Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

VISUAL-INERTIAL INTEGRATION FOR HUMAN MOTION TRACKING AND NAVIGATION IN FREE-LIVING ENVIRONMENTS

The aging population has become a burning issue for all modern societies around the world recently. There are two important issues existing now to be solved. One is how to continuously monitor the movements of those people having suffered a stroke in natural living environment for providing more valuable feedback to guide clinical interventions. The other one is how to guide those old people effectively when they are at home or inside other buildings and to make their life easier and convenient. Therefore, human motion tracking and navigation have been active research fields with the increasing number of elderly people. However, motion capture has been extremely challenging to go beyond laboratory environments and obtain accurate measurements of human physical activity especially in free-living environments, and navigation in free-living environments also poses some problems such as the denied GPS signal and the moving objects commonly presented in free-living environments. This thesis seeks to develop new technologies to enable accurate motion tracking and positioning in free-living environments. This thesis comprises three specific goals using our developed IMU board and the camera from the imaging source company: (1) to develop a robust and real-time orientation algorithm using only the measurements from IMU; (2) to develop a robust distance estimation in static free-living environments to estimate people’s position and navigate people in static free-living environments and simultaneously the scale ambiguity problem, usually appearing in the monocular camera tracking, is solved by integrating the data from the visual and inertial sensors; (3) in case of moving objects viewed by the camera existing in free-living environments, to firstly design a robust scene segmentation algorithm and then respectively estimate the motion of the vIMU system and moving objects. To achieve real-time orientation tracking, an Adaptive-Gain Orientation Filter (AGOF) is proposed in this thesis based on the basic theory of deterministic approach and frequency-based approach using only measurements from the newly developed MARG (Magnet, Angular Rate, and Gravity) sensors. To further obtain robust positioning, an adaptive frame-rate vision-aided IMU system is proposed to develop and implement fast vIMU ego-motion estimation algorithms, where the orientation is estimated in real time from MARG sensors in the first step and then used to estimate the position based on the data from visual and inertial sensors. In case of the moving objects viewed by the camera existing in free-living environments, a robust scene segmentation algorithm is firstly proposed to obtain position estimation and simultaneously the 3D motion of moving objects. Finally, corresponding simulations and experiments have been carried out.