Image Coordinate System (ICS), and Pixel Coordinate System (PCS). The four coordinate systems are independent of each other, and the horizontal coordinates of CCS, ICS, and PCS are parallel to each other, as are their vertical coordinates.

[0021] Step 3: The camera captures LED light and forms an image. Image processing techniques are used to extract visual information about the circle and parallel lines. Combined with the normal vector of the square pyramid Γ1, the normal vector of the ceiling in the CCS coordinate system is calculated.

[0022] Specifically, the receiving end uses the mobile phone camera to simultaneously capture visible light information, LED and ceiling outline information, and uses image processing technology to extract visual information of circles and parallel lines from the outline information.

[0023] Then, based on the extracted visual information of parallel lines, the normal vectors of the four sides of the square pyramid Γ1 are obtained, and are respectively represented as follows:

[0024] Define the direction vectors of the intersection lines of the lateral surface and the base of the square pyramid as follows: The normal vector of the bottom surface, i.e., the ceiling plane, is According to the theorems of spatial geometry:

[0025]

[0026]

[0027]

[0028]

[0029] Where × represents the vector product. Due to the property that opposite sides of a rectangular ceiling are parallel, we obtain...

[0030]

[0031] Where · represents the dot product.

[0032] Finally, the normalized normal vector of the ceiling plane in the camera coordinate system is calculated. Where s1, s2, and s3 are constants;

[0033] Step 4: Establish an auxiliary coordinate system ACS and use circular visual information to solve for the coordinates of the LED center and the four vertices of the ceiling in the CCS coordinate system;

[0034] Specifically:

[0035] First, the projection Π of the LED light fixture onto the image plane e Using projection Π e Rotating the major axis of the elliptical cone Γ, we obtain two circular sections Π1 and Π2. We then select the section whose normal vector is perpendicular to the elliptical cone. The normal vector with the smallest deviation is used as the normal vector of the LED lamp, thereby determining the correct circular cross-section Π. i* The plane equation is expressed as

[0036] in The coefficient b is a constant that determines the orientation of the normal vector of the circular cross section.

[0037] Then, combine the LED lights and the circular cross-section Π i* Projecting them onto the ACS coordinate system respectively, we obtain the projected lines AB and A′B′;

[0038] The length of AB is equal to the diameter of the LED light, 2R; O a It is the origin of the ACS coordinate system, and the straight line O a A' and O a The equation for B′ is λ1 and λ3 are constants.

[0039] Solving the two equations simultaneously, we obtain the coordinates A′ and B′ of A′ and B′ in ACS. Then, based on the similar triangle relationship, we obtain the equation of line AB. in

[0040] Finally, based on the coordinates of the LED center projection point g in the ACS Obtain the straight line O a The equation for g is O a g intersects AB at the center G of the LED fixture. Therefore, by solving the equations of the two lines simultaneously, we can obtain the coordinates G of the LED center in the CCS. c Similarly, we can obtain the four vertices P of the ceiling. i The CCS coordinates of (i∈{1,2,3,4}) are

[0041] Step 5: Based on the normal vector of the ceiling plane Based on the correspondence between WCS and CCS, and combined with the side length of the ceiling, calculate the X value of WCS relative to CCS. c Y c and Z cEuler angles of the axis θ and ψ are then used to calculate the rotation matrix of WCS relative to CCS.

[0042] First, based on the principles of single-view geometry, the normal vector of the ceiling in the WCS and CCS is determined. and The conversion is performed, and it is represented as:

[0043]

[0044] The solution can be obtained by solving the above system of equations. and θ.

[0045] Then, based on the distance D between any two adjacent vertices of the ceiling, we can obtain:

[0046]

[0047] in,

[0048] a1, a2, a3, b1, b2, b3 are all related to Constants related to θ That is, the coordinates of the first vertex of the ceiling. That is, the coordinates of the fourth vertex of the ceiling. ψ can be obtained by solving the above formula.

