A MULTI-RECEIVING-POINT GEOMETRICAL CENTER LOCATING SYSTEM AND METHOD FOR VISIBLE LIGHT COMMUNICATION

Abstract

It discloses a precise locating method of utilizing indoor visible light communication system, which belongs to the field of visible light communication; arranging any number of light emitting diode (LED) lamps indoors, setting the signal transmission power of each LED lamp to be the same and fixing the absolute location of each LED lamp, the terminal required for locating is equipped with several receiving devices, whose relative positions are known, then a position coordinate of the terminal can be obtained by determining the geometric center position of this set of receiving devices through calculating the measured light signal power of the receiving devices on the terminal.

Claims

1. A multi-receiving-point geometrical center locating system and method for visible light communication, characterized by comprising steps of: 1) arranging several LED lamps with same light transmission power as an optical signal transmitter on the ceiling indoor, configuring the terminal required for locating with several light receiving devices as a signal receiver, the several light receiving devices is arranged as a regular polygon with the geometrical center point of the terminal being its center, the location relation of the light receiving devices relative to the terminal is known: ${\begin{matrix} x_{R_{i}} = x + r .Math. .Math. \cos (δ + \frac{2 .Math. π}{N} .Math. (i - 1)) \\ y_{R_{i}} = x + r .Math. .Math. \sin (δ + \frac{2 .Math. π}{N} .Math. (i - 1)) \end{matrix} .Math. i = 1, 2, .Math. .Math., N$ and the sum number of the LED lamps and the light receiving devices arranged is greater than or equal to 4; wherein x.sub.R.sub.i, y.sub.R.sub.i (i=1, 2, . . . , N) are horizontal axis and vertical axis of the light receiving devices within a two-dimensional plane respectively, N is the number of the lighting devices; x,y are horizontal axis and vertical axis of the terminal geometrical center within a two-dimensional plane; r is the distance from the center of the polygon to each vertex; establishing a polar coordinate with the center of the polygon being the polar point, and setting any one of the light receiving devices as a first light receiving device with δ being a polar coordinate angle of the first light receiving device; 2) measuring the optical signal power received by each light receiving device to get a linear distance d from each LED lamp to each light receiving device, measuring a vertical distance h from the plane where the LED lamps are located to the plane where the light receiving devices are located, and then a horizontal distance D between each LED lamp and each light receiving device is obtained according to the principle of right triangle; 3) obtaining the horizontal distance D from each LED lamp to each light receiving device through the coordinate relation of the LED lamps and the light receiving devices within the two-dimensional plane, and listing all the equation of the horizontal distance D obtained by coordinate relation equaling with the horizontal distance D obtained by step 2); wherein the horizontal axis and the vertical axis of the LED lamps within the two-dimensional plane are x.sub.T.sub.a, y.sub.T.sub.a (a=1, 2 . . . , M) and the number of the LED lamps is M; establishing a linear equation with terminal coordinates according to the location relation in step 1) and all the equations of the horizontal distance D, expressing the linear equation as a matrix, and then the horizontal axis and vertical axis for the geometrical center point of the light receiving devices, i.e. the coordinate for the geometrical center point of terminal required for locating, are obtained by calculating according to classical estimation method.

