## 1 Introduction  
The outdoor global navigation satellite system (GNSS) has been developed and widely applied, but it is difficult to obtain reliable GNSS signals in sheltered environments or indoors. A pseudolite system can make up for the shortage of GNSS in these environments [1; 2]. However, there are also many problems in the indoor pseudolite systems, such as clock synchronization, multipath effect, noise, fixed satellite constellations, the high precision requirement of initial values, and so on. All of them are significant challenges for indoor pseudolite positioning. At present, the most mature indoor pseudolite system is produced by LOCATA. A proprietary TimeLoc technology for tight time synchronization, allowing the clock difference in the carrier phase measurement equation to be ignored is utilized [3], which brings a large additional cost at the stage of system deployment. The clock synchronization error can be controlled within 30 ps in the LOCATA system. The horizontal error of the non-differential positioning is less than 6 cm, and the precision of the altitude direction is about 15 cm [4]. [PERSON] et al. proposed a new concept of pseudolite-based navigation to overcome the receiver modification problem of the pseudolite-based positioning systems. The precision at the meter level can be obtained even in poor geometry tests [5]. [PERSON] et al. built a new pseudolite-based indoor positioning system. The satellites clock can be synchronized with each other and signal can be processed by the standard receivers. High-accuracy horizontal positioning in both static and dynamic situations could be provided based on the simulation results [6]. [PERSON] et al. used the simulated data of indoor pseudolites to verify the high positioning precision after the ambiguities are fixed through the LAMBDA method and the extended Kalman filter (EKF). [PERSON] et al. used carrier interferometry to conduct analyses on indoor pseudolite positioning [7]. [PERSON] et al. used the improved particle swarm algorithm to improve the search efficiency of AFM to achieve high precision positioning of a single epoch and the precision can reach the centimeter level [8]. [PERSON] et al. introduced a novel use of pseudolites to cope with pseudolites' conventional problems. The results showed that the positioning accuracy varies from the centimeter- to the meter-level according to the geometric structure. They believed that the convergence precision of initial value was also important for positioning [9]. By using commercial pseudolites and independently-developed software receivers, an indoor pseudolite observation system was realized in our group. The fixed ambiguity resolution (AR) was obtained through the high accuracy carrier phase observations. The dynamic positioning precision can reach the centimeter level. Considering the current research status, the key to achieve high-precision indoor pseudolite positioning is the use of carrier phase observations, and the core problem is how to fix the ambiguities correctly [10]. Generally speaking, the methods of AR can be divided into two categories. One is searching based on the coordinate domain. The integer nature of ambiguity is used to obtain the coordinates directly instead of solving the ambiguity explicitly in such methods [11]. The common method is the ambiguity function method (AFM) [12; 13; 14; 15]. The other is searching in the ambiguity domain. The most popular method is LAMBDA [16; 17; 18]. This method is reliable and accurate, but a higher accuracy of initial values is needed in indoor pseudolite positioning [8]. On the acquisition of the initial values, due to the fixed constellation of the pseudolites, the static observations are almost the same. Most of the research institutes prefer to use KPI [19], including LOCATA. Nevertheless, it is difficult to obtain the known fixed point in a practical application, and it is not convenient to operate in dynamic observation.