Orbital Constellation Design and Analysis Using Spherical Trigonometry and Genetic Algorithms: A Mission Level Design Tool for Single Point Coverage on Any Planet

Recent interest surrounding large scale satellite constellations has increased analysis efforts to create the most efficient designs. Multiple studies have successfully optimized constellation patterns using equations of motion propagation methods and genetic algorithms to arrive at optimal solutions. However, these approaches are computationally expensive for large scale constellations, making them impractical for quick iterative design analysis. Therefore, a minimalist algorithm and efficient computational method could be used to improve solution times. This thesis will provide a tool for single target constellation optimization using spherical trigonometry propagation, and an evolutionary genetic algorithm based on a multi-objective optimization function. Each constellation will be evaluated on a normalized fitness scale to determine optimization. The performance objective functions are based on average coverage time, average revisits, and a minimized number of satellites. To adhere to a wider audience, this design tool was written using traditional Matlab, and does not require any additional toolboxes. To create an efficient design tool, spherical trigonometry propagation will be utilized to evaluate constellations for both coverage time and revisits over a single target. This approach was chosen to avoid solving complex ordinary differential equations for each satellite over a long period of time. By converting the satellite and planetary target into vectors of latitude and longitude in a common celestial sphere (i.e. ECI), the angle can be calculated between each set of vectors in three-dimensional space. A comparison of angle against a maximum view angle, , controlled by the elevation angle of the target and the satellite’s altitude, will determine coverage time and number of revisits during a single orbital period. Traditional constellations are defined by an altitude (a), inclination (I), and Walker Delta Pattern notation: T/P/F. Where T represents the number of satellites, P is the number of orbital planes, and F indirectly defines the number of adjacent planes with satellite offsets. Assuming circular orbits, these five parameters outline any possible constellation design. The optimization algorithm will use these parameters as evolutionary traits to iterate through the solutions space. This process will pass down the best traits from one generation to the next, slowly evolving and converging the population towards an optimal solution. Utilizing tournament style selection, multi-parent recombination, and mutation techniques, each generation of children will improve on the last by evaluating the three performance objectives listed. The evolutionary algorithm will iterate through 100 generations (G) with a population (n) of 100. The results of this study explore optimal constellation designs for seven targets evenly spaced from 0° to 90° latitude on Earth, Mars and Jupiter. Each test case reports the top ten constellations found based on optimal fitness. Scatterplots of the constellation design solution space and the multi-objective fitness function breakdown are provided to showcase convergence of the evolutionary genetic algorithm. The results highlight the ratio between constellation altitude and planetary radius as the most influential aspects for achieving optimal constellations due to the increased field of view ratio achievable on smaller planetary bodies. The multi-objective fitness function however, influences constellation design the most because it is the main optimization driver. All future constellation optimization problems should critically determine the best multi-objective fitness function needed for a specific study or mission

Communication Platform Payload Definition (CPPD) study. Volume 1: Executive summary

This is Volume 1 (Executive Summary) of the Ford Aerospace & Communications Corporation Final Report for the Communication Platform Payload Definition (CPPD) Study program conducted for NASA Lewis Research Center under contract No. NAS3-24235. This report presents the results of the study effort leading to five potential platform payloads to service CONUS and WARC Region 2 traffic demand as projected to the year 2008. The report addresses establishing the data bases, developing service aggregation scenarios, selecting and developing 5 payload concepts, performing detailed definition of the 5 payloads, costing them, identifying critical technology, and finally comparing the payloads with each other and also with non-aggregated equivalent services

Satellite Constellation Pattern Optimization for Complex Regional Coverage

The use of regional coverage satellite constellations is on the rise, urging the need for an optimal constellation design method for complex regional coverage. Traditional constellations are often designed for continuous global coverage, and the few existing regional constellation design methods lead to suboptimal solutions for periodically time-varying or spatially-varying regional coverage requirements. This paper introduces a new general approach to design an optimal constellation pattern that satisfies such complex regional coverage requirements. To this end, the circular convolution nature of the repeating ground track orbit and common ground track constellation is formalized. This formulation enables a scalable constellation pattern analysis for multiple target areas and with multiple sub-constellations. The formalized circular convolution relationship is first used to derive a baseline constellation pattern design method with the conventional assumption of symmetry. Next, a novel method based on binary integer linear programming is developed, which aims to optimally design a constellation pattern with the minimum number of satellites. This binary integer linear programming method is shown to achieve optimal constellation patterns for general problem settings that the baseline method cannot achieve. Five illustrative examples are analyzed to demonstrate the value of the proposed new approach.Comment: 47 pages, 23 figures, Journal of Spacecraft and Rockets (Published

Optimization of Reconfigurable Satellite Constellations Using Simulated Annealing and Genetic Algorithm

Agile Earth observation can be achieved with responsiveness in satellite launches, sensor pointing, or orbit reconfiguration. This study presents a framework for designing reconfigurable satellite constellations capable of both regular Earth observation and disaster monitoring. These observation modes are termed global observation mode and regional observation mode, constituting a reconfigurable satellite constellation (ReCon). Systems engineering approaches are employed to formulate this multidisciplinary problem of co-optimizing satellite design and orbits. Two heuristic methods, simulated annealing (SA) and genetic algorithm (GA), are widely used for discrete combinatorial problems and therefore used in this study to benchmark against a gradient-based method. Point-based SA performed similar or slightly better than the gradient-based method, whereas population-based GA outperformed the other two. The resultant ReCon satellite design is physically feasible and offers performance-to-cost(mass) superior to static constellations. Ongoing research on observation scheduling and constellation management will extend the ReCon applications to radar imaging and radio occultation beyond visible wavelengths and nearby spectrums. Keywords: Earth observation; remote sensing; satellite constellation; reconfigurability; repeat ground tracks; simulated annealing; genetic algorith

