3D WIRELESS OPTICAL POSITIONING METHOD AND SYSTEM

Abstract

The present invention provides a 3D wireless optical positioning method and system, including the steps of: arranging two LED lamps on the ceiling to transmit optical information and provide illumination; arranging a receiver including two photodetectors in a receiving plane; calculating the distance between the LED lamps and the photodetectors respectively through the TOA (Time of Arrival) method; and finally determining the actual position and orientation angle of the receiver based on the geometrical relationship between the LED lamps and the photodetectors in the XYZ coordinate system, the two photodetectors having a distance determined as l therebetween and being situated in the same receiving plane, the receiver being situated below the two LED lamps, the range where the receiver is to be positioned being on any side of the plane consisting of the two LED lamps and the origin.

Claims

1. A 3D wireless optical positioning method comprising steps of: arranging LED lamps on a ceiling to transmit optical information and providing illumination and arranging a receiver on a receiving plane to receive the optical information, wherein the LED lamps include a first LED lamp and a second LED lamp with a coordinate of (x.sub.t1, y.sub.t1, z.sub.t1) and (x.sub.t2, y.sub.t2, z.sub.t2) respectively, a first photodetector and a second photodetector with a coordinate of ({circumflex over (x)}.sub.r1, ŷ.sub.r1, {circumflex over (z)}.sub.t1) and ({circumflex over (x)}.sub.r2, ŷ.sub.r2, {circumflex over (z)}.sub.r2) respectively are arranged on the receiver, a distance between the first photodetector and the second photodetector is defined as l, meanwhile the first photodetector and the second photodetector both face upwards on the receiving plane, a middle point between the first photodetector and the second photodetector defines an actual position of a receiving terminal to be predicted, and a direction from the first photodetector to the second photodetector defines an orientation of the receiving terminal, that is, an included angle between the line interconnecting the first photodetector and the second photodetector and the positive half of the X axis is a orientation angle η; through the Time of Arrival principle, measuring the time required for the optical signal to be transmitted from the first LED lamp and the second LED lamp to and received by the first photodetector and the second photodetector respectively, and multiplying the propagation time by the speed of light to calculate the distance d.sub.1 between the first LED lamp and the first photodetector, the distance d.sub.2 between the second LED lamp and the first photodetector, the distance d.sub.3 between the first LED lamp and the second photodetector and the distance d.sub.4 between the second LED lamp and the second photodetector; and obtaining the actual position and orientation angle of the receiver based on the geometrical relationship between the LED lamps and the receiver in the XYZ coordinate system, the first photodetector and the second photodetector having a distance determined as l therebetween and being situated in the same receiving plane, the receiver being situated below the first LED lamp and the second LED lamp, the range where the receiver is to be positioned being on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin.

2. The 3D wireless optical positioning method of claim 1, wherein the corresponding photodetector and LED lamp are in time synchronization in calculating the distances d.sub.1-d.sub.4.

3. The 3D wireless optical positioning method of claim 1, wherein the following equation set is obtained for the distances d.sub.1˜d.sub.4 in the XYZ coordinate system:
d.sub.1.sup.2=({circumflex over (x)}.sub.r1−x.sub.t1).sup.2+(ŷ.sub.r1−y.sub.t1).sup.2+({circumflex over (z)}.sub.r1−z.sub.t1).sup.2  (1)
d.sub.2.sup.2=({circumflex over (x)}.sub.r1−x.sub.t2).sup.2+(ŷ.sub.r1−y.sub.t2).sup.2+({circumflex over (z)}.sub.r1−z.sub.t2).sup.2  (2)
d.sub.3.sup.2=({circumflex over (x)}.sub.r2−x.sub.t1).sup.2+(ŷ.sub.r2−y.sub.t1).sup.2+({circumflex over (z)}.sub.r2−z.sub.t1).sup.2  (3)
d.sub.4.sup.2=({circumflex over (x)}.sub.r2−x.sub.t2).sup.2+(ŷ.sub.r2−y.sub.t2).sup.2+({circumflex over (z)}.sub.r2−z.sub.t2).sup.2  (4) meanwhile, supplementary equations are obtained as the first photodetector and the second photodetector have a distance determined as l therebetween and are situated in the same receiving plane:
l.sup.2=({circumflex over (x)}.sub.r2−{circumflex over (x)}.sub.r1).sup.2+(ŷ.sub.r2−ŷ.sub.r1).sup.2+({circumflex over (z)}.sub.r2−{circumflex over (z)}.sub.r1).sup.2  (5)
{circumflex over (z)}.sub.r2={circumflex over (z)}.sub.r1  (6) and given the known d.sub.1, d.sub.2, d.sub.3 and d.sub.4 and the formulas (5) and (6) and in combination with the fact that the receiver is situated below the first LED lamp and the second LED lamp and the range where the receiver is to be positioned is on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin, the actual position of the receiver (({circumflex over (x)}.sub.r1+{circumflex over (x)}.sub.r2)/2, (ŷ.sub.r1+ŷ.sub.r2)/2, ({circumflex over (z)}.sub.r1+{circumflex over (z)}.sub.r2)/2) and the orientation angle of the receiver are obtained through solution of: $\begin{array}{cc}\hat{\eta }=\mathrm{sign}\left({\hat{y}}_{r2}-{\hat{y}}_{r1}\right)\mathrm{arc}\cos \left[\frac{\left({\hat{x}}_{r2}-{\hat{x}}_{r1}\right)}{\sqrt{{\left({\hat{x}}_{r1}-{\hat{x}}_{r2}\right)}^2+{\left({\hat{y}}_{r1}-{\hat{y}}_{r2}\right)}^2}}\right].& \left(13\right)\end{array}$