[0049] Obtain Euler angles After determining θ and ψ, the rotation matrix of WCS relative to CCS along the three axes is further calculated.

[0050] Represented as:

[0051]

[0052]

[0053]

[0054] The rotation matrix of WCS relative to CCS is expressed as:

[0055]

[0056] Step 6: Based on the coordinates of the LED center G in WCS and CCS, and combined with the rotation matrix... Calculate the location of the receiver in the WCS Complete the receiver pose estimation.

[0057]

[0058] Among them, G w The WCS coordinates of the LED center G are given by G. c These are the CCS coordinates of the LED center G.

[0059] The advantages of this invention are:

[0060] 1) A single-source perspective circular line indoor positioning method assisted by visible light communication uses a single circular light source as the transmitter, which is more suitable for sparse light source scenarios and effectively improves the practicality of the system.

[0061] 2) A visible light communication-assisted single-source perspective circular line indoor positioning method, which uses a common monocular camera as the receiver, gets rid of the complex channel model, and is lower in cost and more portable than the positioning method based on photoelectric sensor (PD).

[0062] 3) A single-source perspective circular line indoor positioning method assisted by visible light communication, which does not require the assistance of other devices and has no restrictions on the attitude of the receiving end, while obtaining more accurate position and attitude estimation. Attached Figure Description

[0063] Figure 1 This is a flowchart of a single-source perspective circular line indoor positioning method assisted by visible light communication according to the present invention;

[0064] Figure 2 This is a typical indoor positioning scenario built by the present invention, including a transmitting end and a receiving end;

[0065] Figure 3 This is a system model established by the transmitting end and the receiving end in the indoor positioning scenario of this invention;

[0066] Figure 4 The elliptical conical surface formed by the receiving end of this invention and the ceiling is located in the auxiliary coordinate system X. a O a Z a A projection on a plane;

[0067] Figure 5 This is a graph showing the cumulative error distribution of the present invention as the LED radius changes;

[0068] Figure 6 This is a graph showing the cumulative error distribution of the present invention as the side length of the ceiling changes;

[0069] Figure 7 This is a comparison chart of the cumulative error distribution curves of this invention and other positioning algorithms;

[0070] Figure 8 This is a comparison chart of the positioning errors of the present invention and other positioning algorithms within a certain noise range;

[0071] Figure 9 This is a comparison chart of the positioning errors of the present invention and other positioning algorithms as the LED radius changes; Detailed Implementation

[0072] To enable those skilled in the art to more clearly understand and implement the present invention, the technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific examples.

[0073] This invention proposes a single-source perspective circle and line indoor positioning method assisted by visible light communication (V-PCL). First, a single circular LED is used as the transmitter. By modulating the LED's flashing frequency, the world coordinates of each LED, along with its radius and the side length of the ceiling, are broadcast, establishing multiple spatial and planar coordinate systems and providing the transformation relationships between them. Then, the receiver uses a mobile phone camera to simultaneously capture visible light information, LED and ceiling outline information, and extracts the visual information of circles and parallel lines from the outline information. Based on spatial geometry theorems, the normal vector of the ceiling plane in the camera coordinate system is calculated using two sets of parallel lines. Then, by establishing an auxiliary coordinate system, the coordinates of the LED center and the four vertices of the ceiling in the camera coordinate system are solved using the circular visual information. Finally, based on single-view geometry theory, the position and orientation of the receiver are estimated according to the transformation relationship between the world coordinate system and the camera coordinate system, as well as the known positioning information. This invention can achieve high-precision 3D positioning in single-light source positioning scenarios without the need for auxiliary equipment such as IMU. Simulation results show that V-PCL can keep the positioning error of more than 95% of sample points within 10cm.

[0074] like Figure 1 As shown, the specific steps of the present invention are as follows:

[0075] Step 1: Set up an indoor positioning scene. The transmitting end is a single circular LED placed on the ceiling, and the receiving end is a camera. The camera and the circular LED form an elliptical cone Γ, which in turn forms a square pyramid Γ1 with the ceiling.

