# Sample-Wise Aiding in GPS/INS Ultra-Tight Integration for High-Dynamic, High-Precision Tracking
## 1 Introduction  
GPS (global positioning system) and INS (inertial navigation system) have complementary characteristics and their integration has been widely explored [1]. High dynamics and high precision impose conflicting requirements on noise bandwidths of conventional tracking loops in GPS receivers [2]. GPS/INS ultra-tight coupling or deep integration can relieve this conflict by aiding the tracking loops with inertial measurements and, thus, boost immunity to high dynamics, severe interferences and brief line-of-sight blockages [3; 4; 5]. The idea of using ultra-tight GPS/INS integration to improve performance in challenging environments has drawn wide attention of the navigation community [6; 7; 8; 9; 10; 11; 12; 13]. [PERSON] & [PERSON] discussed the implementation and performance analysis of a PLL (phase locked loop) aided by a MEMS (micro electromechanical system) IMU (inertial measurement unit) [10]. Details of the IMU mechanization and state propagation can be found in [8]. [PERSON], _et al._, used a feed-forward aided PLL model and its transfer function to facilitate the performance analysis of carrier tracking loops with external aiding [11]. [PERSON], _et al._, quantified the effects of tracking loop bandwidth, receiver clock jitter, aiding Doppler error and platform vibration on the quality of the carrier phase estimate provided by the aided PLL [12]. [PERSON] took account of different orders of carrier tracking loops with external aiding and detailed the process of data collection and experimental setup [13]. With the development of vector tracking based receiver techniques [14], the GPS/INS deep coupling architecture (where the tracking loops are implemented as part of a larger navigation filter) has been studied increasingly by a number of authors. [PERSON], _et al._, proposed a vector-based GPS receiver which can be deeply integrated with inertialand alternate sensors [15]. [PERSON] & [PERSON] investigated three different Kalman filter implementation options in both scalar-tracking mode and vector-tracking mode with particular consideration for carrier phase tracking [16]. The analyses and tests in [17; 18] showed improved tracking and reacquisition performances of vector-based deep integration at the cost of increased computational loads. [PERSON], [PERSON] & [PERSON] noticed that, typically, the integration filter runs at a rate of 1 to 100 Hz, while the carrier tracking loop normally runs at about 1000 Hz [19]. An interpolator based on a CIC (cascaded integrator comb) filter is proposed to interpolate the low rate Doppler measurements from the navigation filter to 1000 Hz. [PERSON], [PERSON] & [PERSON], [PERSON] concerned the quality of IMU-derived Doppler estimates for integration, and derived the relationship between the baseband I (in-phase)/Q (quadrature) and the INS error for performance analysis [20]. Several studies addressed the algorithms of the pre-filter and the centralized navigation filter [21; 22]. [PERSON], [PERSON], _et al._, provided a unified frame applicable to several different algorithms of GPS/INS deep fusion [23]. [PERSON], [PERSON], _et al._, proposed an adaptive robust deeply coupled GNSS/INS system based on a federated architecture which can process the GPS L1 and BeiDou B1 signals together [24]. [PERSON], [PERSON], _et al._, assessed the performance using low-cost IMU and vector tracking-based integration for high dynamic applications [25]. Recent work in [26] presented a federated GPS/INS deep coupling system employing three Kalman filters and providing adaptation ability to improve the navigation performance under various jamming conditions. All of these reported aiding methods, however, inject the externally-estimated carrier Doppler directly into the tracking loop as a constant during the coherent integration period, which is at least 1 millisecond (ms). This limits the aiding rate not higher than 1000 Hz which is insufficient to the suppression of high dynamic stress errors.