4. The 3D wireless optical positioning method of claim 3, wherein the process of solving the actual position of the receiver (({circumflex over (x)}.sub.r1+{circumflex over (x)}.sub.r2)/2, (ŷ.sub.r1+ŷ.sub.r2)/2, ({circumflex over (z)}.sub.r1+{circumflex over (z)}.sub.r2)/2) and the orientation angle of the receiver specifically comprises steps of: S1: as the formulas (1) and (2) each represent on the physical sense a sphere, subtracting the formula (2) from the formula (1) to obtain an equation for the plane P1 where the two spheres intersect each other, the first photodetector being positioned on a circle where this plane intersects the sphere represented by the formula (1), this circle having a centre at K.sub.1, a coordinate of which being (a.sub.1, b.sub.1, c.sub.1), and a radius of R.sub.1; and likewise, subtracting the formula (4) from the formula (3) to obtain the equation for the plane P2 where the two spheres intersect each other, the second photodetector being positioned on a circle where this plane intersects the sphere represented by the formula (3), this circle having a centre at K.sub.2, a coordinate of which being (a.sub.2, b.sub.2, c.sub.2), and a radius of R.sub.2, a coordinate of the circle centre and a radius of the circle being represented by the formulas: $\begin{array}{cc}{K}_i\left(a_i,b_i,c_i\right)=\left(x_{t1}+\left(x_{t2}-x_{t1}\right)\frac{w_i}{L},y_{t1}+\left(y_{t2}-y_{t1}\right)\frac{w_i}{L},z_{t1}+\left(z_{t2}-z_{t1}\right)\frac{w_i}{L}\right),i=1,2.Math.& \left(7\right)\end{array}$ $\begin{array}{cc}\begin{array}{c}{R}_1=\sqrt{d_1^2-w_1^2}\\ R_2=\sqrt{d_3^2-w_2^2}\end{array}& \left(8\right)\end{array}$ where w.sub.i represents a distance between the first LED lamp and a plane P.sub.i (i=1, 2) where the two spheres intersect each other and L represents a distance between the first LED and the second LED lamp; S2: performing two coordinate system transformations, where in a first coordinate transformation, an XYZ coordinate system is transformed into an X′Y′Z′ coordinate system, the X′Y′Z′ coordinate system having a circle centre K.sub.1 as its origin of coordinate, a straight line K.sub.1 K.sub.2 as a new Z′ axis, an intersecting line of the circle K.sub.1 and the original XY plane as a new X′; and in the second coordinate transformation, a new X′Y′Z′ coordinate system is transformed into a cylindrical coordinate system, whereupon after the two coordinate transformations, the coordinates of the first photodetector and the second photodetector are changed into (R.sub.1, Φ.sub.1, 0) and (R.sub.2, Φ.sub.2, S) respectively, and meanwhile, in a cylindrical coordinate system, the formula (5) and the formula (6) are represented respectively as:
Φ.sub.1−Φ.sub.2=±arcos M  (9)
β(R.sub.2 sin Φ.sub.2−R.sub.1 sin Φ.sub.1)=−γS  (10) where M=(R.sub.1.sup.2+R.sub.2.sup.2+S.sup.2−l.sup.2)/(2R.sub.1R.sub.2), a distance between the two circle centres K.sub.1 and K.sub.2 is expressed as S=√{square root over (a.sup.2+b.sup.2+c.sup.2)}, β=−√{square root over ((a.sup.2+b.sup.2))}/S, γ=c/S, a=a.sub.2−a.sub.1, b=b.sub.2−b.sub.1, c=c.sub.2−c.sub.1; and S3: calculating Φ.sub.1 and Φ.sub.2 according to the formula (9) and the formula (10), then performing two inverse coordinate transformations to recover the coordinates of the first photodetector and the second photodetector in the XYZ coordinate system through the formulas (11) and (12):
({circumflex over (x)}.sub.r1,ŷ.sub.r1,{circumflex over (z)}.sub.r1)′=(e.sub.x,e.sub.y,e.sub.z)(R.sub.1 cos Φ.sub.1,R.sub.1 sin Φ.sub.1,0)′+(a.sub.1,b.sub.1,c.sub.1)′  (11)
({circumflex over (x)}.sub.r2,ŷ.sub.r2,{circumflex over (z)}.sub.r2)′=(e.sub.x,e.sub.y,e.sub.z)(R.sub.2 cos Φ.sub.2,R.sub.2 sin Φ.sub.2,S)′+(a.sub.2,b.sub.2,c.sub.2)′  (12) where e.sub.x=(b/√{square root over (a.sup.2+b.sup.2)}, −a/√{square root over (a.sup.2+b.sup.2)}, 0)′, e.sub.y=[ac/(S√{square root over ((a.sup.2+b.sup.2))}), bc/(S√{square root over ((a.sup.2+b.sup.2))}), −√{square root over ((a.sup.2+b.sup.2)}/S]′, e.sub.z=(a/S, b/S, c/S)′ are the orthogonal basis of the first coordinate transformation.

