Many multi-sensor navigation systems urgently demand accurate positioning initialization from global navigation satellite systems (GNSSs) in challenging static scenarios. However, ground blockages against line-of-sight (LOS) signal reception make it difficult for GNSS users. Steering local codes in GNSS basebands is a desiring way to correct instantaneous signal phase misalignment, efficiently gathering useful signal power and increasing positioning accuracy. Besides, inertial navigation systems (INSs) have been used as a well-complementary dead reckoning (DR) sensor for GNSS receivers in kinematic scenarios resisting various interferences since early. But little work focuses on the case of whether the INS can improve GNSS receivers in static scenarios. Thus, this paper proposes an enhanced navigation system deeply integrated with low-cost INS solutions and GNSS high-accuracy carrier-based positioning. First, an absolute code phase is predicted from base station information, and integrated solution of the INS DR and real-time kinematic (RTK) results through an extended Kalman filter (EKF). Then, a numerically controlled oscillator (NCO) leverages the predicted code phase to improve the alignment between instantaneous local code phases and received ones. The proposed algorithm is realized in a vector-tracking GNSS software-defined radio (SDR). Real-world experiments demonstrate the proposed SDR regarding estimating time-of-arrival (TOA) and positioning accuracy.