The evaluation of the effectiveness of global navigation satellite system (GNSS) spoofing and jamming equipment is not only an important means of enhancing the power of modern satellite navigation countermeasures, but also a dynamic decision-making problem, whose complexity manifests as the uncertainty of information used to make decisions (e.g., fuzziness, randomness, and dynamics). Previously, full consideration was given to the dynamics of decision information, as well the fuzzy, stochastic problems of quantitative and qualitative data when integrated with subjective and objective information. In this study, first, a spoofing mode index was established based on the performance analysis results of the spoofing equipment and target receivers during antagonized navigation. Second, a combined interval number eigenvalue method (IEM) algorithm with ternary association numbers, and entropy-weighting of the interval were used to combine weights, while considering the uncertainty of judged index weights and their subjectivity. Using a fuzzy comprehensive assessment of the interval and the superposition of multiple expertderived joint scores, a profit matrix was constructed and solved using game theory to reveal the advantages of this approach in dealing with dynamic problems. Finally, the uncertainty of decision information was fully considered by applying the proposed method to practical application and dynamic analysis. INDEX TERMS GNSS spoofing and jamming equipment, spoofing mode index, game theory, combination weighting, interval-valued fuzzy comprehensive assessment, interval number eigenvalue method.
The use of low earth orbit (LEO) satellites to enhance the performance of global navigation satellite system navigation and positioning services has become a popular research topic. In this study, NSGA‐III optimisation algorithm was used to design two hybrid configurations of 177 and 186 LEO constellations for enhancing the BeiDou Satellite Navigation System (BDS). Under the enhanced effect of optimisation constellation, the global average geometric dilution of precision (GDOP) of BDS was reduced to 0.8 ± 0.1, and the maximum GDOP was reduced from 2.4 to less than 1.1 (54.2% reduction). In order to verify the contribution of the two constellations to the convergence time and positioning accuracy of BDS precise point positioning (PPP), a LEO enhanced BDS PPP simulation experiment was carried out using International GNSS Service data from five stations. The results show that after 10 min of static positioning, both LEO constellations improved the positioning accuracy of BDS from the decimetre level to less than 5 cm. The maximum improvement for 177 and 186 LEO was 95.0% and 96.9%, respectively. Additionally, the convergence time for 177 and 186 LEO reduced to less than 3.5 and 3 min, and the maximum improvement was 93.5% and 95.2%, respectively. Overall, both constellations can improve the positioning accuracy and convergence time of BDS PPP.
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