5. The 3D wireless optical positioning method of claim 4, wherein in the step S3, four sets of solution are obtained by solving Φ.sub.1 and Φ.sub.2, and accordingly, four sets of coordinates of the first photodetector and the second photodetector in the XYZ coordinate system are obtained through two inverse coordinate transformations, whereas the actual position includes only one set, and as the four sets of solution are spatially symmetrical with respect to the line interconnecting the first LED lamp and the second LED lamp, the real solution is obtained through determination based on the following conditions, including steps of: S4: excluding two sets of solution representing a position above the first LED lamp and the second LED lamp considering the fact that the position of the receiver is below the first LED lamp and the second LED lamp; S5: obtaining a single real solution out of the remaining two sets of solution by restricting the receiver in movement on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin; S6: obtaining the coordinate of the receiver as (({circumflex over (x)}.sub.r1+{circumflex over (x)}.sub.r2)/2, (ŷ.sub.r1+ŷ.sub.r2)/2, ({circumflex over (z)}.sub.r1+{circumflex over (z)}.sub.r2)/2) through the single set of solution, in which the orientation angle η of the receiver has a value expressed by the formula (13) as: $\begin{array}{cc}\hat{\eta }=\mathrm{sign}\left({\hat{y}}_{r2}-{\hat{y}}_{r1}\right)\mathrm{arc}\cos \left[\frac{\left({\hat{x}}_{r2}-{\hat{x}}_{r1}\right)}{\sqrt{{\left({\hat{x}}_{r1}-{\hat{x}}_{r2}\right)}^2+{\left({\hat{y}}_{r1}-{\hat{y}}_{r2}\right)}^2}}\right]& \left(13\right)\end{array}$ where sign is the sign function.

6. The 3D wireless optical positioning method of claim 1, wherein the number of the LED lamps is defined depending on the region where they are to be positioned.