[0076] In the indoor positioning scenario of the transmitting and receiving ends, each LED broadcasts its world coordinates and radius, ceiling side length, and other positioning information based on VLC broadcast; the receiving end uses a standard pinhole camera. The receiving end and the circular LED light fixture form an elliptical cone Γ, which in turn forms a rectangular pyramid Γ1 with the ceiling where the light fixture is located.

[0077] Step 2: By modulating the LED flashing frequency, and combining the LED's world coordinates, LED radius, and ceiling side length, establish four coordinate systems for the visible light positioning system model;

[0078] The four coordinate systems include: World Coordinate System (WCS), Camera Coordinate System (CCS), Image Coordinate System (ICS), and Pixel Coordinate System (PCS). The four coordinate systems are independent of each other, and the horizontal coordinates of CCS, ICS, and PCS are parallel to each other, as are their vertical coordinates.

[0079] Step 3: The camera captures LED light and forms an image. Image processing techniques are used to extract visual information about the circle and parallel lines. Combined with the normal vector of the square pyramid Γ1, the normal vector of the ceiling in the CCS coordinate system is calculated.

[0080] Specifically, the receiving end uses the mobile phone camera to simultaneously capture visible light information, LED and ceiling outline information, and uses image processing technology to extract visual information of circles and parallel lines from the outline information.

[0081] Then, based on the extracted visual information of parallel lines, the normal vectors of the four sides of the square pyramid Γ1 are obtained, and are respectively represented as follows: Define the direction vectors of the intersection lines of the lateral surface and the base of the square pyramid as follows: The normal vector of the bottom surface, i.e., the ceiling plane, is According to the theorems of spatial geometry:

[0082]

[0083]

[0084]

[0085]

[0086] Where × represents the vector product. Due to the property that opposite sides of a rectangular ceiling are parallel, we obtain...

[0087]

[0088] Where · represents the dot product. The normalized normal vector of the ceiling plane in the camera coordinate system can be calculated from the above formula. in, make Π base For Oc The square pyramid O at the vertex c -The bottom surface P1P2P3P4 in P1P2P3P4; For the bottom Π base The equation coefficients.

[0089] Step 4: Establish an auxiliary coordinate system ACS and use circular visual information to solve for the coordinates of the LED center and the four vertices of the ceiling in the camera coordinate system;

[0090] Specifically:

[0091] First, establish an auxiliary coordinate system ACS, and the projection Π of the LED lights onto the image plane. e , around the projection Π e The major axis is rotated to cut the elliptical cone Γ, resulting in two circular sections Π1 and Π2, with corresponding normal vectors. and By solving

[0092]

[0093] Choose one of the normal vectors The normal vector with the smallest deviation is used as the normal vector of the LED lamp, thereby determining the correct circular cross-section Π parallel to the ceiling plane. i* The plane equation:

[0094]

[0095] in The coefficient b is a constant that determines the orientation of the normal vector of the circular cross section.

[0096] Then, combine the LED lights and the circular cross-section Π i* Projected onto the X coordinate system of the ACS a O a Z a On the plane, the projected lines are AB and A′B′, respectively. The length of AB is equal to the diameter of the LED, 2R. The equation of A′B′ is denoted as...

[0097] O a It is the origin of ACS, and the straight line O a A' and O a The equation for B′ is λ1 and λ3 are constants.

[0098] Solving the two equations simultaneously, we can find the coordinates A′ and B′ of A′ and B′ in ACS. Then, based on the relationship between similar triangles, we can find the equation of line AB. in

[0099] Finally, based on the coordinates of the LED center projection point g in the ACS Obtain the straight line O a The equation for g is O a g intersects AB at the center G of the LED lamp. Therefore, by solving the equations of the two lines simultaneously, we can find the coordinates G of the center G of the LED lamp in the CCS. c .