2. The multi-receiving-point geometrical center locating system and method for visible light communication according to claim 1, characterized in that step 2) comprises the steps of: M LED lamps are arranged on the ceiling provided indoors: the first LED lamp T.sub.1 (x.sub.T.sub.1, y.sub.T.sub.1), the second LED lamp T.sub.2 (x.sub.T.sub.2, y.sub.T.sub.2), . . . the Mth LED lamp T.sub.M (x.sub.T.sub.M, y.sub.T.sub.M), wherein x.sub.T.sub.a, y.sub.T.sub.a (a=1, 2, . . . , M) are the horizontal axis and vertical axis of the LED lamps within the two-dimensional plane respectively; N light receiving devices are arranged on the terminal, the light receiving devices being expressed as: the first light receiving device R.sub.1 (x.sub.R.sub.1, y.sub.R.sub.1), the second light receiving device R.sub.2 (x.sub.R.sub.2, y.sub.R.sub.2), . . . the Nth light receiving device R.sub.N (x.sub.R.sub.N, y.sub.R.sub.N); x.sub.R.sub.i, y.sub.R.sub.i (i=1, 2, . . . , N); 21) measuring the optical signal power Pr received by each light receiving device to get M×N received optical signal power; 22) obtaining a linear distance from each LED lamp to each light receiving device according to formula
Pr=H(0)*Ptd; wherein H(0) is channel DC gain, $H (0) = \frac{n + 1}{2 .Math. π .Math. .Math. d^{2}} .Math. A .Math. .Math. \cos^{n} (φ) .Math. \cos (θ),$ n is Lambert model order; A represents the area of light received by the surface of each light receiving device, φ the radiation angle of the LED lamps, θ is the incident angle of the light receiving devices; Pt is the signal transmission power of the LED lamps; 23) the horizontal distance D from each LED lamp to the light receiving devices can be obtained by D=√{square root over (d.sup.2−h.sup.2)}.

3. The multi-receiving-point geometrical center locating system and method for visible light communication according to claim 2, characterized in that step 3) comprises the steps of: 31) obtaining M×N horizontal distance D through the coordinate relation of the LED lamps and the light receiving devices, and listing an equation of M×N horizontal distance D obtained by coordinate relation equaling with M×N horizontal distance D obtained by step 2); establishing a linear equation with terminal coordinates according to the location relation in step 1) and all the equations of M×N horizontal distance D to obtain MN−1 equations, expressing MN−1 equations as a matrix:
Ax=b wherein X is the location coordinate of the terminal; $A = {[\begin{matrix} \frac{x_{T_{1}} - x_{T_{2}}}{r} & \frac{y_{T_{1}} - y_{T_{2}}}{r} \\ .Math. \\ \frac{x_{T_{1}} - x_{T_{m}}}{r} & \frac{y_{T_{1}} - y_{T_{m}}}{r} \\ \cos (δ + \frac{2 .Math. π}{N}) - \cos .Math. .Math. δ & \sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N}) - \cos .Math. .Math. δ + \frac{x_{T_{1}} - x_{T_{m}}}{r} & \sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ + \frac{y_{T_{1}} - y_{T_{m}}}{r} \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ & \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ + \frac{x_{T_{1}} - x_{T_{m}}}{r} & \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ + \frac{y_{T_{1}} - y_{T_{m}}}{r} \end{matrix}]}_{(MN - 1) \times 2}$ $b = {[\begin{matrix} \frac{R_{R_{1} .Math. T_{2}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{2}}^{2} + y_{T_{1}}^{2} - y_{T_{2}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} - x_{T_{2}}) .Math. \cos .Math. .Math. δ - (y_{T_{1}} - y_{T_{2}}) .Math. \sin .Math. .Math. δ \\ .Math. \\ \frac{R_{R_{1} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} - x_{T_{M}}) .Math. \cos .Math. .Math. δ - (y_{T_{1}} - y_{T_{M}}) .Math. \sin .Math. .Math. δ \\ \frac{R_{R_{2} .Math. T_{1}}^{2} - R_{R_{1} .Math. T_{1}}^{2}}{2 .Math. .Math. r} - X_{T_{1}} (\cos (δ + \frac{2 .Math. .Math. π}{N}) - \cos .Math. .Math. δ) - y_{T_{1}} (\sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ) \\ .Math. \\ \frac{R_{R_{2} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} .Math. \cos .Math. .Math. δ - x_{T_{M}} .Math. \cos (δ + \frac{2 .Math. π}{N})) - (y_{T_{1}} .Math. \sin .Math. .Math. δ - y_{T_{M}} .Math. \sin (δ + \frac{2 .Math. π}{N})) \\ .Math. \\ \frac{R_{R_{2} .Math. T_{1}}^{2} - R_{R_{1} .Math. T_{1}}^{2}}{2 .Math. .Math. r} - X_{T_{1}} * (\cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ) - y_{T_{1}} (\sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ) \\ .Math. \\ \frac{R_{R_{N} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} .Math. \cos .Math. .Math. δ - x_{T_{M}} .Math. \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1))) - (y_{T_{1}} .Math. \sin .Math. .Math. δ - y_{T_{M}} .Math. \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1))) \end{matrix}]}_{(MN - 1) \times 1}$ 32) estimating the geometrical center location of the light receiving devices through utilizing least squares criterion according to the formula below:
x=(A.sup.TA).sup.−1A.sup.Tb wherein (.).sup.T is the transpose of the matrix, and (.).sup.−1 is the matrix inversion operator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a block diagram of the method and system of the present invention;