7. A 3D wireless optical positioning system comprising: LED lamps including a first LED lamp and a second LED lamp with a coordinate of (x.sub.t1, y.sub.t1, z.sub.t1) and (x.sub.t2, y.sub.t2, z.sub.r2) respectively, arranged on the ceiling to transmit optical information and provide illumination; a receiver provided with a first photodetector and a second photodetector with a coordinate of ({circumflex over (x)}.sub.r1, ŷ.sub.r1, {circumflex over (z)}.sub.r1) and ({circumflex over (x)}.sub.r2, ŷ.sub.r2, {circumflex over (z)}.sub.r2) respectively, arranged on a receiving plane to receive the optical information; wherein a distance between the first photodetector and the second photodetector is defined as l, meanwhile the first photodetector and the second photodetector both face upwards on the receiving plane, a middle point between the first photodetector and the second photodetector defines an actual position of a receiving terminal to be predicted, and a direction from the first photodetector to the second photodetector defines an orientation of the receiving terminal, that is, an included angle between a line interconnecting the first photodetector and the second photodetector and the positive half of the X axis is a orientation angle η; through the Time of Arrival principle, the time required for the optical signal to be transmitted from the first LED lamp and the second LED lamp to and received by the first photodetector and the second photodetector respectively is measured, and the propagation time is multiplied by the speed of light to calculate a distance d.sub.1 between the first LED lamp and the first photodetector, a distance d.sub.2 between the second LED lamp and the first photodetector, a distance d.sub.3 between the first LED lamp and the second photodetector and a distance d.sub.4 between the second LED lamp and the second photodetector; and an actual position and orientation angle of the receiver are obtained based on a geometrical relationship between the LED lamps and the receiver in the XYZ coordinate system, the first photodetector and the second photodetector having a distance determined as l therebetween and being situated in the same receiving plane, the receiver being situated below the first LED lamp and the second LED lamp, the range where the receiver is to be positioned being on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin.

8. The 3D wireless optical positioning system of claim 7, wherein the first LED lamp and the second LED lamp and the first photodetector and the second photodetector have synchronized operation time.

9. The 3D wireless optical positioning system of claim 7, wherein a set of equations for the distances d.sub.1 to d.sub.4 in the XYZ coordinate system is obtained based on the geometrical relationship between the LED lamps and the receiver in the XYZ coordinate system:
d.sub.1.sup.2=({circumflex over (x)}.sub.r1−x.sub.t1).sup.2+(ŷ.sub.r1−y.sub.t1).sup.2+({circumflex over (z)}.sub.r1−z.sub.t1).sup.2  (1)
d.sub.2.sup.2=({circumflex over (x)}.sub.r1−x.sub.t2).sup.2+(ŷ.sub.r1−y.sub.t2).sup.2+({circumflex over (z)}.sub.r1−z.sub.t2).sup.2  (2)
d.sub.3.sup.2=({circumflex over (x)}.sub.r2−x.sub.t1).sup.2+(ŷ.sub.r2−y.sub.t1).sup.2+({circumflex over (z)}.sub.r2−z.sub.t1).sup.2  (3)
d.sub.4.sup.2=({circumflex over (x)}.sub.r2−x.sub.t2).sup.2+(ŷ.sub.r2−y.sub.t2).sup.2+({circumflex over (z)}.sub.r2−z.sub.t2).sup.2  (4), meanwhile, supplementary equations are obtained as the first photodetector and the second photodetector have a distance determined as l therebetween and are situated in the same receiving plane:
l.sup.2=({circumflex over (x)}.sub.r2−{circumflex over (x)}.sub.r1).sup.2+(ŷ.sub.r2−ŷ.sub.r1).sup.2+({circumflex over (z)}.sub.r2−{circumflex over (z)}.sub.r1).sup.2  (5)
{circumflex over (z)}.sub.r2={circumflex over (z)}.sub.r1  (6); and given the known d.sub.1, d.sub.2, d.sub.3 and d.sub.4 and the formulas (5) and (6) and in combination with the fact that the receiver is situated below the first LED lamp and the second LED lamp and the range where the receiver is to be positioned is on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin, the actual position of the receiver (({circumflex over (x)}.sub.r1+{circumflex over (x)}.sub.r2)/2, (ŷ.sub.r1+ŷ.sub.r2)/2, ({circumflex over (z)}.sub.r1+{circumflex over (z)}.sub.r2)/2) and the orientation angle of the receiver are obtained through solution of: $\begin{array}{cc}\hat{\eta }=\mathrm{sign}\left({\hat{y}}_{r2}-{\hat{y}}_{r1}\right)\mathrm{arc}\cos \left[\frac{\left({\hat{x}}_{r2}-{\hat{x}}_{r1}\right)}{\sqrt{{\left({\hat{x}}_{r1}-{\hat{x}}_{r2}\right)}^2+{\left({\hat{y}}_{r1}-{\hat{y}}_{r2}\right)}^2}}\right].& \left(13\right)\end{array}$

10. The 3D wireless optical positioning system of claim 9, wherein the first LED lamp, the second LED lamp, the first photodetector and the second photodetector are provided with a time synchronization device.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0041] FIG. 1 is a schematic structural view of a system according to the present invention;

[0042] FIG. 2 is a schematic view showing intersection of two spheres in the step S1 according to the present invention;

[0043] FIG. 3 is a schematic view showing coordinate transformations in the step S2 according to the present invention;

[0044] FIG. 4 is a schematic view of 3D positioning results according to an embodiment of the present invention; and

[0045] FIG. 5 is the diagram of an accumulated distribution function of the estimation error for the orientation angle according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] The invention will be further explained with reference to the following drawings and particular embodiments, so that those skilled in the art can better understand and implement the present invention. However, the listed embodiments should not be taken as limitation of the present invention.