[0100] Similarly, we can obtain the four vertices P of the ceiling. i The CCS coordinates of (i∈{1,2,3,4}) are

[0101] Step 5: Based on the normal vector of the ceiling plane Based on the correspondence between WCS and CCS, and combined with the side length of the ceiling, calculate the X value of WCS relative to CCS. c Y c and Z c Euler angles of the axis θ and ψ are then used to calculate the rotation matrix of WCS relative to CCS.

[0102] First, based on the principles of single-view geometry, the normal vector of the ceiling in the WCS and CCS is determined. and Using rotation matrix Perform the transformation, the transformation relationship is as follows: Further expressed as:

[0103]

[0104] The solution can be obtained by solving the above system of equations. and θ.

[0105] Then, according to the spatial geometry theorem, the four vertices P of the suspended ceiling i WCS coordinates of (i∈{1,2,3,4}) With CCS coordinates The following conditions must be met:

[0106]

[0107] Among them, a i ,b i ,c i (i∈{1,2,3}) is related to Constants related to θ These are the WCS coordinates of the receiving end. Although they are unknown, they can be eliminated by subtracting the coordinates.

[0108] Based on the distance D between any two adjacent vertices of the ceiling, substituting the coordinates of adjacent vertices P1 and P4 of the ceiling into the above formula yields:

[0109]

[0110] in, a1, a2, a3, b1, b2, b3 are all related to Constants related to θ That is That is ψ can be obtained by solving the above formula.

[0111] Obtain Euler angles After determining θ and ψ, the rotation matrix of WCS relative to CCS along the three axes is further calculated.

[0112] Represented as:

[0113]

[0114]

[0115]

[0116] The rotation matrix of WCS relative to CCS is expressed as:

[0117]

[0118] Step 6: Based on the coordinates of the LED center G in WCS and CCS, and combined with the rotation matrix... Calculate the location of the receiver in the WCS Complete the receiver pose estimation.

[0119]

[0120] Among them, G w The WCS coordinates of the LED center G are given by G. c These are the CCS coordinates of the LED center G.

[0121] Example:

[0122] In indoor positioning scenarios, such as Figure 2 As shown, the transmitting end is a circular LED light source, fixed on a rectangular ceiling, providing lighting and communication functions. By modulating the LED flashing frequency, it broadcasts information such as the world coordinates of each LED, the LED radius, and the side length of the ceiling. The receiving end is a general-purpose camera, which can also be replaced by the camera built into mobile devices such as mobile phones and tablets.

[0123] Step 1: Construct a visible light positioning system model;

[0124] like Figure 3 As shown, the receiver and the circular LED light fixture form an elliptical cone Γ, with the center of the light fixture at G and the radius at R. Point g is the projection of the center point G of the LED light fixture onto the image plane. The ceiling has a length of D, a width of W, and four vertices at P. i (i∈{1,2,3,4)}, the projection of the vertex onto the image plane is p. i (i∈{1,2,3,4}), the marker point M is used to distinguish the four vertices, vector Always pointing to P1, point m is the projection of M onto the image plane.

[0125] The receiver and the ceiling where the light fixture is located form a rectangular pyramid O. c -P1P2P3P4, where O c The vertex is P1P2P3P4, and the base is Π. base Let P i P j (i,j∈{1,2,3,4},i≠j) are two adjacent vertices of the ceiling. Π ij For P i P j and O c The side profile formed by L ij Indicated by P i P j For the edge at vertex l ij It is its projection onto the image plane.

[0126] vector Parallel to X w positive direction of axis and vector Parallel to Y w positive axis direction and G w R, D, and W are known and can be transmitted to the receiving end via VLC.

[0127] Step 2: Establish four coordinate systems, including the world coordinate system O. w -X w Y w Z w Camera coordinate system O c -X c Y c Z c Image coordinate system O i -X i Y i and pixel coordinate system O p -U pV p Among them, O c To O i The distance is the focal length f of the optical camera, and the distance is any point in the CCS. Its projection on the image plane The following transformation relationship exists:

[0128]

[0129] Any point in ICS It can also be converted into points in PCS.

