Dongkai Dai

An Improved Method for Dynamic Measurement of Deflections of the Vertical Based on the Maintenance of Attitude Reference

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 bodys 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.

Extraction methed of the motion blurred star image for the star sensor under high dynamic conditions

Star sensor is beyond dispute the most accuracy absolute attitude determination sensor and it is widely used in deep space exploring and earth observing. Star image spots captured in the image sensor of the star sensor will elongate when it is under high dynamic conditions especially the rotation motion resulting in the blurred star images. The motion blurred star images with low SNR lead to the increase of difficulty in the extraction of the star areas. Normal processing procedures as the estimation of background threshold, image binarization and connected components analysis are not profitable anymore. A extraction method of the motion blurred star image based on template-correlation matching of the star sensor under high dynamic conditions is proposed in this paper. Parameters of the motion degradation function is precisely measured with the strap down laser gyro unit. So the template is generated in real time according to different dynamic conditions through the degradation model of the motion blurred image. Correlation matching criterion like minimum correlation difference and maximum correlation product are alternatives. Simulation and experimental results show that this method readily identifies and extracts the star spot area and removes the noises outside its region simultaneously. It is effective in extracting faint blurred star images unless they are totally submerged by the noise.

Centroid error compensation method for a star tracker under complex dynamic conditions

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.

Analysis of response delay of the attitude in a single-axis rotation INS/GPS system

Deflections of the vertical (DOV) are normally ignored in the gravity compensation procedure, which become one of the primary error sources in inertial navigation. In a single-axis rotation INS/GPS system, bias of the gyro and the accelerometer can be ignored, the attitude error is mainly affected by DOV. In this paper, the ideal system assumption is abandoned and the influence of DOV on the attitude is comprehensively discussed, which can be divided into two parts i.e. the direct influence and the indirect influence. The attitude error tracks the DOV along the trajectory belongs to the former. A relatively fixed delay between the attitude error and the DOV belongs to the latter. The delay is essentially induced by the weak observability of the system to the violent DOV. Factors which affect the delay are carefully analyzed. The simulation results show that the delay is mainly affected by accuracies of the inertial sensors and the GPS. It decreases with the GPS accuracy increasing, but increases with the inertial sensor accuracy increasing. The process noise covariance matrix Q plays an important role. With analysis of the characteristics of the delay, influence of the DOV on attitude is studied further, which is necessary for the attitude correction in future.

Advances and accuracy performance of the star trackers

Star trackers are beyond dispute the most accuracy absolute attitude determination sensors which are widely applied in spacecraft, satellites, rockets, etc. High precision autonomous star tracker has accuracy better than one arc second and generally resulting in a low update rate less than 10Hz. Typically, an autonomous star tracker consist two physically independent components, the optical head and the associated processing electronic system. High accuracy attitude is obtained through their cooperation. Basic principles of star navigation and components of a star tracker will be introduced. Star trackers used to be with big body size, heavy mass, high power consumption and complicated structure but with low accuracy. The state-of-the-art development will decrease the power consumption and mass of autonomous star trackers significantly while increase update rate and improve dynamic accuracy and system robustness. Advance of different generations of star trackers will be reviewed here. The accuracy performance of the star tracker depends on the sensitivity to the starlight of the image sensor, the star detection threshold, the field of view (FOV), the number of stars in the FOV, the accuracy of the star centroid, the dynamic maneuvering, the calibration and etc. Star centroid is a key procedure and contributes much more to the final performance of a star track. Accuracy degradation will occur when the carrier of the star track is in the state of high dynamic maneuvering. Hardware design and algorithms remedies have to been adopted to reduce the degradation effects. Detailed discussion of accuracy performance will be presented.

A Comprehensive Calibration Method for a Star Tracker and Gyroscope Units Integrated System

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., Ψx and Ψy) 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.

Q-adjusting technique applied to vertical deflections estimation in a single-axis rotation INS/GPS integrated system

Former studies have proved that the attitude error in a single-axis rotation INS/GPS integrated system tracks the high frequency component of the deflections of the vertical (DOV) with a fixed delay and tracking error. This paper analyses the influence of the nominal process noise covariance matrix Q on the tracking error as well as the response delay, and proposed a Q-adjusting technique to obtain the attitude error which can track the DOV better. Simulation results show that different settings of Q lead to different response delay and tracking error; there exists optimal Q which leads to a minimum tracking error and a comparatively short response delay; for systems with different accuracy, different Q-adjusting strategy should be adopted. In this way, the DOV estimation accuracy of using the attitude error as the observation can be improved. According to the simulation results, the DOV estimation accuracy after using the Q-adjusting technique is improved by approximate 23% and 33% respectively compared to that of the Earth Model EGM2008 and the direct attitude difference method.

An improved method for gravity disturbances compensation in INS/GPS integrated navigation

Though the gravity-induced velocity and position errors can be easily dumped in GPS/INS integrated navigation, the attitude estimation errors are more affected by the gravity disturbance errors. In this paper, an improved gravity disturbance compensation method is performed to reduce the gravity-induced attitude measurement error in inertial navigation system (INS) and global positioning system (GPS) integrated navigation. Specifically, the long and medium wavelength components of the gravity disturbance are compensated by using the EGM2008 global gravity model, and then a derivative second-order Gauss-Markov process is adopted as a statistical model of the short-wavelength components, which are estimated and removed online by a Kalman filter. Simulations results show that the proposed statistical model can decouple the short-wavelength components of gravity disturbances from the attitude errors. Therefore, the attitude errors are reduced effectively when the improved compensation method is applied.