An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Method of Using Collinearity Condition <s> This paper proposes a new positioning method using an image sensor and visible light LEDs (Light Emitting Diode). The color LEDs are used to detect position. We achieved position accuracy of less than 5cm using our method. We applied our method to a robot and demonstrated that accurate position control of a robot was feasible. <s> BIB001 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Method of Using Collinearity Condition <s> A simple, accurate, secure, long-lasting, and portable hybrid positioning system is proposed and designed in this paper. It ::: consists of a lighting LED that generates visible light data corresponding to position information of a target and a Zigbee ::: wireless network communication module with low power, security, and service area expansion characteristics. Under an ::: indoor environment where there is 23.62m distance between an observer and the target, the presented hybrid positioning ::: system is tested and is verified with the functions of Zigbee three hop wireless networking and visible light ::: communication (VLC) scheme. The test results are analyzed and discussed. <s> BIB002 </s> An in-Depth Survey of Visible Light Communication Based Positioning Systems <s> Method of Using Collinearity Condition <s> We propose a method for determining the indoor position based on a Visible Light Communication (VLC) system that uses a high-speed fish-eye lens-equipped camera. In VLC, lights are used as data transmitters and users can receive location information using a receiving device. Since the lights are configured to meet a pre-determined illumination level, the system requires neither space nor additional power. The lights serve their usual function as sources of illumination, and as a means of transmitting digitized information. Up to now, photo sensors or a normal lens-equipped camera have been used as receiving devices. However, the number of lights that can be received by a photo sensor is limited, and the receiving angle of the image that a normal lens-equipped camera takes is also limited. Since a camera with a fish-eye lens commands a 180-degree view of the ceiling, the number of detectable LED lights increases and positioning accuracy is improved. In terms of data transmission in VLC, the LED lights transmit data at 9.6 kbps. Thus, we use a high-speed complementary metal-oxide-semiconductor image sensor to receive the digitized information. The sampling frequency of the image sensor is up to 48 kHz. The LED lights send ID frames containing a prefix, ID, and Cyclic Redundancy Check (CRC) code. The ID and CRC are modulated with 4 Pulse-Position Modulation. The receiver detects the LED lights from the ceiling image. Then, variations in intensity at the center of the LED lights are stored as light signals. Since received data can be separated into two segments within a small buffer, according to the measurement period, received data are occasionally swapped. The receiver obtains the world coordinates of the LED light from the received ID. Finally, self-location estimation is performed using the relationship between the fish-eye image coordinates and the world coordinates. We conducted an experiment using the VLC platform in Niigata University, with the receiver position fixed at 24 measuring points. The platform area measures 5.4 m by 7.5 m, and the ceiling height is 3 m.The results show that the maximum horizontal error is 10 cm.We conclude that it is possible to determine a horizontal position within merely 10 cm, using the proposed method. <s> BIB003
Each set of reference information including the 2D image coordinate (x, y) and the 3D world coordinate (X, Y, Z) corresponding to one LED base station creates a set of two collinearity equations, which are the explicit representations of the geometric relations in Equation   : where f is the focal length, (X 0 , Y 0 , Z 0 ) is the world coordinate of the camera projection center, and R is the rotation matrix defined as  : Usually the focal length f is a known parameter for a specific system, and the world coordinate of the camera projection center which is considered as the position of the mobile device (X 0 , Y 0 , Z 0 ) is the parameter that needed to be determined. Since there are six unknown parameters in Equations (21) and (22) : X 0 , Y 0 , Z 0 , φ, ω and κ, at least three pairs of x, y and (X, Y, Z) reference information must be known to find these values of the unknowns parameters. Various solutions are possible under different assumptions for the parameters in Equations (21) and BIB002 . In  , the collinearity condition equations was solved using the least squares method. At least three LED base stations and their projections on the image sensor were required to find the position of the camera. The simulation showed that with a sensor of 1000 × 1000 pixels resolution used, a distance error of about 7 cm was achieved. The approach taken in BIB003 used a fish-eye lens to take pictures of multiple LED base stations in the same image. With at least three LEDs detected, the collinearity condition equations were solved using the nonlinear least square Levenberg-Marquardt algorithm to estimate the position. Since the fish-eye lens introduces a lot of distortion in the image, an calibration process must be used to correct the image before applying the positioning algorithm. The experiment showed that the maximum horizontal error of the system was less than 10 cm. In BIB001 , an acceleration sensor was used to obtain information about the orientation of the camera, which is defined by φ, ω and κ. Since only three parameters, which are X 0 , Y 0 and Z 0 in Equation (21) are unknown, the system can determine the camera position with two or more LED base stations captured in the image.