[0130]

[0131] Where, d x and d y These represent the physical size of a single pixel. O i Coordinates in PCS;

[0132] Step 3: The transmitting end broadcasts positioning information, and the receiving end captures visible light and visual information and forms an image. The unit normal vector of the ceiling plane in the CCS is calculated using the two sets of parallel lines characteristic of the rectangular ceiling.

[0133] In ICS, the projected line l ij The two endpoints p i p j From the image coordinates, we obtain l ij The point-normal form of the line is: x i cosφ ij +y i sinφ ij =ρ ij ;

[0134] Where (x) i ,y i ) T It is the projected line l ij The image coordinates of a point on the graph, φ ij For the projected line l ij With Y i The angle between the positive axes, ρ ij For O i To the projected line l ij The distance;

[0135] Then the projected line l ij There are two points above and Its CCS coordinates are and

[0136] because and O c All are on the plane Π ij Up, so Π ij The plane equation in CCS can be expressed as:

[0137]

[0138] in, Then Π ij The normal vector is represented as

[0139] In CCS, the plane Π base The general form of the equation is:

[0140]

[0141] Due to the plane Π ij and Π base The normal vectors are all perpendicular to L. ij Therefore, L can be obtained. ij The direction vector is:

[0142]

[0143] Where × represents the vector product. Since L 12 ∥L 34 L 41 ∥L 23 ,So

[0144] Solving (5) yields the unit normal vector of the ceiling plane in the CCS. make So It can be represented as:

[0145]

[0146] in

[0147] Step 4: Establish an auxiliary coordinate system and determine the circular cross-section parallel to the ceiling plane under the auxiliary coordinate system;

[0148] The elliptical projection Π of the circular LED outline on the image plane e The general expression is:

[0149] A(x i ) 2 +Bx i y i +C(y i ) 2 +Dx i+Ey i +1=0 (7)

[0150] A, B, C, D, and E are the coefficients of the equation, which can generally be obtained by extracting points on the LED contour through image processing and performing curve fitting.

[0151] lateral surface of an elliptic cone in CCS c The general expression is:

[0152] Af 2 (x c ) 2 +Bf 2 x c y c +Cf 2 (y c ) 2 +Dfx c z c +Efy c z c +(z c )2=0 (8)

[0153] It can also be represented as a quadratic form:

[0154] [x c y c z c ]Q[x c y c z c ] T =0 (9)

[0155] in

[0156]

[0157] Q is a real symmetric matrix, but not a diagonal matrix, which makes Γ c The equations are quite complex; therefore, an auxiliary coordinate system (ACS) is established to simplify the lateral surface Γ of the elliptic cone. c The expression, the origin O of ACS a With O c Coincident, and one of its coordinate axes coincides with Γ c Let the central symmetry axes coincide, and let the rotation matrix from ACS to CCS be... It is equal to the matrix composed of the eigenvectors of Q.

[0158] By diagonalizing Q, the lateral surface Γ of the elliptic cone is obtained. c The standard quadratic curve is in the form of:

[0159] λ1(xa ) 2 +λ2(y a ) 2 +λ3(z a ) 2 =0 (11)

[0160] Where λ1, λ2, and λ3 are the three eigenvalues ​​of Q, λ i The values ​​of (i = 1, 2, 3) determine the spatial relationship between the elliptical cone Γ and the ACS coordinate axes. When λ3 < 0 < λ2 < λ1, the central axis of Γ and the Z-axis of ACS are related. a Coincident axis, elliptical projection Π e The major axis is parallel to the Y-axis of the ACS. a The minor axis is parallel to the X axis. a Axis. When λ i When (i=1,2,3) satisfies other relationships, there is also a similar relationship between Γ and the ACS coordinate axes, which can be solved in a similar way.

