# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 1 Introduction  
The application value of high-precision indoor positioning technology in emerging fields such as the industrial Internet of Things, smart cities, and autonomous driving. Terminal positioning based on 5G mobile communication networks can avoid the construction of large-scale positioning network-dedicated infrastructure, reduce the cost of obtaining high-precision indoor location information, promote the application and promotion of new generation information technology, assist in the construction of a smart society, and promote high-quality economic and social development [1]. The 5G network has greatly increased the types of supported positioning observation information. Integrating this observation information can increase information redundancy, improve positioning accuracy, and enhance positioning reliability, making observation information fusion positioning one of the research hotspots. The support of Multiple-Input Multiple-Output (MIMO) technology for antenna arrays in 5G networks enables base stations to measure the Direction of Arrival (DOA) of uplink signals [2], while the power enhancement of the Ultra Dense Network (UDN) [3] and the Sounding Reference Signal (SRS) enables 5G networks to measure the Time of Arrival (TOA) between terminals and neighboring base stations [4]. Therefore, 5G networks can support various heterogeneous observation information such as the TDOA and the DOA with multiple base stations [5]. Integrating this observation information can compensate for the respective disadvantages of different types of observation information [6], increase information redundancy, improve positioning accuracy, and enhance positioning reliability, making observation information fusion positioning technology one of the research hotspots in the 5G network positioning, 3 GPP has also listed observation information fusion positioning as one of the future research directions for 5G networks. High-precision measurement based on 5G networks requires precise time-frequency synchronization of 5G signals to improve positioning performance. For 5G systems, synchronization to chip accuracy is sufficient to meet communication requirements, but for positioning, precise measurement to chip accuracy is required to obtain more accurate ranging information. 5G high-precision ranging requires time-frequency synchronization first, followed by fine time delay estimation. The accuracy and efficiency of time-frequency synchronization determine the speed of localization convergence. In complex environments, the received signal power may be low, leading to a decrease in synchronization accuracy. Therefore, it is urgent to conduct research on improving synchronization accuracy under low signal-to-noise ratio. After time-frequency synchronization, the time delay estimation determines the ranging accuracy. Currently, the mainstream time delay estimation methods are divided into super-resolution-based algorithms and correlation discrimination-based algorithms. Super resolution algorithms include high-resolution ranging algorithms based on the Multiple Signal Classification (MUSIC) [7], signal parameter estimation algorithms based on Rotational Invariance Techniques (ESPRIT) [8], and related series of variant algorithms [9]. The algorithm based on correlation discrimination captures and continuously tracks the pilot signal transmitted by the positioning system to obtain time delay and phase measurement values. In traditional capture methods, using cross-correlation (CC) or Matched Filter (MF) methods only achieves a rough estimation of half the symbol width [10; 11]. The signal-tracking stage starts from obtaining rough estimates in the acquisition stage and gradually refines the estimation of carrier frequency and code phase parameters through the tracking loop [12; 13]. After obtaining 5G distance and angle information, high positioning accuracy can be achieved through fusion positioning at the observation level, which can be divided into filter-based methods and optimization-based methods [14].