[0047] Referring to FIGS. 1-3, an embodiment of the present invention provides a 3D wireless optical positioning method, including the following steps: [0048] arranging LED lamps on the ceiling to transmit optical information and providing illumination and arranging a receiver on a receiving plane to receive the optical information, in which the LED lamps include a first LED lamp and a second LED lamp with a coordinate of (x.sub.t1, y.sub.t1, z.sub.t1) and (x.sub.t2, y.sub.t2, z.sub.t2) respectively, a first photodetector and a second photodetector with a coordinate of ({circumflex over (x)}.sub.r1, ŷ.sub.r1, {circumflex over (z)}.sub.t1) and ({circumflex over (x)}.sub.r2, ŷ.sub.r2, {circumflex over (z)}.sub.r2) respectively are arranged on the receiver, the distance between the first photodetector and the second photodetector is defined as l, meanwhile the first photodetector and the second photodetector both face upwards on the receiving plane, the middle point between the first photodetector and the second photodetector defines the actual position of the receiving terminal to be predicted, and the direction from the first photodetector to the second photodetector defines the orientation of the receiving terminal, that is, the included angle between the line interconnecting the first photodetector and the second photodetector and the positive half of the X axis is the orientation angle η; [0049] through the TOA (Time of Arrival) principle, measuring the time required for the optical signal to be transmitted from the first LED lamp and the second LED lamp to and received by the first photodetector and the second photodetector respectively, and multiplying the propagation time by the speed of light to calculate the distance d.sub.1 between the first LED lamp and the first photodetector, the distance d.sub.2 between the second LED lamp and the first photodetector, the distance d.sub.3 between the first LED lamp and the second photodetector and the distance d.sub.4 between the second LED lamp and the second photodetector respectively; and [0050] obtaining the actual position and orientation angle of the receiver based on the geometrical relationship between the LED lamps and the receiver in the XYZ coordinate system, the first photodetector and the second photodetector having a distance determined as l therebetween and being situated in the same receiving plane, the receiver being situated below the first LED lamp and the second LED lamp, the range where the receiver is to be positioned being on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin.

[0051] Specifically, it is proposed that the system consists of two elements as a transmitter and a receiver. The transmitter includes two LED lamps installed on the ceiling, LED1 and LED2, with a coordinate of (x.sub.t1, y.sub.t1, z.sub.t1) and (x.sub.t2, y.sub.t2, z.sub.t2) respectively, that can provide illumination. The plane where the receiver is situated is the receiving plane. A pair of (two) photodetectors is installed on the receiver. The two photodetectors are PD1 and PD2 respectively, with a coordinate of ({circumflex over (x)}.sub.r1, ŷ.sub.r1, {circumflex over (z)}.sub.r1) and ({circumflex over (x)}.sub.r2, ŷ.sub.r2, {circumflex over (z)}.sub.r2) respectively, configured to receive the optical information transmitted from the light source. The distance between PD1 and PD2 is l, and PD1 and PD2 both face upwards. The middle point between PD1 and PD2 defines the actual position of the receiving terminal to be predicted. The direction from PD1 to PD2 defines the orientation of the receiving terminal. The included angle between the line interconnecting PD1 and PD2 and the positive half of the X axis is defined as the orientation angle η.

