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.

PHYLOGENETIC ANALYSES, GENE DOSAGE EFFECT AND SELECTION IN MEMBERS OF THE LATERAL BOUNDARY DOMAIN (LBD) GENES TRANSCRIPTION FACTOR FAMILY

Wood formation is an economically and environmentally important process and has played a significant role in the evolution of terrestrial plants. Despite its significance, the molecular underpinnings of the process are still poorly understood. We have previously shown that four Lateral Boundary Domain (LBD) transcription factors have important roles in the regulation of wood formation with two (LBD1 and LBD4) involved in secondary phloem and ray cell development and two (LBD15 and LBD18) in secondary xylem formation. Here, we used comparative phylogenetic analyses to test potential roles of the four LBD genes in the evolution of woodiness. We studied the copy number and variation in DNA and amino acid sequences of the four LBDs in a wide range of woody and herbaceous plant taxa with fully sequenced and annotated genomes. LBD1 showed the highest gene copy number across the studied species, and LBD1 gene copy number was strongly and significantly correlated with the level of ray seriation. The lianas, cucumber and grape, with multiseriate ray cells showed the highest gene copy number (12 and 11, respectively). Because lianas’ growth habit requires significant twisting and bending, the less lignified ray parenchyma cells likely facilitate stem flexibility and maintenance of xylem conductivity. We further demonstrate conservation of amino acids in the LBD18 protein sequences that are specific to woody taxa. Neutrality tests showed evidence for strong purifying selection on these gene regions across various orders, indicating adaptive convergent evolution of LBD18. Structural modeling demonstrates that the conserved amino acids have a significant impact on the tertiary protein structure and thus are likely of significant functional importance.