Optimal Walker Constellation Design of LEO-Based Global Navigation and Augmentation System

Abstract

Low Earth orbit (LEO) satellites located at altitudes of 500 km~1500 km can carry much stronger signals and move faster than medium Earth orbit (MEO) satellites at about a 20,000 km altitude. Taking advantage of these features, LEO satellites promise to make contributions to navigation and positioning where global navigation satellite system (GNSS) signals are blocked as well as the rapid convergence of precise point positioning (PPP). In this paper, LEO-based optimal global navigation and augmentation constellations are designed by a non-dominated sorting genetic algorithm III (NSGA-III) and genetic algorithm (GA), respectively. Additionally, a LEO augmentation constellation with GNSS satellites included is designed using the NSGA-III. For global navigation constellations, the results demonstrate that the optimal constellations with a near-polar Walker configuration need 264, 240, 210, 210, 200, 190 and 180 satellites with altitudes of 900, 1000, 1100, 1200, 1300, 1400 and 1500 km, respectively. For global augmentation constellations at an altitude of 900 km, for instance, 72, 91, and 108 satellites are required in order to achieve a global average of four, five and six visible satellites for an elevation angle above 7 degrees with one Walker constellation. To achieve a more even coverage, a hybrid constellation with two Walker constellations is also presented. On this basis, the GDOPs (geometric dilution of precision) of the GNSS with and without an LEO constellation are compared. In addition, we prove that the computation efficiency of the constellation design can be considerably improved by using master–slave parallel computing.

Potential of a SAR Small-Satellite Constellation for Rapid Monitoring of Flood Extent

“…Supposing the reference satellite's RAAN is RAAN o [ • ] and its mean anomaly (MA) -the position of satellites on each orbit plane-is MA o [ • ]. Following the WC method, as shown in Figure A1 (right), RAAN i [ • ]-the RAAN of the i-th orbit-and MA i,j [ • ]-the MA of the j-th satellite on the i-th orbit-can be calculated as follows [24]:…”

Survey on Optimization Methods for LEO-Satellite-Based Networks with Applications in Future Autonomous Transportation

“…In [13], a Genetic Algorithm (GA)-based optimization, with Geometric Dilution of Precision (GDOP) and the number of satellites as optimization metrics, was employed for space-segment optimization of a LEO-based navigation system relying on a Walker constellation. It was found that good LEO coverage for navigation purposes can be reached with constellations between 180 and 264 and satellites placed at orbital altitudes between 900 and 1500 km.…”

“…With regards to the space segment, an objective function can simply be any of the already mentioned metrics (i.e., C/N 0 for GNSS or LEO-PNT applications as well as for high communication throughputs), some combination of them (i.e., C/N 0 and GDOP), or completely custom crafted as in [20,74]. As an example, we present Equation (13), which defines an objective function f (x) that combines the C/N 0 and the launch cost C launch using some weights w 1 and w 2 , where x is the vector of the required parameters for the calculations. Note that in a typical ML-based method, these weights are fine-tuned by the optimization process, but they can also be tuned manually, which is typical for evolutionary algorithms.…”

Simulation Experiment and Analysis of GNSS/INS/LEO/5G Integrated Navigation Based on Federated Filtering Algorithm

“…Both GNSS and LEO constellation simulations in this paper are Walker constellations and aim to optimize constellation coverage with a given number of satellites. Walker constellation is proposed after Ballard's improvement in literature [31], forming a constellation system widely used in the field of orbit design [32].…”