{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T16:28:45Z","timestamp":1785256125473,"version":"3.55.0"},"reference-count":19,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The rapid development of low earth orbit (LEO) satellite constellations for navigation augmentation represents significant challenges in optimizing coverage performance while minimizing system complexity. A hybrid optimization algorithm based on pelican optimization algorithm and quantum particle swarm optimization (POA-QPSO) is proposed in this paper for multi-objective optimization design of dual-layer Walker constellations. The algorithm integrates the global search capability of the POA and the local exploitation ability of QPSO, effectively balancing exploration and exploitation through a probability-driven dual-phase search mechanism, a three-tier adaptive parameter adjustment strategy, and a pareto frontier maintenance mechanism. Probability factor and quantum tunneling facilitate low-cost deep search in complex non-convex environments. Experiments demonstrate that the algorithm outperforms MOPOA and MOPSO on ZDT test functions, with an 18.5% improvement in IGD metrics. In LEO constellation optimization, the designed dual-layer configuration (800 km\/144 satellites in the first layer and 1426 km\/56 satellites in the second layer) achieves a 92.7% global coverage, with an average PDOP of 1.78 and 5.8 visible satellites in polar regions. Furthermore, comparative benchmark tests show that the proposed solution outperforms most mainstream algorithms and performs better than traditional medium Earth orbit satellite systems in mid-to-high latitude regions. This research provides an efficient solution for LEO navigation augmentation system design.<\/jats:p>","DOI":"10.3390\/s26041391","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T08:58:21Z","timestamp":1771837101000},"page":"1391","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A POA-QPSO Hybrid Algorithm for Multi-Objective Optimization of Dual-Layer Walker Constellations"],"prefix":"10.3390","volume":"26","author":[{"given":"Yinuo","family":"Wang","sequence":"first","affiliation":[{"name":"School of Sensing Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyuan","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Sensing Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianwen","family":"Du","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Nanjing Audit University Jinshen College, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuchu","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Sensing Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, Z., Tian, F., Jin, J., and Liu, H. 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