## 1 Introduction  
With the emergence of mobile device location-based services, such as the Internet of Things (IoT) and Machine Type Communication (MTC), location-based services (LBS) have been attracting intensive attention recently. As one of the most popular wireless positioning technologies, the Global Navigation Satellite System (GNSS) has achieved great success in outdoor open-scene positioning. However, GNSS becomes infeasible for indoor scenarios due to the signal strength attenuation and multi-path effects [1]. Thus, it is imperative to develop efficient indoor positioning schemes to meet the requirements of numerous and booming indoor location-aware applications, such as indoor emergency rescue, smart factory asset management and tracking, mobile medical services, virtual reality games, etc. Traditional positioning methods can be roughly categorized as geometry-based and feature-matching-based methods [2]. The geometry-based methods, such as Angle of Arrival (AOA), Angle of Departure (AOD), Time Difference of Arrival (TDOA), and Multi-Round Trip Time (Multi-RTT), rely on the measurement of positioning information and estimation of the target location. Feature matching-based methods are mainly regarded as fingerprint recognition methods, which have also received widespread attention in positioning technology in the era of 5G and beyond [3]. Specifically, the primary approach of fingerprint recognition is based on the Received Signal Strength (RSS) or Channel State Information (CSI) [4]. Recently, the 3 rd Generation Partnership Project (3 GPP) emphasized the importance of the LBS in 5G networks, and in 3 GPP Rel-16, it ultimately established the direction of 5G positioning enhancement [5]. Specifically, the New Radio (NR) specification includes reference signals introduced for positioning. These signals include the Positioning Reference Signal (PRS) for the downlink and the Sounding Reference Signal (SRS) for the uplink. Based on these signals, 3 GPP Rel-16 has introduced a number of advanced positioning schemes suitable for 5G NR, including angle-based positioning schemes based on downlink AOD or uplink AOA, downlink TDOA, uplink TDOA, and Multi-RTT. Although these methods can provide high positioning accuracy, they heavily depend on the availability of line-of-sight (LOS) components [6]. Unfortunately, in many indoor scenarios, such as the industrial environment, there could be many obstacles that can cause signal refraction, reflection, and diffraction, which leads to poor performance under some specific scenarios [7]. Hence, it is imperative to explore efficient techniques to improve the positioning performance in heavy non-line-of-sight (NLOS) scenarios for the 5G system and beyond. In order to achieve higher positioning accuracy, the standardization work of 3 GPP Rel-18 is introducing Carrier Phase Positioning (CPP) technology. The carrier phase information of a signal contains distance information between the signal receiver and transmitter, which can be used to accurately calculate the user's position. CPP technology has been widely applied in GNSS, enabling centimeter or even millimeter-level positioning accuracy [8]. However, the low power of the GNSS signals can be blocked and discontinuous in indoor scenarios. Due to the high power of cellular network signals and their resistance to environmental interference, carrier phase positioning based on cellular signals is not limited to outdoor environments, and because the carrier phase contains the distance between the signal receiver and transmitter, it can be used to precisely calculate targets' position [1]. Compared to satellite-based CPP, using CPP in indoor scenarios can achieve similar positioning accuracy and lower positioning latency. In the measurement of the carrier phase from the Positioning Reference Signal (PRS), the estimated value of the Channel Frequency Response (CFR) is first used to obtain the Channel Impulse Response (CIR) by an Inverse Discrete Fourier Transform (IDFT).