The integration of a star tracker and gyroscope units (GUs) can take full advantage of the benefits of each, and provide continuous and accurate attitude information with a high update rate. The systematic error calibration of the integrated system is a crucial step to guarantee its attitude accuracy. In this paper, a comprehensive calibration method for the star tracker and GUs integrated system is proposed from a global perspective. Firstly, the observation model of the predicted star centroid error (PSCE) with respect to the systematic errors including the star tracker intrinsic parameter errors, GUs errors and fixed angle errors is accurately established. Then, the systematic errors are modeled by a series of differential equations, based on which the state-space model is established. Finally, the systematic errors are decoupled and estimated by a Kalman filter according to the established state-space model and observation model. The coupling between the errors of the principal point and subcomponents of the fixed angles (i.e., ${\mathrm{\Psi }}_x$ and ${\mathrm{\Psi }}_y$ ) is analysed. Both simulations and experiments indicate that the proposed method is effective at estimating the systematic errors of the star tracker and GUs integrated system with high accuracy and robustness with respect to different star centroid accuracies and gyroscope noise levels.

The stellar/inertial integrated navigation system, which combines the inertial navigation system (INS) and the star tracker, can restrain the accumulated INS errors. In the traditional loosely coupled stellar/inertial integration method, the star tracker needs to observe more than two navigation stars on an image for attitude determination and to use the attitude information as the observation to estimate the systematic errors of the INS. However, under strong background radiation conditions, the star number in the field of view (FOV) usually drops below 3; thus, the loosely coupled method fails to work. To overcome this difficulty, an improved tightly coupled stellar/inertial integration method based on the observation of the star centroid prediction error (SCPE) is proposed in this paper. It calculates the difference between the extracted star centroid and the predicted star centroid, namely, the SCPE, as the observation and then estimates the INS errors with a Kalman filter. Numerical simulations and ground experiments are conducted to validate the feasibility of the tightly coupled method. It is proved that the proposed method, which makes full use of all star observation information, can improve the navigation accuracy compared with the loosely coupled method and is more robust when there are not enough stars in the FOV.

A star tracker should be well calibrated before it is equipped in order to achieve high accuracy. There exists, however, the coupling problem between the internal and external parameters for most commonly used laboratory calibration methods, which affect the star tracker’s performance. We theoretically analyze the major aspects of the coupling mechanism based on the star tracker laboratory calibration model, which means the coupling between the principal point and the installation angle. The concept of equivalent principal point error, which illustrates the effectiveness of the calibration even with poor decoupling accuracy between the principal point and the installation angle, is introduced. Simulation and bench experiments are conducted to verify the laboratory calibration method and its coupling mechanism. The decoupling accuracy can be improved with more samples during calibration. In addition, the equivalent principal point error converges quickly and hardly affects the attitude of the star tracker, which is verified by both theory and experiment. The comprehensive calibration accuracy can still reach a high level even with poor decoupling accuracy.

Limited by the detection principle, an electromagnetic log (EML) can only output a velocity measurement relative to the ocean current in marine applications, which thus leads to a negative effect on a strapdown inertial navigation system (SINS)/EML integrated navigation system. The current velocity usually can be modeled as a first-order Gaussian Markov process, while the Markov time correlation constant should be determined in advance and used as a constant during the navigation process. The integrated navigation system will suffer performance degradation if an incorrect time correlation constant is applied. In order to tackle the problem, an ocean current coefficient estimation method is proposed in this manuscript. According to the Markov nature, the current velocity at the present time epoch is determined by that at the previous time epoch. Consequently, the current velocity corrected by the Kalman filter (KF) at the previous time epoch is utilized as the measurement information at the present time epoch, where the current coefficient is introduced into the state vector. The observability analysis shows that the current coefficient is totally observable. Simulation and field test results indicate that the proposed method can accurately estimate the current coefficient. Compared to the SINS/EML integrated navigation system without considering the current effects, the system with an estimated current coefficient minimizes the effect caused by ocean currents.

In order to address the issue of rapidly divergent positioning errors of a single-platform inertial navigation system (INS) in GNSS-denied environments, this paper proposes a cross-platform cooperative navigation method based on relative range and angle measurements. The observability of the cooperative navigation system under different motion strategies is investigated using Fisher information matrix (FIM) right null-space analysis combined with singular value decomposition (SVD). The results show that with relative range and angle measurement constraints, all inertial sensor biases can be effectively estimated by two strapdown inertial navigation systems (SINSs) moving along a simple trajectory, thereby improving the navigation accuracy. Experimental results demonstrate that compared to the autonomous navigation mode, the average positioning accuracy of the two SINSs improves by 77.4% and 68.4% respectively after 3 h of cooperative navigation along the prescribed trajectory. Using relative range and angle measurements, the proposed method requires only two SINSs and relatively simple planar motion, without the need for high-precision reference benchmarks, complex three-dimensional excitation trajectories, or turntable modulation. It reduces system complexity and motion requirements, providing an effective and easy-to-implement solution for ground vehicular positioning and orientation and other cross-platform cooperative navigation tasks in GNSS-denied environments.