[0052] Positioning: through the TOA (Time of Arrival) principle, the time required for the optical signal to be transmitted from LED1 and LED2 to and received by PD1 and PD2 respectively is measured, and the propagation time is multiplied by the speed of light to calculate the distance d.sub.1 between LED1 and PD1, the distance d.sub.2 between LED2 and PD1, the distance d.sub.3 between LED1 and PD2 and the distance d.sub.4 between LED2 and PD2. The following set of equations is obtained:

d.sub.1.sup.2=({circumflex over (x)}.sub.r1−x.sub.t1).sup.2+(ŷ.sub.r1−y.sub.t1).sup.2+({circumflex over (z)}.sub.r1−z.sub.t1).sup.2  (1)

d.sub.2.sup.2=({circumflex over (x)}.sub.r1−x.sub.t2).sup.2+(ŷ.sub.r1−y.sub.t2).sup.2+({circumflex over (z)}.sub.r1−z.sub.t2).sup.2  (2)

d.sub.3.sup.2=({circumflex over (x)}.sub.r2−x.sub.t1).sup.2+(ŷ.sub.r2−y.sub.t1).sup.2+({circumflex over (z)}.sub.r2−z.sub.t1).sup.2  (3)

d.sub.4.sup.2=({circumflex over (x)}.sub.r2−x.sub.t2).sup.2+(ŷ.sub.r2−y.sub.t2).sup.2+({circumflex over (z)}.sub.r2−z.sub.t2).sup.2  (4)

[0053] Meanwhile, the following supplementary equations can be obtained as PD1 and PD2 have a distance determined as l therebetween and are situated in the same receiving plane:

l.sup.2=({circumflex over (x)}.sub.r2−{circumflex over (x)}.sub.r1).sup.2+(ŷ.sub.r2−ŷ.sub.r1).sup.2+({circumflex over (z)}.sub.r2−{circumflex over (z)}.sub.r1).sup.2  (5)

{circumflex over (z)}.sub.r2={circumflex over (z)}.sub.r1  (6)

[0054] The equation set including formulas (1)-(6) is solved by the following steps:

[0055] First step: as shown in FIG. 2, as the formulas (1) and (2) each represent on the physical sense a sphere, the formula (2) is subtracted from the formula (1) to obtain the equation for the plane P1 where the two spheres intersect each other, PD1 being positioned on the circle where this plane intersects the sphere represented by the formula (1), this circle having the centre at K.sub.1, the coordinate of which being (a.sub.1, b.sub.1, c.sub.1), and the radius of R.sub.1; and likewise, the formula (4) is subtracted from the formula (3) to obtain the equation for the plane P2 where the two spheres intersect each other, PD2 being positioned on the circle where this plane intersects the sphere represented by the formula (3), this circle having the centre at K.sub.2, the coordinate of which being (a.sub.2, b.sub.2, c.sub.2) and the radius of R.sub.2, the coordinate of the circle centre and the radius of the circle being represented by the formulas:

K.sub.i(a.sub.i,b.sub.i,c.sub.i)=(x.sub.t1+(x.sub.t2−x.sub.t1)w.sub.i/L, y.sub.t1+(y.sub.t2−y.sub.t1)w.sub.i/L, z.sub.t1+(z.sub.t2−z.sub.t1)w.sub.i/L), i=1,2 . . .   (7)

R.sub.1=√{square root over (d.sub.1.sup.2−w.sub.1.sup.2)}

R.sub.2=√{square root over (d.sub.3.sup.2−w.sub.2.sup.2)}   (8)

[0056] where w.sub.i represents the distance between LED1 and the plane P.sub.i (i=1, 2) where the two spheres intersect each other and L represents the distance between LED1 and LED2.

[0057] Second step: as shown in FIG. 3, two coordinate transformations are performed, where in the first coordinate transformation, an XYZ coordinate system is transformed into an X′Y′Z′ coordinate system, the X′Y′Z′ coordinate system having the circle centre K.sub.1 as its origin of coordinate, the straight line K.sub.1 K.sub.2 as the new Z′ axis, the intersecting line of the circle K.sub.1 and the original XY plane as the new X′ axis; and in the second coordinate transformation, the new X′Y′Z′ coordinate system is transformed into a cylindrical coordinate system, whereupon after the two coordinate transformations, the coordinates of PD1 and PD2 are changed into (R.sub.1, Φ.sub.1, 0) and (R.sub.2, Φ.sub.2, S) respectively, and meanwhile, in the cylindrical coordinate system, the formulas (5) and (6) are represented respectively as:

Φ.sub.1−Φ.sub.2=±arcos M  (9)

β(R.sub.2 sin Φ.sub.2−R.sub.1 sin Φ.sub.1)=−γS  (10)

[0058] where M=(R.sub.1.sup.2+R.sub.2.sup.2+S.sup.2−l.sup.2)/(2R.sub.1R.sub.2), the distance between the two circle centres K.sub.1 and K.sub.2 is expressed as S=√{square root over (a.sup.2+b.sup.2+c.sup.2)}, β=−√{square root over ((a.sup.2+b.sup.2))}/S, γ=c/S, a=a.sub.2−a.sub.1, b=b.sub.2−b.sub.1, c=c.sub.2−c.sub.1.

