## 1 Introduction
By calculating the GDOP, it can be found that the TDOA-only based positioning has a higher GDOP value when the receiver is not surrounded by signal sources [21; 22]. However, in order to achieve better signal coverage and lower deployment costs, the indoor distribution antenna (ANT) of the mobile communication system is typically placed beneath the ceiling of the central area of the room. ANTs are never deployed in the indoor areas, which are near the outer wall. In those areas, UE can only receive signals from one side, resulting in a high GDOP value and low positioning accuracy. The 5G system has the potential to solve this problem. The 5G system would also provide TDOA measurement based on OTDOA technology [23; 24], same as the LTE system. Different from the LTE system, the 5G system could provide high-precision TOA measurement over a large bandwidth and continuous uplink and downlink signals [25; 26; 27]. In both LTE and 5G, due to network optimization, the UE can only transmit and receive signals with the nearest signal source. This means that UE could only estimate one signal's TOA measurement from the nearest source. TOA-only localization algorithms require at least three TOAs to perform two-dimensional position estimation. Therefore, the 5G system cannot support TOA-only based positioning. However, the 5G system could support new hybrid positioning based on multiple TDOA measurements and single TOA. The GDOP of the TOA-only positioning is smaller than the TDOA-only positioning when the receiver is not surrounded by signal sources [28]. Therefore, the hybrid positioning based on multiple TDOAs and single TOA will probably achieve better positioning performance than the TDOA-only positioning. TDOA-only closed-form solutions, such as Chan-Ho, are based on the assumption that measurement errors match Gauss-Markov theory. However, the random errors of TDOA and TOA measurements are not homoscedastic. It means those algorithms cannot be used for the hybrid TDOA and TOA positioning directly. This paper aims to improve the positioning accuracy of the indoor distribution system by using multiple TDOAs and single TOA based hybrid positioning. In this paper, we establish a three-step WLS closed-form localization algorithm for heteroscedastic TDOA and TOA measurements. The first WLS provides an initial position for the last two steps. Then the algorithm uses two-step weighted least square (WLS) to estimate the final position result. We also derived the GDOP of the proposed hybrid positioning. We performed simulations in a typical indoor hall using an indoor distribution system. As shown in the simulation result, the GDOP of the hybrid positioning is lower than the GDOP of TDOA-only positioning. The simulations also show that the proposed method could approximate the CRLB when TDOA measurements errors are small enough and have the potential to achieve a better performance than two widely used closed-form TDOA-only positioning methods. This paper is organized as follows: Section 2 describes the system model of hybrid TDOA and TOA positioning. In Section 3, a new closed-form localization algorithm is developed for the nonlinear and heteroscedastic hybrid TDOA and TOA positioning equations. Section 4 analyzes the GDOP of the hybrid positioning based on multiple TDOAs and single TOA. Simulation results and analysis are presented in Section 5. Finally, we draw our conclusions in Section 6.