The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs.

As a specific force sensor, the tri-axis accelerometer is one of the core instruments in an inertial navigation system (INS). During navigation, its measurement error directly induces constant or alternating navigation errors of the same order of magnitude. Moreover, it also affects the estimation accuracy of gyro drift coefficients during the initial alignment and calibration, which will indirectly result in navigation errors accumulating over time. Calibration can effectively improve measurement accuracy of the accelerometer. Device-level calibration can identify all of the parameters in the error model, and the system-level calibration can accurately estimate part of these parameters. Combining the advantages of both the methods and making full use of the precise angulation of the space-stabilized platform, this paper proposes a three-stage accelerometer self-calibration technique that can be implemented directly in the space-stable INS. The device-level calibration is divided into two steps considering the large amount of parameters. The first step is coarse calibration, which identifies parameters except for the nonlinear terms, and the second step is fine calibration, which not only identifies the nonlinear parameters, but also improves the accuracy of the parameters identified in the first step. The follow-on system-level calibration is carried out on part of the parameters using specific force error and attitude error to further improve the calibration accuracy. Simulation result shows that by using the proposed three-stage calibration technique in the space-stable INS, the estimation accuracy of accelerometer error can reach ${1\times 10}^{-6}\mathrm{g}$ order of magnitude. Experiment results show that after the three-stage calibration, the accuracy of latitude, longitude, and attitude angles has increased by over 45% and the accuracy of velocity has increased by over 22% during navigation.

Transverse navigation has been proposed to help inertial navigation systems (INSs) fill the gap of polar navigation ability. However, as the transverse system does not have the ability of navigate globally, a complicated switch between the transverse and the traditional algorithms is necessary when the system moves across the polar circles. To maintain the inner continuity and consistency of the core algorithm, a hybrid transverse polar navigation is proposed in this research based on a combination of Earth-fixed-frame mechanization and transverse-frame outputs. Furthermore, a thorough analysis of kinematic error characteristics, proper damping technology and corresponding long-term contributions of main error sources is conducted for the high-precision INSs. According to the analytical expressions of the long-term navigation errors in polar areas, the 24-h period symmetrical oscillation with a slowly divergent amplitude dominates the transverse horizontal position errors, and the first-order drift dominates the transverse azimuth error, which results from the $g^0$ gyro drift coefficients that occur in corresponding directions. Simulations are conducted to validate the theoretical analysis and the deduced analytical expressions. The results show that the proposed hybrid transverse navigation can ensure the same accuracy and oscillation characteristics in polar areas as the traditional algorithm in low and mid latitude regions.