[0161] The imaging plane is rotated around Π e When the major axis of an elliptical cone Γ is rotated and cuts it, there must exist two circular sections, denoted as Π1 and Π2, whose normal vectors in the ACS are respectively... and To eliminate incorrect circular cross-sections, by... Will and Convert to CCS to obtain and Then, and and Comparison, through solving

[0162]

[0163] Define the circular cross-section parallel to the ceiling plane as Π. i* (i*∈{1,2}), the equation is:

[0164]

[0165] in, b is a constant.

[0166] Next, based on the geometric projection theorem, we calculate the LED center G and the four vertices P of the ceiling. i The CCS coordinates of the elliptic cone Γ (i∈{1,2,3,4}). a O a Z a Projection on a plane Figure 4As shown, line segment AB is the projection of the LED light fixture, and the length of AB is equal to the LED diameter 2R. Line segment A′B′ is the circular cross-section Π. i* In X a O a Z a Projection onto a plane. Line segments I1 and I2 are projections onto the image plane. Line O a A and O a The equation for B is expressed as:

[0167]

[0168] By solving equations (13) and (14) simultaneously, we can find the coordinates A′ and B′ of A′ and B′ in ACS. According to the similarity relationship of triangles, the equation of line AB is:

[0169] z a =k ceil x a +b ceil (15)

[0170] in, In addition, line O a The equation for g is expressed as:

[0171]

[0172] in, and This represents the coordinates of point g in the ACS, which can be obtained through coordinate transformation. From Figure 4 As can be seen in O a The extension of g intersects AB at point G. Therefore, by combining equations (15) and (16), we can obtain the coordinates G of point G in ACS. a Then through Obtain the coordinates G of point G in CCS. c Similarly, the four vertices P of the ceiling are... i The coordinates of (i∈{1,2,3,4}) in CCS It can also be obtained by solving a series of equations.

[0173] Step 5: Based on the transformation relationship of the ceiling plane normal vector under WCS and CCS and the side length information of the ceiling, calculate the attitude of the receiver, i.e., the rotation matrix.

[0174] WCS relative to CCS X c Y c Z c The rotation angles of the axes are respectively used as Let ψ∈(-π,π] represent the area around X, then WCS relative to CCS. c Yc Z c The rotation matrix of the axis can be represented as:

[0175]

[0176]

[0177]

[0178] Rotation matrix of WCS relative to CCS It can be represented as

[0179]

[0180] Based on the principle of single-view geometry, the normal vector of the ceiling plane in WCS and CCS. and The conversion relationship is This can be further expressed as:

[0181]

[0182] The solution can be obtained by solving the system of equations (21). and θ. For ease of mathematical analysis, we define:

[0183]

[0184] The four vertices P of the suspended ceiling i WCS coordinates of (i∈{1,2,3,4}) With CCS coordinates Between satisfy

[0185]

[0186] in, The WCS coordinates of the receiving end The result has already been obtained in step four, therefore, from Parallel to X w positive axis direction and have to:

[0187]

[0188] Substituting (23) into (24), we have:

[0189]

[0190] in, ψ can be solved using (25). The known... Substitute θ and ψ together into (20), The solution was then found.

[0191] Step 6: Calculate the position of the receiver in the WCS based on the correspondence between the WCS and CCS coordinates of the LED center G.

[0192] Based on the single-view geometry theorem, the transformation relationship between CCS and WCS can be expressed as follows: Among them, P w and P c These represent the coordinates of the same beacon in the WCS and CCS, respectively. and Let G represent the attitude and position of the receiver in the WCS, respectively, and let G be the known WCS coordinates of the LED center G. w Step 4: Obtain the CCS coordinates of G. c The plate, the rotation matrix obtained in step five. Substituting the above formula into the surface, we get:

[0193]

[0194] At this point, the receiver pose estimation is complete.

