## 1 Introduction  
The new Beidou (Compass) Navigation Satellite System network, consisting of five GEO satellites and 30 non-GEO satellites, is designed to provide positioning service with an accuracy of 10 m, speed measurement service with an accuracy of 0.2 m/s and time service with an accuracy of 10 ns within the whole global area. By the end of April 2012, 13 navigation satellites will have been launched. Some signal parameters of Compass were publicized in the 2010 Munich Satellite Navigation Summit [1]. With the establishment of the Compass network and the demand for current high dynamic applications such as spaceflight and aviation, research on Compass/INS integrated navigation system has been gradually receiving more intensive attention. In the Compass/INS integration system, INS measurements and Compass measurements are integrated using Kalman filtering to prevent inertial solution drift and also to aid the baseband tracking loop by adjusting local signal generation. The receiver's baseband tracking loop, normally, consists of a phase locked loop (PLL) for carrier tracking and a delay locked loop (DLL) for code tracking. Generally, the receiver adopts a third-order PLL, and loop parameters are determined with the controlled-root method [2]. Moreover, the PLL based on Kalman filtering has also been widely used. It is possible for the Kalman-PLL to adjust the loop gain according to the discriminator output, achieving adjustment of loop bandwidth, effectively reducing the loop's response time and restraining tracking noise [3,4]. In a weak signal and highly dynamic environment, the PLL without assistance can easily lose lock [5, 6, 7]. However, the integration system feeds the inertial measurements to the tracking loop, so the tracking error caused by receiver dynamics can be eliminated with the aid of inertial information. Therefore, the loop's bandwidth will be reduced and its tracking precision will be improved. Two factors which are seldom concerned need to be considered when using inertial measurements to aid highly dynamic tracking loops:  
1. In a highly dynamic situation, the inertial sensor's bias will be increased. For instance, the bias of an accelerometer with a \(\pm\)100 g measuring range is approximately 0.1 g to 1 g [8, 9, 10]. Under such conditions, will the inertial aid still be efficient? 2. If the integrated navigation system is starting or re-tracking, or the satellite signal is interfered or blocked, the inertial solution error fails to be corrected without the help of integration output. Under such conditions, will the inertial aid still be efficient? These problems will both result in large offsets or drifts in the inertial aid information. Since the code tracking loop is less affected by receiver dynamics, and its dynamic influence can be overcame through carrier frequency aiding, our research emphasis shall be given to inertially-aided PLL. Nowadays most GNSS/INS integrated navigation systems based on inertially aided baseband tracking are in the form of tightly integration or ultra-tightly integration [11]. In the 2000s, the GPS/INS ultra-tightly integration system was designed and applied [12]. The difference between tight integration and ultra-tight integration is that, the tight integration is a cascade of baseband filters and navigation filters, whereas the ultra-tight integration is implemented in a single filter based on the estimation of baseband signal measurement errors [13,14]. Ultra-tight integration may eliminate the time-correlated noise of cascaded filters to improve the tracking sensitivity and navigation precision [15]. Herein, according to the baseband of Compass/INS tightly integration, inertially-aided Kalman-PLL is adopted. Carrier phase, Doppler frequency shift, and Doppler shift rate are taken as state vectors, and the output ofPLL discriminator is used to adjust the Kalman filter gain dynamically. The Doppler shift rate noise is relative to satellite-receiver line-of-sight jerk.