Theory of Functional Connections and Nelder-Mead optimization methods applied in satellite characterization

The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, we propose and analyze the application of two optimization procedures to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder-Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. In this paper, we propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second procedure proposed in this research takes advantage of the Nealder-Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.Comment: Submitted to Acta Astronautic

PRECISE EVALUATION OF GNSS POSITION AND LATENCY ERRORS IN DYNAMIC AGRICULTURAL APPLICATIONS

A method for precisely synchronizing an external serial data stream to the pulse-per-second (PPS) output signal from a global navigation satellite-based system (GNSS) receiver was investigated. A signal timing device was designed that used a digital signal processor (DSP) with serial inputs and input captures to generate time stamps for asynchronous serial data based on an 58593.75 Hz internal timer. All temporal measurements were made directly in hardware to eliminate software latency. The resolution of the system was 17.1 µs, which translated to less than one millimeter of horizontal position error at travel speeds typical of most agricultural operations. The dynamic error of a TTS was determined using a rotary test fixture. Tests were performed at angular velocities ranging from 0 to 3.72 rad/s and a radius of 0.635 m. Average latency from the TTS was shown to be consistently near 0.252 s for all angular velocities and less variable when using a reflector based machine target versus a prism target. Sight distance from the target to the TTS was shown to have very little effect on accuracy between 4 and 30 m. The TTS was determined to be a limited as a position reference for dynamic GNSS and vehicle auto-guidance testing based on angular velocity. The dynamic error of a GNSS receiver was determined using the rotary test fixture and modeled as discrete probability density functions for varying angular velocities and filter levels. GNSS position and fixture data were recorded for angular velocities of 0.824, 1.423, 2.018, 2.618, and 3.222 rad/s at a 1 m radius. Filter levels were adjusted to four available settings including; no filter, normal filter, high filter, and max filter. Each data set contained 4 hours of continuous operation and was replicated three times. Results showed that higher angular velocities increased the variability of the distribution of error while not having a significant effect on average error. The distribution of error tended to change from normal distributions at lower angular velocities to uniform distributions at higher angular velocities. Internal filtering was shown to consistently increase dynamic error for all angular velocities

GLAcier Feature Tracking testkit (GLAFT): a statistically and physically based framework for evaluating glacier velocity products derived from optical satellite image feature tracking

Glacier velocity measurements are essential to understand ice flow mechanics, monitor natural hazards, and make accurate projections of future sea-level rise. Despite these important applications, the method most commonly used to derive glacier velocity maps, feature tracking, relies on empirical parameter choices that rarely account for glacier physics or uncertainty. Here we test two statistics- and physics-based metrics to evaluate velocity maps derived from optical satellite images of Kaskawulsh Glacier, Yukon, Canada, using a range of existing feature-tracking workflows. Based on inter-comparisons with ground truth data, velocity maps with metrics falling within our recommended ranges contain fewer erroneous measurements and more spatially correlated noise than velocity maps with metrics that deviate from those ranges. Thus, these metric ranges are suitable for refining feature-tracking workflows and evaluating the resulting velocity products. We have released an open-source software package for computing and visualizing these metrics, the GLAcier Feature Tracking testkit (GLAFT).</p

GEO-VISUALISATION AND VISUAL ANALYTICS FOR SMART CITIES: A SURVEY

Geo-Visualisation (GV) and Visual Analytics (VA) of geo-spatial data have become a focus of interest for research, industries, government and other organisations for improving the mobility, energy efficiency, waste management and public administration of a smart city. The geo-spatial data requirements, increasing volumes, varying formats and quality standards, present challenges in managing, storing, visualising and analysing the data. A survey covering GV and VA of the geo-spatial data collected from a smart city helps to portray the potential of such techniques, which is still required. Therefore, this survey presents GV and VA techniques for the geo-spatial urban data represented in terms of location, multi-dimensions including time, and several other attributes. Further, the current study provides a comprehensive review of the existing literature related to GV and VA from cities, highlighting the important open white spots for the cities’ geo-spatial data handling in term of visualisation and analytics. This will aid to get a better insight into the urban system and enable sustainable development of the future cities by improving human interaction with the geo-spatial data