[0014] FIG. 2 is a general lay out diagram of the method and system of the present invention;

[0015] FIG. 3 is a layout diagram of the present invention with 1 LED lamp and 3 receiving devices;

[0016] FIG. 4 is a histogram of locating error obtained when signal-to-noise ratio is 10 dB under the layout in FIG. 3;

[0017] FIG. 5 is a relation view between average locating error and signal-to-noise under the layout in FIG. 3.

DETAILED DESCRIPTION

[0018] In conjunction with the drawings, the present invention will be further illustrated.

[0019] In FIGS. 1 to 5, the present invention discloses a multi-receiving-point geometrical center locating system and method for visible light communication, in an indoor visible light communication system, several LED lamps and one terminal carrying with several receiving devices are arranged for locating the terminal target. A multi-receiving-point geometrical center locating system and method for visible light communication comprises steps of:

[0020] 1) Arranging several LED lamps with same light transmission power as an optical signal transmitter, configuring the terminal required for locating with several light receiving devices as a signal receiver, the several light receiving devices is arranged as a regular polygon with the geometrical center point of the terminal being its center, the location relationship of the light receiving devices relative to the terminal is known:

[00004] ${\begin{matrix} x_{R_{i}} = x + r .Math. .Math. \cos (δ + \frac{2 .Math. π}{N} .Math. (i - 1)) \\ y_{R_{i}} = x + r .Math. .Math. \sin (δ + \frac{2 .Math. π}{N} .Math. (i - 1)) \end{matrix} .Math. i = 1, 2, .Math. .Math., N$

and the sum number of the arranged LED lamps and the light receiving devices arranged is greater than or equal to 4, beneficial to locating estimation, wherein x.sub.R.sub.i, y.sub.R.sub.i (i=1, 2, . . . , N) are horizontal axis and vertical axis of the light receiving devices within a two-dimensional plane respectively, N is the number of the lighting devices; x, y are horizontal axis and vertical axis of the terminal geometrical center within a two-dimensional plane; r is the distance from the center of the polygon to each vertex; establishing a polar coordinate with the center of the polygon being the polar point, and setting any one of the light receiving devices as a first light receiving device with δ being a polar coordinate angle of the first light receiving device;
2) Measuring the optical signal power received by each light receiving device to get a linear distance d from each LED lamp to each light receiving device, measuring a vertical distance h from the plane where the LED lamps are located to the plane where the light receiving devices are located, and then a horizontal distance D between each LED lamp and each light receiving device is obtained according to the principle of right triangle;
3) Obtaining the horizontal distance D from each LED lamp to each light receiving device through the coordinate relation of the LED lamps and the light receiving devices within the two-dimensional plane, and listing all the equation of the horizontal distance D obtained by coordinate relation equaling with the horizontal distance D obtained by step 2); wherein the horizontal axis and the vertical axis of the LED lamps within the two-dimensional plane are x.sub.T.sub.a, y.sub.T.sub.a (a=1, 2 . . . , M) and the number of the LED lamps is M; establishing a linear equation with terminal coordinates according to the location relation in step 1) and all the equations of the horizontal distance D, expressing the linear equation as a matrix, and then the horizontal axis and vertical axis for the geometrical center point of the light receiving devices, i.e. the coordinate for the geometrical center point of terminal required for locating, are obtained by calculating according to classical estimation method.