[0059] Third step: Φ.sub.1 and Φ.sub.2 are calculated according to the set of equations (9) and (10), then two inverse coordinate transformations are performed to recover the coordinates of PD1 and PD2 in the XYZ coordinate system through the formulas (11) and (12).

({circumflex over (x)}.sub.r1,ŷ.sub.r1,{circumflex over (z)}.sub.r1)′=(e.sub.x,e.sub.y,e.sub.z)(R.sub.1 cos Φ.sub.1,R.sub.1 sin Φ.sub.1,0)′+(a.sub.1,b.sub.1,c.sub.1)′  (11)

({circumflex over (x)}.sub.r2,ŷ.sub.r2,{circumflex over (z)}.sub.r2)′=(e.sub.x,e.sub.y,e.sub.z)(R.sub.2 cos Φ.sub.2,R.sub.2 sin Φ.sub.2,S)′+(a.sub.2,b.sub.2,c.sub.2)′  (12)

[0060] where

e.sub.x=(b/√{square root over (a.sup.2+b.sup.2)}, −a/√{square root over (a.sup.2+b.sup.2)}, 0)′, e.sub.y=[ac/(S√{square root over ((a.sup.2+b.sup.2))}), bc/(S√{square root over ((a.sup.2+b.sup.2))}), −√{square root over ((a.sup.2+b.sup.2)}/S]′, e.sub.z=(a/S, b/S, c/S)′ are the orthogonal basis of the first coordinate transformation.

[0061] Fourth step: in the step S3, four sets of solution are obtained by solving Φ.sub.1 and Φ.sub.2, and accordingly, four sets of coordinates of PD1 and PD2 in the XYZ coordinate system are obtained through two inverse coordinate transformations, whereas the actual position includes only one set. As the four sets of solution are spatially symmetrical with respect to the line interconnecting LED1 and LED2, the real solution can be obtained through determination based on the following conditions, including specifically the following steps: [0062] excluding two sets of solution representing a position above LED1 and LED2 considering the fact that the position of the receiver is definitely below LED1 and LED2 in practical applications; and [0063] obtaining the single real solution out of the remaining two sets of solution by restricting the receiver in movement only on any side of the plane consisting of LED1, LED2 and the origin. [0064] the coordinates of the receiver as (({circumflex over (x)}.sub.r1+{circumflex over (x)}.sub.r2)/2, (ŷ.sub.r1+ŷ.sub.r2)/2, ({circumflex over (z)}.sub.r1+{circumflex over (z)}.sub.r2)/2) are obtained through the single set of solution, in which the orientation angle η of the receiver has a value expressed by the formula (13) as:

[00004]$\begin{array}{cc}\hat{\eta }=\mathrm{sign}\left({\hat{y}}_{r2}-{\hat{y}}_{r1}\right)\mathrm{arc}\cos \left[\frac{\left({\hat{x}}_{r2}-{\hat{x}}_{r1}\right)}{\sqrt{{\left({\hat{x}}_{r1}-{\hat{x}}_{r2}\right)}^2+{\left({\hat{y}}_{r1}-{\hat{y}}_{r2}\right)}^2}}\right]& \left(13\right)\end{array}$

[0065] where sign is the sign function.

[0066] It is noted that, in the present invention, the range where the terminal is to be positioned is on any side of the plane consisting of LED1, LED2 and the origin.

[0067] According to the present invention, accurate 3D positioning and orientation of the terminal can be achieved. Only two LED lamps are used at the transmitting terminal to enable 3D positioning and orientation while providing illumination. A pair of (2 in total) photodetectors is installed on the terminal to receive signals. These two photodetectors are positioned at the same level in the same receiving plane and have a constant and known distance therebetween. According to the present invention, through the TOA (Time of Arrival) principle, the time required for the optical signal to be transmitted from LED1 and LED2 to and received by PD1 and PD2 respectively is measured and the propagation time is multiplied by the speed of light to calculate the distance d.sub.1 between LED1 and PD1, the distance d.sub.2 between LED2 and PD1, the distance d.sub.3 between LED1 and PD2 and the distance d.sub.4 between LED2 and PD2. Positioning is achieved by the calculation steps in the formulas (1) to (13) described above based on the geometrical relationship between the transmitter and the receiver.

