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 traditional approach of a star tracker for reducing the dynamic error concentrates on a single frame of star images. Through correlating adjacent star images together with their angular relations sensed by a gyroscope unit (GU), the attitude-correlated frames (ACF) approach expands the view from one single frame to frame sequences. However, the star centroid is shifted from the star true position at the center time of the exposure period under complex dynamic conditions, which is called the complex motion induced error (CMIE) in this paper. The CMIE has a large effect on the performance of the ACF approach. This paper presents a method to compensate the CMIE through reconstructing the star trajectory with the angular velocity of the star tracker sensed by a GU, which achieves effective compensation of the CMIE crossing the boresight direction. Since the observation sensitivity to the CMIE along the boresight direction is low, the attitudes from two different fields of view (FOVs) are combined to improve its compensation accuracy. Then the ACF approach is applied to the obtained results where the CMIE has already been compensated completely. Simulations under shipboard dynamic conditions and experiments under oscillating conditions indicate that the proposed method is effective in improving the performance of the ACF approach and reducing the dynamic error of a star tracker under complex dynamic conditions.

A new method for dynamic measurement of deflections of the vertical (DOV) is proposed in this paper. The integration of an inertial navigation system (INS) and global navigation satellite system (GNSS) is constructed to measure the body’s attitude with respect to the astronomical coordinates. Simultaneously, the attitude with respect to the geodetic coordinates is initially measured by a star sensor under quasi-static condition and then maintained by the laser gyroscope unit (LGU), which is composed of three gyroscopes in the INS, when the vehicle travels along survey lines. Deflections of the vertical are calculated by using the difference between the attitudes with respect to the geodetic coordinates and astronomical coordinates. Moreover, an algorithm for removing the trend error of the vertical deflections is developed with the aid of Earth Gravitational Model 2008 (EGM2008). In comparison with traditional methods, the new method required less accurate GNSS, because the dynamic acceleration calculation is avoided. The errors of inertial sensors are well resolved in the INS/GNSS integration, which is implemented by a Rauch–Tung–Striebel (RTS) smoother. In addition, a single-axis indexed INS is adopted to improve the observability of the system errors and to restrain the inertial sensor errors. The proposed method is validated by Monte Carlo simulations. The results show that deflections of the vertical can achieve a precision of better than 1″ for a single survey line. The proposed method can be applied to a gravimetry system based on a ground vehicle or ship with a speed lower than 25 m/s.

When applied inside Earth’s atmosphere, the star tracker is sensitive to sky background produced by atmospheric scattering and stray light. The shot noise induced by the strong background reduces star detection capability and even makes it completely out of operation. To improve the star detection capability, an attitude-correlated frames adding (ACFA) approach is proposed in this paper. Firstly, the attitude changes of the star tracker are measured by three gyroscope units (GUs). Then the mathematical relationship between the image coordinates at different time and the attitude changes of the star tracker is constructed (namely attitude-correlated transformation, ACT). Using the ACT, the image regions in different frames that correspond to the same star can be extracted and added to the current frame. After attitude-correlated frames adding, the intensity of the star signal increases by n times, while the shot noise increases by $\sqrt{n}~\sqrt{n}/2$ times due to its stochastic characteristic. Consequently, the signal-to-noise ratio (SNR) of the star image enhances by a factor of $\sqrt{n}~2\sqrt{n}$. Simulations and experimental results indicate that the proposed method can effectively improve the star detection ability. Hence, there are more dim stars detected and used for attitude determination. In addition, the star centroiding error induced by the background noise can also be reduced.

In order to expand the applications of daytime star tracker to low-altitude platforms, it is necessary to solve the problem of daytime star detection inside the atmosphere. Currently, the short-wave infrared (SWIR) camera with InGaAs sensor is widely used for daytime star tracker, to suppress the strong background radiation during daytime. The Attitude-correlated Frames Adding (ACFA) approach can be used to further improve the sensitivity to starlight by correlating and adding successive star images. However, InGaAs sensor has both temporal and spatial noise charge, distinct from coupled device (CCD) detectors. These two types of noise exhibit different growth trends during the stacking process, which limits the improvement of the star detection capability of the AFCA. To accurately estimate the limitations of daytime star detection after using ACFA, the influence of this approach on the signal-to-noise ratio (SNR) of star images is revealed. The noise model of InGaAs sensor is firstly established in this paper according to the imaging process of the SWIR camera. Then the changing trend of gray value noise and SNR growth factor with the number of correlated frames is theoretically derived for SWIR star images. Finally, the SNR improvement based on ACFA is proved by the results of stacking the star images. It successfully improves the star detection capability of the star tracker under dynamic conditions. The star detection limitation of H-band magnitude is expected to increase from -0.21 to 1.5 by ACFA.

Using a short-wave infrared (SWIR) camera to improve daytime star detection ability has become a trend for near-ground star trackers. However, the noise of SWIR star images greatly decreases the accuracy of the attitude measurement results. Aiming at a real-time application of the star tracker, an adaptive section non-uniformity correction method based on the two-point correction algorithm for SWIR star images is proposed. The correction parameters of different sections are first calculated after the defective pixels are detected and excluded, and the real-time image is corrected using adaptive section parameters according to its gray value distribution. Finally, the defective pixels are compensated for by their adjacent corrected pixels. The correction results of both simulated and live-shot star images have verified the validity of the proposed method. It adapts to different sky background radiation, which is effective for the application of a star tracker. By comparing with other linear correction methods, it has the advantages of low calculation complexity, better real-time performance, and easier implementation in the hardware.