# LSOS: An FG Position Method Based on Group Phase Ranging Ambiguity Estimation of BeiDou Pseudolite
## 1 Introduction  
According to the National Human Activity Pattern Survey (NHAPS), people spend 86.9% of their time in indoor spaces. With the acceleration of urbanization, location-based service demand and applications have been expanding from outdoors to indoors. Many indoor scenes such as shopping malls, factories, parking and so on have a strong demand for location. Especially with the development of the new generation of artificial intelligence technology, a large number of unmanned equipment are expected to achieve continuous high-precision location service in indoor environment. However, due to the complex physical space, it is difficult to provide mature indoor positioning technology. The mainstream location methods such as WIFI, Bluetooth, near-ultrasonic and ultra-wideband (UWB) still need further research [1]. The most important problem currently is how to integrate with the existing user platform. The biggest advantage of pseudolite indoor positioning technology is its good compatibility with GNSS [2; 3; 4; 5]. Using the existing terminal can realize the data parsing without any hardware modification. In contrast, the research of pseudo-satellite indoor positioning technology is easier to achieve the promotion of landing. The research of this papermainly focuses on the indoor application of BeiDou pseudo-satellite technology. For ease of analysis, this article divides indoor spaces into typical large-scale space (large stadium, airport, station, exhibition hall, etc. ), small-scale space (office, toilet, conference room, etc. ), and narrow-long space (corridor, tunnel, underground pipe corridor, etc.). In this paper, the BeiDou pseudo-satellite positioning problem in large-scale occluded space is studied, and the application problems in other scenarios will be given in the following papers. As we all know, carrier phase measurement is necessary for high precision positioning of GNSS. The GNSS navigation receiver will output the carrier phase as the original observation for the user. The specific form of carrier phase \(\Phi_{m}\) is shown below. \[\left\{ \begin{array}{l}\Phi_{1}=\|\mathbf{r}_{t}^{1}-\mathbf{r}_{u}\|+c( \delta t_{u}-\delta T^{1})-\lambda N^{1}+\xi^{1}\\ \Phi_{2}=\|\mathbf{r}_{t}^{m}-\mathbf{r}_{u}\|+c(\delta t_{u}-\delta T^{2})- \lambda N^{2}+\xi^{2}\\ \ldots\ldots\\ \Phi_{m}=\|\mathbf{r}_{t}^{m}-\mathbf{r}_{u}\|+c(\delta t_{u}-\delta T^{m})- \lambda N^{m}+\xi^{m}\end{array} \right. \tag{1}\]  
In the formula, \(\lambda\) is the wavelength of the received navigation signal, \(\mathbf{r}_{t}^{m}\) is the coordinate position of the m pseudolite signal, \(\mathbf{r}_{u}\) is the position of the user's receiver, \(c\) is the speed of light (m/s), \(\delta t_{u}\) is the clock difference of the user's receiver, \(\delta T\) is the clock error of pseudolite signal, \(N^{m}\) is the integer ambiguity of carrier phase estimation relative to k-channel pseudolite signal, and \(\xi^{m}\) is the noise error..  
As above, we obtain the range equations of the pseudo-satellite signals based on the carrier phase. Since the pseudo-satellite signals are generated by the same phase locked loop (PLL) control at each frequency during the design process, the clock difference of all signals is consistent. It can be found that the pseudo-satellite clock error \(\delta t\) and the receiver clock error \(\delta T\) can be eliminated by making the difference between the signals. Here we only give the difference equation based on the channel 1 signal. From this we can get the difference formula as follows:  
\[\left\{ \begin{array}{l}\Phi_{2}-\Phi_{1}=\|\mathbf{r}_{t}^{2}-\mathbf{r}_{u }\|-\|\mathbf{r}_{t}^{1}-\mathbf{r}_{u}\|+\lambda N^{21}+\xi^{21}\\ \Phi_{3}-\Phi_{1}=\|\mathbf{r}_{t}^{3}-\mathbf{r}_{u}\|-\|\mathbf{r}_{t}^{1}- \mathbf{r}_{u}\|+\lambda N^{31}+\xi^{31}\\ \ldots\ldots\\ \Phi_{m}-\Phi_{1}=\|\mathbf{r}_{t}^{m}-\mathbf{r}_{u}\|-\|\mathbf{r}_{t}^{1}- \mathbf{r}_{u}\|+\lambda N^{m1}+\xi^{m1}\end{array} \right.