Abstract—In a variety of satellite navigation and positioning applications, choosing the right satellites for positioning is crucial to ease the computational load on satellite selection systems. To further alleviate the processing demands on receivers, a satellite selection method using the Gibbs sampler has been developed. This process begins by randomly selecting visible satellites and grouping them as an initial selection strategy. The effectiveness of this strategy is assessed using the geometric dilution of precision as a key metric. The strategy is refined through the Gibbs sampler algorithm's conditional probability distribution model, progressively moving towards the most efficient satellite combination that offers an improved geometric distribution in space. Our research demonstrates that by employing a neural network-based model, we can optimize satellite constellations for minimal latency. We have found that deploying 12 satellites results in latency levels of less than 5 milliseconds and continuous uptime, significantly enhancing communication efficiency. This research highlights the potential for neural network models to revolutionize satellite constellation design for improved performance.