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Optimizing the correlation properties of spreading codes is critical for minimizing inter-channel interference in satellite navigation systems. By improving the codes' correlation sidelobes, we can enhance navigation performance while minimizing the required spreading code lengths. In the case of low-earth orbit (LEO) satellite navigation, shorter code lengths (on the order of a hundred) are preferred due to their ability to achieve fast signal acquisition. Additionally, the relatively high signal-to-noise ratio in LEO systems reduces the need for longer spreading codes to mitigate inter-channel interference. In this work, we propose a two-stage block coordinate descent (BCD) method which optimizes the codes' correlation properties while enforcing the autocorrelation sidelobe zero property. In each iteration of the BCD method, we solve a mixed-integer convex program over a block of 25 binary variables. Our method is applicable to spreading code families of arbitrary sizes and lengths, and we demonstrate its effectiveness for a problem with 66 length-127 codes and a problem with 130 length-257 codes. [ABSTRACT FROM AUTHOR]

There has been a growing interest in using small satellites (SmallSats) for a future lunar navigation and communication satellite system (LNCSS). We conceptualize the design of a SmallSat-based LNCSS with Earth-global positioning system (GPS) time transfer that provides navigation and communication services near the lunar south pole. A hybrid constellation design is formulated, wherein all satellites provide navigation services while only a fraction are communication-enabled. Using Systems Tool Kit software, we examine various LNCSS case studies based on an elliptical lunar frozen orbit with a lower-grade chip-scale atomic clock. Case studies are evaluated in terms of (1) navigation considerations, including position and timing accuracy, lunar user equivalent ranging error, and dilution of precision, (2) communication considerations, including data volume, availability, and data rate, and (3) SmallSat factors, including cost, size, weight, and power. We performed a trade-off analysis for satisfying the criteria outlined by international space agencies while designing low-cost, low-SWaP lunar constellations. [ABSTRACT FROM AUTHOR]

There is growing interest in designing a future lunar navigation satellite system (LNSS) while utilizing a SmallSat platform. However, many design decisions, e.g., regarding the satellite clock and lunar orbit, are yet to be finalized. In our prior work, we developed an LNSS architecture that leverages intermittently available Earth-GPS signals to compute timing corrections, thereby alleviating the need for a higher-grade onboard clock. In this work, we formulate twenty case studies with different grades of clocks and lunar orbits to analyze the trade-offs in designing a SmallSat-based LNSS with time transfer from the Earth GPS. For each case study, the accuracy of ranging signals is assessed via the lunar user equivalent range error (UERE). Even with lower-grade clocks, the lunar UERE exhibits performance comparable to that of the Earth GPS. Furthermore, variations in the lunar UERE are also examined when the available Earth-GPS measurements are processed at different rates. [ABSTRACT FROM AUTHOR]

For the future lunar navigation satellite system (LNSS), a GPS-like constellation for the Moon, NASA has expressed interest in using a smallsat platform. However, many design decisions have yet to be finalized, including the orbit, constellation, and onboard clock. Furthermore, designing a dedicated smallsat-based LNSS limits the payload capacity, thus restricting the size, weight, and power (SWaP) of the onboard clock. We propose an LNSS design with time transfer from intermittently available GPS signals wherein we design a Kalman filter to estimate timing corrections for a low-SWaP clock. Additionally, we devise a lunar User Equivalent Range Error (UERE) metric to characterize the ranging accuracy of signals transmitted by an LNSS satellite. We further validate our time-transfer technique with simulations of an LNSS satellite in an elliptical lunar frozen orbit (ELFO) with an onboard chip scale atomic clock (CSAC) while analyzing the visibility effects of GPS, timing errors, and lunar UERE across ELFOs. [ABSTRACT FROM AUTHOR]

With the birth of the next-generation GPS III constellation and the upcoming launch of the Navigation Technology Satellite-3 (NTS-3) testing platform to explore future technologies for GPS, we are indeed entering a new era of satellite navigation. Correspondingly, it is time to revisit the design methods of the GPS spreading code families. In this work, we develop a natural evolution strategy (NES) machine-learning algorithm with a Gaussian proposal distribution which constructs high-quality families of spreading code sequences. We minimize the maximum between the mean-squared auto-correlation and the mean-squared cross-correlation and demonstrate the ability of our algorithm to achieve better performance than well-chosen families of equal-length Gold codes and Weil codes, for sequences of up to length-1023 and length-1031 bits and family sizes of up to 31 codes. Furthermore, we compare our algorithm with an analogous genetic algorithm implementation assigned the same code evaluation metric. To the best of the authors' knowledge, this is the first work to explore using a machine-learning approach for designing navigation spreading code sequences. [ABSTRACT FROM AUTHOR]