## 1 Introduction  
With the development of mobile Internet and industrial Internet of Things, there has been a growing demand for high-efficiency indoor data access and high-accuracy positioning. Indoor visible light communication (VLC) based on light-emitting diodes (LEDs) has emerged as a promising solution, leveraging the advantages of visible light for lighting, communication, and positioning purposes [1; 2; 3], providing an additional communication channel in indoor environments where radio frequency (RF) communication may face challenges like data insecurity, interference, and limited spectrum availability. Specifically, VLC can be applied to indoor positioning, often referred to as visible light positioning (VLP) [4], offering benefits such as high accuracy, low cost, and immunity to electromagnetic interference [5; 6]. However, conventional VLC and VLP systems are typically designed and deployed independently. When deployed within the same indoor environment to provide both communication and positioning services simultaneously and share similar bandwidth resources, these systems may struggle to deliver high-quality performance in their respective functions due to frequency interference. Thus, integrated visible light communication and positioning (VLCP) systems using multiplexing techniques like time division multiplexing (TDM), frequency division multiplexing (FDM), and code division multiplexing (CDM) can address this issue. TDM, the simplest method, segregates VLC and VLP signals into different time slots [7; 8]. With FDM, VLC and VLP signals occupy distinct frequency subcarriers for simultaneous transmission and positioning [9; 10; 11; 12; 13]. CDM assigns unique spreading codes to VLC and VLP signals, which are then differentiated through despreading codes [8; 14; 15]. However, commercial LEDs typically offer a narrow bandwidth, often just a few megahertz. Consequently, in scenarios where both communication and positioning are equally vital, effectively managing limited bandwidth resources to ensure reliable communication and accurate positioning poses a significant challenge for integrated VLCP design. The mentioned schemes may fail to allocate sufficient communication resources for both VLC and VLP simultaneously. To optimize the utilization of constrained bandwidth resources, researchers have proposed realizing VLP based on the channel state information (CSI) during VLC [16; 17; 18]. In [16], the estimated frequency domain transfer function (FDTF) of VLC channels was utilized for ranging, enabling VLP. In [17], the distances between LEDs and the PD were estimated through the received signal strength (RSS) of VLC channels, followed by trilateration to achieve VLP. However, the above studies focus on the scenario where the terminal was stationary and do not consider the case of terminal movement. From the user's perspective, terminal mobility poses a significant and challenging issue in mobile VLCP systems. On one hand, in mobile VLC, terminal mobility causes fluctuations in the optical channel, impacting the VLC performance [19]. Various strategies have been proposed to enhance the link performance. In [20], a decision feedback channel estimation (DFCE) scheme was proposed to estimate the time-varying CSI in mobile VLC systems. In [21; 22], space-time block coding (STBC) was employed to enhance the robustness of mobile VLC against time-varying CSI. However, these studies mainly focus on single-input-single-output (SISO) or multiple-input-single-output (MISO) systems, overlooking the potential of multiple-input-multiple-output (MIMO) systems, which have been demonstrated to boost the capacity and reliability of VLC systems [23; 24]. On the other hand, in mobile VLP, the optical channel fluctuation also affects the positioning performance. While studies have targeted mobile VLP, they often involve fixing terminals at discrete locations to receive VLP signals [25; 26]. Few studies have considered the continuous movement of terminals.