[0068] The present invention further provides a 3D wireless optical positioning system, including:

[0069] LED lamps including a first LED lamp and a second LED lamp with a coordinate of (x.sub.t1, y.sub.t1, z.sub.t1) and (x.sub.t2, y.sub.t2, z.sub.t2) respectively, arranged on the ceiling to transmit optical information and provide illumination; [0070] a receiver provided with a first photodetector and a second photodetector with a coordinate of ({circumflex over (x)}.sub.r1, ŷ.sub.r1, {circumflex over (z)}.sub.r1) and ({circumflex over (x)}.sub.r2, ŷ.sub.r2, {circumflex over (z)}.sub.r2) respectively, arranged on a receiving plane to receive the optical information; [0071] in which the distance between the first photodetector and the second photodetector is defined as l, meanwhile the first photodetector and the second photodetector both face upwards on the receiving plane, the middle point between the first photodetector and the second photodetector defines the actual position of the receiving terminal to be predicted, and the direction from the first photodetector to the second photodetector defines the orientation of the receiving terminal, that is, the included angle between the line interconnecting the first photodetector and the second photodetector and the positive half of the X axis is the orientation angle η; [0072] through the TOA (Time of Arrival) principle, the time required for the optical signal to be transmitted from the first LED lamp and the second LED lamp to and received by the first photodetector and the second photodetector respectively is measured, and the propagation time is multiplied by the speed of light to calculate the distance d.sub.1 between the first LED lamp and the first photodetector, the distance d.sub.2 between the second LED lamp and the first photodetector, the distance d.sub.3 between the first LED lamp and the second photodetector and the distance d.sub.4 between the second LED lamp and the second photodetector; and [0073] the actual position and orientation angle of the receiver are obtained based on the geometrical relationship between the LED lamps and the receiver in the XYZ coordinate system, the first photodetector and the second photodetector having a distance determined as l therebetween and being situated in the same receiving plane, the range where the receiver is to be positioned being restricted to be on any side of the plane consisting of the first LED lamp, the second LED lamp and the origin and the range of the receiver being restricted to be below the first LED lamp and the second LED lamp.

EMBODIMENT

[0074] To evaluate the performance of the proposed 3D wireless optical positioning method and system, a specific indoor space scenario of a size of 3 m×5 m×3 m (length×width×height) is considered for positioning. The LED lamps are deployed on the ceiling. LED1 has a coordinate of (0, 1.5, 3) and LED2 has a coordinate of (0, 3.5, 3). The distance between the transmitting terminal and the receiving terminal is estimated by using the TOA method. Assuming that a random error Δd is present in distance estimation for d.sub.1, d.sub.2, d.sub.3 and d.sub.4 measured through TOA, and the individual random errors are independent and subject to normal distribution. The mobile terminal is positioned on the receiving plane and has a orientation angle (orientation) that is randomly distributed. Tests are conducted at various positions at an interval of 0.5 m, as shown by the cross line in FIG. 4. A photodetector PD1 and a photodetector PD2 are installed on the terminal and have a constant distance l therebetween of 0.2 m, and the estimation error Δd has a standard deviation of 0.025 m. As can be seen from the drawings, after the 3D positioning and orientation solution propose by the present invention is adopted, when the receiving plane is at a level of 0.5 m, the 3D positioning error is 9.5 cm and the orientation error is 10.2°; when the receiving plane is at a level of 1 m, the 3D positioning error is 9.1 cm and the orientation error is 7.8°; when the receiving plane is at a level of 1.5 m, the 3D positioning error is 9.0 cm and the orientation error is 10.4°; and three planes at different levels have an overall average 3D positioning error of 9.2 cm and an overall terminal orientation angle error of 9.5°.

[0075] FIG. 5 is the diagram of an accumulated distribution function (CDF) of the estimation error for the orientation angle η as the distance 1 between the photodetector PD1 and the photodetector PD2 changes. The level of the receiving plane is at 1 m, the light source 1 is positioned at (0, 1.5, 3) and the light source 2 is positioned at (0, 3.5, 3), and the standard deviation of Δd is 0.025 m. According to the statistical results, when 1 is 0.1 m, 0.2 m, 0.5 m and 1 m, there are 90% orientation angle errors that are less than 4.1°, 2.0°, 0.8° and 0.4° respectively. These results prove the feasibility and reliability of the proposed method.

[0076] The embodiments described above are only preferred embodiments listed for fully explaining the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art on the basis of the present invention shall fall within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.