[0021] Further, the step 2) comprises steps of:

M LED lamps are arranged on the ceiling provided indoors: the first LED lamp T.sub.1 (x.sub.T.sub.1, y.sub.T.sub.1), the second LED lamp T.sub.2 (x.sub.T.sub.2, y.sub.T.sub.2), . . . the Mth LED lamp T.sub.M (x.sub.T.sub.M, y.sub.T.sub.M), wherein x.sub.T.sub.a, y.sub.T.sub.a (a=1, 2, . . . , M) are the horizontal axis and vertical axis of the LED lamps within the two-dimensional plane respectively; N light receiving devices arranged on the terminal, the light receiving devices being expressed as: the first light receiving device R.sub.1 (x.sub.R.sub.1, y.sub.R.sub.1), the second light receiving device R.sub.2 (x.sub.R.sub.2, y.sub.R.sub.2), . . . the Nth light receiving device R.sub.N (x.sub.R.sub.N, y.sub.R.sub.N); x.sub.R.sub.i, y.sub.R.sub.i (i=1, 2, . . . , N); [0022] 21) Measuring the optical signal power Pr received by each light receiving device to get M×N received optical signal power;
22) Obtaining a linear distance from each LED lamp to each light receiving device according to a formula

Pr=H(0)*Ptd;

wherein) H(0) is channel DC gain,

[00005] $H (0) = \frac{n + 1}{2 .Math. π .Math. .Math. d^{2}} .Math. A .Math. .Math. \cos^{n} (φ) .Math. \cos (θ),$

n is Lambert model order; A represents the area of light received by the surface of each light receiving device, φ the radiation angle of the LED lamps, θ is the incident angle of the light receiving devices; Pt is the signal transmission power of the LED lamps;
23) The horizontal distance D from each LED lamp to the light receiving devices can be obtained by D=√{square root over (d.sup.2−h.sup.2)}.

[0023] Further, the step 3) comprises steps of:

31) Obtaining M×N horizontal distance D through the coordinate relation of the LED lamps and the light receiving devices, and listing an equation of M×N horizontal distance D obtained by coordinate relation equaling with M×N horizontal distance D obtained by step 2); establishing a linear equation with terminal coordinates according to the location relation in step 1) and all the equations of M×N horizontal distance D to obtain MN−1 equations, expressing MN−1 equations as a matrix:

Ax=b

wherein x is the location coordinate of the terminal;

