## 1 Introduction  
The widespread use of location-based services requires accurate user positioning information both outdoors and indoors. In the outdoor environment, Global Navigation Satellite System (GNSS) effectively provides accurate user position and is widely used in personal navigation devices (e.g., the smartphone). In indoor situation applications, however, it is difficult for GNSS to provide reliable positioning information due to the 20-30 dB additional signal attenuation and blocking caused by buildings and construction materials [1]. In indoor environments, different positioning methods have been proposed, such as the ultrasound [2, 3], infrared [4], Bluetooth [5], Wi-Fi [6], image recognition [7], inertial navigation [8], and pseudolite (or pseudo-satellite) [9, 10, 11]. The ultrasound-based indoor positioning system can provide positioning solution with an accuracy of 1-3 cm [2, 3]. However, some special equipment is required for this system. If the mobile device is used to receive the ultrasound signals, people will hear noises due to the non-ideal impulse response of speakers [12]. The infrared and Bluetooth methods have short coverage distance [4, 5]. To cover the whole indoor area, a large number of signal sources are needed. The same requirement is also true for Wi-Fi systems in order to improve the positioning accuracy. Additionally, commonly based on the Received Signal Strength (RSS) and fingerprinting methods, Wi-Fi positioning systems have some shortcomings, such as large positioning errors due to the RSS offset between reference and user devices and long-duration fingerprinting updates. The image recognition method needs an _a priori_ database of considerable image nodes to identify the location, commonly involving increased memory size and computing load [7]. For inertial navigation, there are two typical shortcomings: the positioning accuracy depends on the initial location and the positioning error increases with time [8]. Compared to these methods, the pseudolite system has relatively larger coverage area (up to 50 km) and more accurate positioning solution (carrier phase) with 4-5 transmitters [13]. If the pseudolite system uses specially designed GPS-like signals, a commercial GPS receiver can be used with minor modifications of the firmware and/or software [11]. There are three types of pseudolite architectures for indoor positioning system, named pseudolite, repeater and repealite [14]. The pseudolite represents the typical pseudolite architecture. Several pseudolites are located at the corners of the building to simulate the satellite constellation. Each pseudolite generates and transmits GPS-like signals. Commonly, the generated signals and real GPS signals have the same signal structure but differ in carrier frequency, PRN code or navigation data [13, 15]. These differences require hardware-level modifications of the user receiver. In addition, pseudolites have some more drawbacks, such as clock synchronization issues and, multi-path and near-far effects [16]. To overcome one or more of these drawbacks, two variant architectures, the repeater and repealite, are proposed. The repeater simplifies the synchronization of the constellation and reduces near-far effects. It consists of an outdoor antenna to collect GPS signals and several switching modules to forward the GPS signals. In this process, the GPS signal is amplified and transmitted without any further treatment [17]. To identify the switching module, each module transmits signals over a definite period while others are turned off. The signal switching period received by the indoor terminal corresponds to the time difference of arrival (TDOA) between two successive repeaters. Then, more than four TDOA measurements are used to estimate the position [17]. The repealite is a combination of pseudolite and repeater. It is able to overcome the problems of synchronization and multipath effects.