[0195] The cumulative distribution function (CDF) of the indoor positioning method proposed in this invention, which varies with the LED radius and the side length of the ceiling, is as follows: Figure 5 and Figure 6 As shown, from Figure 5 It can be seen that as the LED radius increases from 7cm to 17cm, the positioning error gradually decreases. When the LED radius is 17cm, the positioning error of more than 99% of the sample points is less than 10cm. Figure 6 As can be seen, when the side length of the ceiling increases from 25cm to 40cm, the positioning error gradually decreases, indicating that increasing the LED radius or increasing the side length of the ceiling can significantly improve the positioning accuracy.

[0196] A comparison between the indoor positioning method proposed in this invention and the IMU-assisted visible light positioning algorithm (V-IMU) and the traditional PnP algorithm. Figure 7 , Figure 8 and Figure 9 As shown;

[0197] The cumulative distribution function of the positioning error of the three algorithms is as follows: Figure 7 As shown in the figure, V-PCL has better positioning accuracy than the other two algorithms. More than 95% of its positioning errors are less than 12cm, while the P3P algorithm has about 66% of its positioning errors within 12cm, and the V-IMU algorithm can only achieve about 11% of its positioning errors within 12cm.

[0198] Comparison of the effects of image noise on the localization errors of the three algorithms (e.g., [example]). Figure 8 As shown, image noise is modeled as Gaussian white noise with zero expectation and a standard deviation of 0 to 4 pixels. The figure shows that the average localization error of all three algorithms increases with increasing image noise. When the image noise is 0 pixels, the average localization error of both V-PCL and P3P algorithms is 0, indicating that their localization error is entirely caused by image noise. However, as the noise increases from 0 pixels to 4 pixels, the average localization error of this invention only increases by 10 cm, compared to 29 cm for the V-IMU algorithm and 80 cm for the P3P algorithm. This invention exhibits higher stability.

[0199] Comparison of the impact of LED radius on the positioning error of the three algorithms Figure 9 As shown, it can be observed that the accuracy of all three algorithms increases with the LED radius. Among them, V-PCL consistently maintains the highest accuracy, with a maximum average positioning error not exceeding 10cm. The error of the P3P algorithm rapidly decreases from 120cm to 11cm, while the error of the V-IMU algorithm decreases from 55cm to 33cm.

[0200] In summary, this invention utilizes common circular and line features found in real-world scenarios and, based on single-view geometry principles, achieves high-precision positioning under conditions of a single light source and no auxiliary equipment. Compared to other positioning methods, this invention offers higher positioning accuracy, is less affected by environmental noise and positioning equipment, and exhibits greater stability. Simulation results show that the positioning error for over 95% of sample points is less than 10 cm.

[0201] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A single-source perspective circular line indoor positioning method assisted by visible light communication, characterized in that, The specific steps are as follows: First, an indoor positioning scenario is set up, with a single circular LED as the transmitter, placed on the ceiling, and a camera as the receiver; the camera and the circular LED form an elliptical cone Γ, and the camera and the ceiling form a square pyramid Γ1. By modulating the LED flashing frequency and combining the LED's world coordinates, LED radius, and ceiling side length, four coordinate systems are established for the visible light positioning system model: WCS, CCS, ICS, and PCS. Then, the camera captures LED light and forms an image. Image processing techniques are used to extract visual information about circles and parallel lines. Combined with the normal vector of the square pyramid Γ1, the normal vector of the ceiling in the CCS coordinate system is calculated. At the same time, an auxiliary coordinate system ACS is established, and the circular visual information is used to solve the coordinates of the LED center and the four vertices of the ceiling in the CCS coordinate system; Next, based on the normal vector of the ceiling plane Based on the correspondence between WCS and CCS, and combined with the side length of the ceiling, calculate the X value of WCS relative to CCS. c Y c and Z c Euler angles of the axis θ and ψ are then used to calculate the rotation matrix of WCS relative to CCS. Specifically: First, based on the principles of single-view geometry, the normal vector of the ceiling in the WCS and CCS is determined. and The conversion is performed, and it is represented as: Where s1, s2, and s3 are constants; the solution can be obtained by solving the above system of equations. and θ; Then, based on the distance D between any two adjacent vertices of the ceiling, we can obtain: in, a1, a2, a3, b1, b2, b3 are all related to Constants related to θ That is, the coordinates of the first vertex of the ceiling. That is, the coordinates of the fourth vertex of the ceiling. ψ can be obtained by solving the above formula; Obtain Euler angles After determining θ and ψ, the rotation matrix of WCS relative to CCS along the three axes is further calculated. Represented as: The rotation matrix of WCS relative to CCS is then expressed as: Finally, based on the coordinates of the LED center G under WCS and CCS, combined with the rotation matrix... Calculate the location of the receiver in the WCS Complete receiver pose estimation: Among them, G w The WCS coordinates of the LED center G are given by G. c These are the CCS coordinates of the LED center G.