[00006] $A = {[\begin{matrix} \frac{x_{T_{1}} - x_{T_{2}}}{r} & \frac{y_{T_{1}} - y_{T_{2}}}{r} \\ .Math. \\ \frac{x_{T_{1}} - x_{T_{m}}}{r} & \frac{y_{T_{1}} - y_{T_{m}}}{r} \\ \cos (δ + \frac{2 .Math. π}{N}) - \cos .Math. .Math. δ & \sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N}) - \cos .Math. .Math. δ + \frac{x_{T_{1}} - x_{T_{m}}}{r} & \sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ + \frac{y_{T_{1}} - y_{T_{m}}}{r} \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ & \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ \\ .Math. \\ \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ + \frac{x_{T_{1}} - x_{T_{m}}}{r} & \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ + \frac{y_{T_{1}} - y_{T_{m}}}{r} \end{matrix}]}_{(MN - 1) \times 2}$ $b = {[\begin{matrix} \frac{R_{R_{1} .Math. T_{2}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{2}}^{2} + y_{T_{1}}^{2} - y_{T_{2}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} - x_{T_{2}}) .Math. \cos .Math. .Math. δ - (y_{T_{1}} - y_{T_{2}}) .Math. \sin .Math. .Math. δ \\ .Math. \\ \frac{R_{R_{1} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} - x_{T_{M}}) .Math. \cos .Math. .Math. δ - (y_{T_{1}} - y_{T_{M}}) .Math. \sin .Math. .Math. δ \\ \frac{R_{R_{2} .Math. T_{1}}^{2} - R_{R_{1} .Math. T_{1}}^{2}}{2 .Math. .Math. r} - X_{T_{1}} (\cos (δ + \frac{2 .Math. .Math. π}{N}) - \cos .Math. .Math. δ) - y_{T_{1}} (\sin (δ + \frac{2 .Math. π}{N}) - \sin .Math. .Math. δ) \\ .Math. \\ \frac{R_{R_{2} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} .Math. \cos .Math. .Math. δ - x_{T_{M}} .Math. \cos (δ + \frac{2 .Math. π}{N})) - (y_{T_{1}} .Math. \sin .Math. .Math. δ - y_{T_{M}} .Math. \sin (δ + \frac{2 .Math. π}{N})) \\ .Math. \\ \frac{R_{R_{2} .Math. T_{1}}^{2} - R_{R_{1} .Math. T_{1}}^{2}}{2 .Math. .Math. r} - X_{T_{1}} * (\cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \cos .Math. .Math. δ) - y_{T_{1}} (\sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1)) - \sin .Math. .Math. δ) \\ .Math. \\ \frac{R_{R_{N} .Math. T_{M}}^{2} - R_{R_{1} .Math. T_{1}}^{2} + x_{T_{1}}^{2} - x_{T_{M}}^{2} + y_{T_{1}}^{2} - y_{T_{M}}^{2}}{2 .Math. .Math. r} - (x_{T_{1}} .Math. \cos .Math. .Math. δ - x_{T_{M}} .Math. \cos (δ + \frac{2 .Math. π}{N} .Math. (N - 1))) - (y_{T_{1}} .Math. \sin .Math. .Math. δ - y_{T_{M}} .Math. \sin (δ + \frac{2 .Math. π}{N} .Math. (N - 1))) \end{matrix}]}_{(MN - 1) \times 1}$

32) Estimating the geometrical center location of the light receiving devices through utilizing least squares criterion according to the formula below:

x=(A.sup.TA).sup.−A.sup.Tb [0024] wherein (.).sup.T is the transpose of the matrix, and (.).sup.−1 is the matrix inversion operator.

[0025] The invention will be further described through simulation with reference to FIG. 3;

[0026] Simulation parameters are: arranging a LED lamp on the ceiling in a room sized by 6 m×6 m×2 m (length, width, height); establishing a Cartesian coordinate system with any one corner in the room being the origin: the coordinate (x.sub.T.sub.1, y.sub.T.sub.1) of LED mapped to the Cartesian coordinate is (3,3); the vertical distance h from the plane where the LED lamps located to the plane where the light receiving devices located is 2 m; the signal transmission power signal Pt of the LED lamp is 1 W; setting one terminal to be carrying with three light receiving devices B, C and E, as the relative location relation of the light receiving devices is known, arranging the three light receiving devices to be a positive triangle with the locating terminal target being the center, and the positive triangle is connected with a circle, the distance r form the center point of the positive triangle to each vertex is 0.2 m; the area A of three light receivers are all 1.0 square centimeters; polar coordinate δ:45 degree.

[0027] The relation of three light receiving devices relative to the terminal is:

[00007] ${\begin{matrix} x_{R_{i}} = x + 0.2 .Math. .Math. \cos (45 .Math. ° + \frac{2 .Math. π}{3} .Math. (i - 1)) \\ y_{R_{i}} = x + 0.2 .Math. .Math. \sin (45 .Math. ° + \frac{2 .Math. π}{3} .Math. (i - 1)) \end{matrix} .Math. i = 1, 2, .Math. .Math., 3$

[0028] Wherein x.sub.R.sub.i, y.sub.R.sub.i (i=1,2,3) are the horizontal axis and vertical axis of the light receiving devices in the two-dimensional plane respectively; x,y are the horizontal axis and vertical axis of the terminal geometrical center in the two-dimensional plane

1) Measuring the optical signal power Pr received by each light receiving device to get 1×3 received optical signal power;
2) Obtaining the linear distance d from LED lamps to each light receiving devices according to the formula Pr=H(0)*Pt; wherein H(0) is channel DC gain,