A PARETO-FRONTIER ANALYSIS OF PERFORMANCE TRENDS FOR SMALL REGIONAL COVERAGE LEO CONSTELLATION SYSTEMS

As satellites become smaller, cheaper, and quicker to manufacture, constellation systems will be an increasingly attractive means of meeting mission objectives. Optimizing satellite constellation geometries is therefore a topic of considerable interest. As constellation systems become more achievable, providing coverage to specific regions of the Earth will become more common place. Small countries or companies that are currently unable to afford large and expensive constellation systems will now, or in the near future, be able to afford their own constellation systems to meet their individual requirements for small coverage regions. The focus of this thesis was to optimize constellation geometries for small coverage regions with the constellation design limited between 1-6 satellites in a Walker-delta configuration, at an altitude of 200-1500km, and to provide remote sensing coverage with a minimum ground elevation angle of 60 degrees. Few Pareto-frontiers have been developed and analyzed to show the tradeoffs among various performance metrics, especially for this type of constellation system. The performance metrics focus on geometric coverage and include revisit time, daily visibility time, constellation altitude, ground elevation angle, and the number of satellites. The objective space containing these performance metrics were characterized for 5 different regions at latitudes of 0, 22.5, 45, 67.5, and 90 degrees. In addition, the effect of minimum ground elevation angle was studied on the achievable performance of this type of constellation system. Finally, the traditional Walker-delta pattern constraint was relaxed to allow for asymmetrical designs. These designs were compared to see how the Walker-delta pattern performs compared to a more relaxed design space. The goal of this thesis was to provide both a framework as well as obtain and analyze Pareto-frontiers for constellation performance relating to small regional coverage LEO constellation systems. This work provided an in-depth analysis of the trends in both the design and objective space of the obtained Pareto-frontiers. A variation on the εNSGA-II algorithm was utilized along with a MATLAB/STK interface to produce these Pareto-frontiers. The εNSGA-II algorithm is an evolutionary algorithm that was developed by Kalyanmoy Deb to solve complex multi-objective optimization problems. The algorithm used in this study proved to be very efficient at obtaining various Pareto-frontiers. This study was also successful in characterizing the design and solution space surrounding small LEO remote sensing constellation systems providing small regional coverage

Dynamic Constellation Tasking and Management

Responsive orbits have gained much attention in recent years and many AFIT theses have addressed this topic. Specifically, the following topics have been studied: phasing within an orbit, adjusting time of arrival, avoidance, and maneuver detection. This thesis seeks to determine the feasibility of maneuvering satellites from circular (600 km) orbits to eccentric (600 km by 175 km) orbits in order to collect high resolution images for Earth surveillance. Coverage is calculated for multiple 6-satellite constellations. Perturbations for the subject orbits are analyzed and compared to simulation results

Analysis of GPS Satellite Allocation for the United States Nuclear Detonation Detection System (USNDS)

We present an approach for identifying salient input features in high feature to exemplar ratio conditions. Basically we modify the SNR saliency-screening algorithm to improve the solution of the optimal salient feature subset problem. We propose that applying the SNR method to randomly selected subsets (SRSS) has a superior potential to identify the salient features than the traditional SNR algorithm has. Two experimental studies are provided to demonstrate the consistency of the SRSS. In the first experiment we used a noise-corrupted version of the Fisher s Iris classification problem. The first experiment designed to prove the fidelity of the SRSS method. The second application is a real-life industrial problem. The salient features of this dataset are not known beforehand. We compared the performances of the salient feature subsets created by the traditional SNR and the SRSS method. We also realized that the SRSS algorithm improved the current solution to this industrial application

A novel satellite mission concept for upper air water vapour, aerosol and cloud observations using integrated path differential absorption LiDAR limb sounding

We propose a new satellite mission to deliver high quality measurements of upper air water vapour. The concept centres around a LiDAR in limb sounding by occultation geometry, designed to operate as a very long path system for differential absorption measurements. We present a preliminary performance analysis with a system sized to send 75 mJ pulses at 25 Hz at four wavelengths close to 935 nm, to up to 5 microsatellites in a counter-rotating orbit, carrying retroreflectors characterized by a reflected beam divergence of roughly twice the emitted laser beam divergence of 15 µrad. This provides water vapour profiles with a vertical sampling of 110 m; preliminary calculations suggest that the system could detect concentrations of less than 5 ppm. A secondary payload of a fairly conventional medium resolution multispectral radiometer allows wide-swath cloud and aerosol imaging. The total weight and power of the system are estimated at 3 tons and 2,700 W respectively. This novel concept presents significant challenges, including the performance of the lasers in space, the tracking between the main spacecraft and the retroreflectors, the refractive effects of turbulence, and the design of the telescopes to achieve a high signal-to-noise ratio for the high precision measurements. The mission concept was conceived at the Alpbach Summer School 2010

Navigation/traffic control satellite mission study. Volume 1 - Summary

System of satellites, ground stations, and hardware of various user craft for transoceanic traffic contro