## 1 Introduction  
The Global Navigation Satellite System (GNSS), using space satellites to achieve positioning and navigation, is widely used in civil and military applications, such as positioning, timing, and navigation. At present, the main GNSS in the world include the Global Positioning System (GPS) of the United States, the Global Navigation Satellites System (GLONASS) of Russia, the BeiDou Navigation Satellite System (BDS) of China and the Galileo Navigation Satellite System (Galileo) of the European Union [1,2]. However, their performance may be subject to the impact of environmental factors, including signal interference and dynamic factors. The Inertial Navigation System (INS) can provide continuous high-precision position, velocity and attitude data for a short time, but after a while gyro and accelerometer errors accumulate and the navigation errors grow. The integration of GNSS/INS has many peculiarities and offers a way for high-accurate positioning. There are three architectures of integrated navigation systems: loosely coupled, tightly coupled and deeply coupled (also called ultra-tightly coupled) [3, 4, 5]. The deeply coupled integration has been widely studied in recent years,due to the fact that it can achieve the fusion of GNSS and INS information at the signal processing level. What's more, it has better performances in highly dynamic environments due to the adaptable dynamic characteristics of INS. However, most research about GNSS/INS integration is concentrated on integration architectures and solutions instead of the signal acquisition issues. Acquisition is the first step of the signal processing for a GNSS receiver, and it is a time-consuming process. Under highly dynamic conditions, the Doppler shift between the carrier and the satellite changes greatly, resulting in a larger frequency search range and longer search time. According to the nature of signal acquisition, the common approach for improving signal acquisition performance is by reducing the carrier frequency and code phase search range. Compared with unaided acquisition methods, the INS-aided acquisition has many advantages under highly dynamic and harsh environment conditions, such as the lower C/N\({}_{0}\) (carrier to noise ratio) signal acquisition for the higher sensitivity receivers, and the accurate estimation of Doppler frequency shift and code phase to reduce the search space [6; 7]. Because of these outstanding performance features, it has been studied for many different applications [7; 8; 9; 10; 11]. [PERSON] and [PERSON] made the effort to investigate the methodology of the Doppler estimation [12; 13]. In [14], the effects of IMU accuracy on the Doppler estimation error were analyzed. [PERSON] and [PERSON] presented the INS-aided acquisition scheme and analyzed the acquisition performance [15; 16]. Reference [17] presented a fast acquisition method for GPS receivers aided by INS information and performed acquisition experiment under low dynamics. However, the addressed methods have some disadvantages: (i) the traditional INS-aided acquisition mostly uses INS velocity information to estimate the carrier Doppler frequency shift without reducing the uncertainty of code phase search; (ii) the mathematical model of Doppler shift and code phase estimation errors contributed by the INS velocity error and position error were not derived in detail; (iii) the literature has been focused on low dynamics, and not on high dynamics situations. Hence, due to the small Doppler shift caused by low dynamics, the former studies have had limited success in proving any INS-aided acquisition performance improvement. Furthermore, concerning the limitations under high dynamics, there is a little related literature. Thus, the performance analysis of GNSS signal acquisition aided by different grade INS under high dynamic conditions is still necessary. Figure 1 illustrates in a schematic diagram the search scope under three conditions: non-assisted acquisition, INS velocity-assisted acquisition and INS velocity, position-assisted acquisition.