[00008] $H (0) = \frac{n + 1}{2 .Math. π .Math. .Math. d^{2}} .Math. A .Math. .Math. \cos^{n} (φ) .Math. \cos (θ),$

n is Lambert model order; A represents the area of light received by the surface of each light receiving device, φ the radiation angle of the LED lamps, θ is the incident angle of the light receiving devices;
3) The horizontal distance D from each LED lamp to the receiving devices can be obtained by D=√{square root over (d.sup.2−h.sup.2)}. And the horizontal distance from the three devices B, C, E can be expressed as D.sub.B, D.sub.C, D.sub.E.

[0029] Further, the step 3) comprises steps of:

31) Obtaining 1×3 horizontal distance D through the coordinate relation of the LED lamps and the light receiving devices, and listing an equation of 1×3 horizontal distance D obtained by coordinate relation equaling with 1×3 horizontal distance D obtained by step 2); establishing a linear equation with terminal coordinates according to the location relation in step 1) and the equations of 1×3 horizontal distance D to obtain MN−1=2 equations, expressing these two equations as a matrix:

Ax=b

wherein x is the location coordinate of the terminal;

[00009] $A = 2 [\begin{matrix} 0.2 .Math. (\cos (45 .Math. ° + \frac{2 .Math. π}{3}) .Math. x - \cos .Math. .Math. 45 .Math. °) & 0.2 .Math. (\sin (45 .Math. ° + \frac{2 .Math. π}{3}) .Math. x - \sin .Math. .Math. 45 .Math. °) \\ 0.2 .Math. (\cos (45 .Math. ° + \frac{4 .Math. π}{3}) .Math. x - \cos .Math. .Math. 45 .Math. °) & 0.2 .Math. (\sin (45 .Math. ° + \frac{2 .Math. π}{3}) .Math. x - \sin .Math. .Math. 45 .Math. °) \end{matrix}]$ $b = [\begin{matrix} D_{C}^{2} - D_{B}^{2} - 2 .Math. x_{1} * 0.2 .Math. (\cos .Math. .Math. 45 .Math. ° - \cos (45 .Math. ° + \frac{2 .Math. π}{3}) .Math. x) - 2 .Math. y_{1} * 0.2 .Math. (\sin .Math. .Math. 45 .Math. ° - \sin (45 .Math. ° + \frac{2 .Math. π}{3})) \\ D_{E}^{2} - D_{B}^{2} - 2 .Math. x_{1} * 0.2 .Math. (\cos .Math. .Math. 45 .Math. ° - \cos (45 .Math. ° + \frac{4 .Math. π}{3}) .Math. x) - 2 .Math. y_{1} * 0.2 .Math. (\sin .Math. .Math. 45 .Math. ° - \sin (45 .Math. ° + \frac{4 .Math. π}{3})) \end{matrix}$

[0030] According to:

x=(A.sup.TA).sup.−1A.sup.Tb

the target location can be obtained through solving the matrix equation.

[0031] The average locating error in the whole room from simulation is 4.03 cm, the maximum locating error is 12.58 cm.

[0032] FIG. 4-5 illustrates performance simulation results through utilizing the locating method of the present invention with reference to FIG. 3.

[0033] FIG. 4 illustrates a histogram for the proportion of the locating error when in the range of 0-14 cm if signal-noise-ratio is 10 dB under the condition in FIG. 3, it is shown that the proportion of the locating error in the range of 3-4 cm is maximum.

[0034] FIG. 5 illustrates the relation between average locating error and the 0-30 dB signal-noise-ratio under the condition in FIG. 3. It is known that the higher the signal-noise-ratio, the less the average error.

[0035] The preferred embodiments of the present invention are only described above, it should be noted that: for those in the art, several improvements and ornaments that should be considered within the protection scope of the present invention can also be made without departing from the principle of the present invention.

A MULTI-RECEIVING-POINT GEOMETRICAL CENTER LOCATING SYSTEM AND METHOD FOR VISIBLE LIGHT COMMUNICATION

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Abstract

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Description