## 1 Introduction  
GNSS/INS deeply coupled technology is an important branch of current research in the field of integrated navigation systems. The theory around the loop assistance mechanism and the navigation performance improvement is quite mature, and the deeply coupled system has been applied in the field already.  
The deeply coupled system introduces the inertial information into the tracking loop of the receiver, which means that the dynamic stress on the receiver could be highly reduced. Hence, this kind of system performs very well in highly dynamic environments. Around this topic, many research institutions and scholars have been working hard to improve the system performance. In terms of loop theory research, [PERSON] proposed an error analysis method to make the connection between most error sources and the PLL (Phase Lock Loop) tracking loop in 2015 [1]. [PERSON] studied the relationship between MEMS (Micro Electro Mechanical Systems) IMU precision and tracking loop stability in 2013, and the bias stability of the IMUs was proposed from the angle of usability [2]. [PERSON] studied the loop control scheme between loop measurements and INS navigation data in 2016, and two control schemes were derived which were proved to be correct [3]. In 2014, [PERSON] studied the jamming mitigation performance of a deeply coupled GNSS-INS system with a low-cost MEMS IMU and gave actual experimental results instead of simulations [4]. [PERSON] developed a good structure for a tracking loop containing a multicarrier VPLL (Vector PLL) in 2015, and the performance of the proposed architecture was validated by means of tests under different conditions [5].  
Moreover, the implementation of actual deeply coupled systems has been under development. In 2014, KIT (Karlsruhe Institute of Technology) set up a highly dynamic and deeply coupled verification prototype; a Simulink software receiver was used to complete the algorithm verification on the Matlab platform for the first time, and a real-time solution for deeply coupled architecture was achieved [6]. In 2015, the Rockwell Collins Company launched the NavFire-E Series of high-performance integrated navigation systems, which represent the highest standards of the current practical applications. The highly integrated micro-inertial and anti-jamming receiver technology were used to achieve high output accuracy and high reliability of the system [7].  
However, the performance of inertial devices will be affected seriously by highly dynamic environments. The key point is to make sure that the assistance information used to reduce the dynamic stress is reliable. How to select correct inertial devices and receiver parameters to satisfy the loop dynamic requirement is still a problem for the system. However, quite a few articles have studied this: [PERSON] discussed the usability of a MEMS IMU in a deeply coupled system, but the g-sensitivity error of gyroscope under high dynamic environments was ignored [2]; [PERSON] built an actual experimental platform with a MEMS IMU, but it was not clear how to select the appropriate IMU devices [4]. In this paper, a mathematic model of the deeply coupled system including the g-sensitivity error of gyroscope is introduced. Then, according to the norm principle, the error propagation properties are analyzed by mathematical deduction and this process gives the quantitative velocity error caused by IMU error. In addition, a new method which combines with the tracking error model to determine the loop stability is introduced. It will eventually make a judgment about the stability of the tracking loop under certain parameter settings. Finally, the correctness of the proposed method was verified by several simulations based on a digital simulation platform.