## 1 Introduction  
Due to the growing demand for accurate Location-Based Services (LBS), indoor positioning has been a hot research direction for the past few years. With the increase of large constructions, such as shopping malls and underground parking lots, the requirements for indoor positioning accuracy are getting higher and higher. Nevertheless, traditional indoor positioning systems such as WLAN, Zigbee, Ultra-Wideband (UWB), Bluetooth and Radio-frequency Identification (RFID) can only achieve tens of centimeters to a few meters of precision [1]. To meet the needs of high accuracy and instantaneity, a high-precision LED-based indoor positioning system using VLC technology is proposed. Visible light positioning (VLP) systems have the following advantages: First, multipath is more significant in VLP based on phase of arrival, however VLP based on angle of arrival or image sensors are more immune to multipath effects. Second, in some situations, such as hospitals and airplanes, VLC-based methods can still be used because LEDs do not generate radio frequency (RF) interference, and RF radiation is limited or even prohibited. Finally, as long as lighting infrastructures exist, VLC technology can be used to minimize hardware costs [2]. The indoor positioning method based on VLC can be divided into two categories: photodiode (PD)-based VLC [3,4] and image sensor-based VLC. Since the direction of the light beam can affect PD to a large extent, the mobility of the positioning terminal is extremely limited. Another drawback of PD-based positioning is that a large error is usually generated due to the angular measurements, the measuring of received signal strength, varying intensities of light, and the solving of quadratic equations for position estimation jointly determining the result of the positioning [5]. In addition, it requires high-precision devices when it exploits phase difference of arrival (PDOA) or phase of arrival (POA), and time difference of arrival (TDOA) or time of arrival (TOA) to estimate the position of terminal [1]. Therefore, a promising alternative is using an image sensor as a receiver, which, according to the coordinates of LEDs in the real world and in the image, determines the location of the positioning. Unlike PD, we can use the image sensor not only in experimental conditions but also in practice without peripheral because of the combination of image sensor and commercial mobile phone. At the same time, it is immune to reflected light and generally able to provide a capture rate of 30 frames per second [6]. Thus far, there have been many image sensor-based VLC methods proposed, but few of them are practically available due to the lack of consideration for the actual scene and there is no preparation for high-speed indoor positioning in practical applications. For example, in [7], an additional six-axis sensor is used to determine the direction of the receiver and its position. This scheme uses collinearity condition to relate the 3-D coordinates of the LEDs to the 2-D coordinates of the image sensor. Simulation results show that the position of the receiver can be accurately estimated within 1.5 m if the pixel size is \(36\times 10^{-6}\) m. In [8], the 3-D coordinate information is transmitted by at least three LEDs from the LED lighting array. The 2-D image sensor receives the spatially separated lights by a lens and demodulates the 3-D coordinate information of each LED. Then, by solving two sets of quadratic equations that may lead to calculation errors, the position of the receiver is calculated. Analysis of those works shows that the accurate angle measurement and the solution of the quadratic equation for position estimation may lead to the positioning error of the original scheme. In [9, 10, 11], two image sensors near the unknown position receive and demodulate the 3-D coordinate information transmitted by at least four LEDs from an LED array.