2. The visible light communication-assisted single-source perspective circular line indoor positioning method as described in claim 1, characterized in that, In the elliptical cone Γ, the circular LED light fixture is the base and the optical center of the camera is the vertex; in the square pyramid Γ1, the rectangular ceiling is the base and the optical center of the camera is the vertex.

3. The visible light communication-assisted single-source perspective circular line indoor positioning method as described in claim 1, characterized in that, The four coordinate systems include: World Coordinate System (WCS), Camera Coordinate System (CCS), Image Coordinate System (ICS), and Pixel Coordinate System (PCS); the four coordinate systems are independent of each other, and the horizontal coordinates of CCS, ICS, and PCS are parallel to each other, as are their vertical coordinates.

4. The visible light communication-assisted single-source perspective circular line indoor positioning method as described in claim 1, characterized in that, The calculation of the normal vector of the ceiling in the CCS coordinate system Specifically: First, the receiving end uses the mobile phone camera to simultaneously capture visible light information, LED and ceiling outline information, and uses image processing technology to extract visual information of circles and parallel lines from the outline information. Then, based on the extracted visual information of parallel lines, the normal vectors of the four sides of the square pyramid Γ1 are obtained, and are respectively represented as follows: Define the direction vectors of the intersection lines of the lateral surface and the base of the square pyramid as follows: The normal vector of the bottom surface, i.e., the ceiling plane, is According to the theorems of spatial geometry: Where × represents the vector product; due to the property that opposite sides of a rectangular ceiling are parallel, we get: Where · represents the dot product; Finally, the normalized normal vector of the ceiling plane in the camera coordinate system is calculated.

5. The visible light communication-assisted single-source perspective circular line indoor positioning method as described in claim 1, characterized in that, The method utilizes circular visual information to solve for the coordinates of the LED center and the four vertices of the ceiling in the CCS coordinate system; Specifically: First, the projection Π of the LED light fixture onto the image plane e Using projection Π e Rotating the major axis of the elliptical cone Γ, we obtain two circular sections Π1 and Π2. We then select the section whose normal vector is perpendicular to the elliptical cone. The normal vector with the smallest deviation is used as the normal vector of the LED lamp, thereby determining the correct circular cross-section Π. i* The plane equation is expressed as in b is a constant and is the coefficient that determines the orientation of the normal vector of the circular cross section. Then, combine the LED lights and the circular cross-section Π i* Projecting them onto the ACS coordinate system respectively, we obtain the projected lines AB and A′B′; The length of AB is equal to the diameter of the LED light, 2R; O a It is the origin of the ACS coordinate system, and the straight line O a A' and O a The equation for B′ is λ1 and λ3 are constants; Solving the two equations simultaneously, we obtain the coordinates A′ and B′ of A′ and B′ in ACS. Then, based on the similar triangle relationship, we obtain the equation of line AB. in Finally, based on the coordinates of the LED center projection point g in the ACS Obtain the straight line O a The equation for g is O a g intersects AB at the center G of the LED fixture. Therefore, by solving the equations of the two lines simultaneously, we can obtain the coordinates G of the LED center in the CCS. c Similarly, we can obtain the four vertices P of the ceiling. i The CCS coordinates of (i∈{1,2,3,4}) are

Images