## 1 Introduction  
Interest in visible light positioning (VLP) systems has witnessed a dramatic increase in recent years [1]. This has been driven by the need for a reliable localization system that works indoors and by the widespread adoption of light emitting diodes (LEDs) for lighting applications [2]. There has been a long history of indoor positioning techniques using radio frequency (RF) technologies, with many excellent survey papers on the topic [3]. The most commonly used RF technologies are WiFi, Bluetooth low energy (BLE) and ultra-wideband (UWB). In WiFi positioning, the existing access points that are commonly deployed in buildings for wireless communication, are also used as positioning beacons [4; 5]. This contrasts with BLE positioning where a dedicated infrastructure is deployed, typically using battery operated beacons [6; 7]. Bluetooth systems are commonly used for location-based services and point of interest broadcast. UWB systems also need to deploy specialized transmitters, but unlike BLE, the receivers are not commonly available in current consumer electronic devices like smartphones [8; 9; 10]. Compared to other indoor positioning technologies, VLP has several important characteristics. Indoor positioning technologies that use radio waves, such as WiFi and Bluetooth, tend to be heavily impacted by multipath propagation. This means that these technologies often use fingerprinting techniques where measurements are gathered during an offline stage to generate a map [4; 6; 11]. In operation, position estimates are based on matching the received signals to the previously generated map. Due to the ever-changing environment inside, it is challenging to keep the maps up to date and accuracy can be degraded. Light-based systems do not suffer as much from issues related to reflections [12], thus, it is possible to use line of sight techniques, such as received signal strength (RSS), time of arrival (TOA) and angle of arrival (AOA), in VLP. This means very accurate and reliable positioning is possible. Although UWB does not suffer as much from the multipath problem, it does require expensive dedicated infrastructure. VLP only needs minor modifications to existing infrastructure as almost all indoor areas are already illuminated. Communication is a key part of VLP systems where each luminaire serves as a beacon for indoor positioning and must transmit information about its location, such as its local coordinates. This can be achieved because LEDs can be switched at very high speeds, and this facilitates their dual usage for illumination and data transmission [13]. In VLP systems, a receiver must combine two capabilities. It must detect the source of light so that the location of the receiver relative to the luminaire can be found. In addition, it must also decode a signal from the luminaire which gives information on the location of the luminaire. Combined, this information yields the location of the receiver. The angular diversity aperture (ADA) receiver was initially developed for use in visible light communication (VLC) systems [14]. An ADA is a directional optical receiver that consists of multiple receiving elements, each of which is composed of a photodiode (PD) placed below an aperture. It has been shown that when used for VLC systems, the ADA is capable of providing a wide field of view (FOV) and excellent angular diversity within a compact and flat structure, which makes it easily embedded into modern portable devices, such as smartphones. The ADA has a flexible structure that can be tailored to specific applications by varying its parameters [15]. For example, the ADA design can be optimized for use in cellular or multiple-input multiple-output (MIMO) systems. A related receiver, the quadrature angular diversity aperture (QADA) receiver, has been specifically designed for VLP systems [16; 17]. For QADA to be used in VLP systems, it must perform two tasks, it must calculate the angle of arrival, and decode the signal which is transmitted.