Minimum of PDOP and its applications in inter-satellite links (ISL) establishment of Walker-δ constellation

Within the next decade, there will be a number of GNSS (Global Navigation Satellite System) available, i.e. modernized GPS, Galileo, restored GLONASS, BeiDou and many other regional GNSS augmentation systems. Thus, measurement redundancies and geometry of the satellites can be improved. GDOP (Geometric Dilution of Precision) and PDOP (Position Dilution of Precision) are associated with the constellation geometry of satellites, and they are the geometrically determined factors that describe the effect of geometry on the relationship between measurement error and position error. GDOP and PDOP are often used as standards for selecting good satellites to meet the desired positioning precision. In this paper, the related conclusions of minimum of GDOP which was discussed are given, and it is used to study the minimum of PDOP for two cases that the receiver is on the earth’s surface and the receiver is on satellite. The corresponding theorem and constructive solutions of minimum of PDOP are given. Then, the rationality of the ISL (inter-satellite link) establishment criteria in Walker-δ constellation is discussed by using the theory of minimum of PDOP. Finally, the minimum of PDOP is calculated when the number of satellites is 4–10, and these results are verified by using Monte Carlo method.     

GEO/IGSO混合区域导航星座的设计与优化算法

区域导航星座能够以较低成本和较短时间获得目标区域导航能力,且地球同步轨道是构建非极区区域导航星座的重要轨道类型.提出一种基于GEO(地球静止轨道)和IGSO(倾斜地球同步轨道)的区域导航星座设计方法.基于星下点轨迹特性构造对称星座设计参数和优化参数集,并考虑地球扁率长期摄动影响,计算星座轨道参数.以导航服务区的统计GD...     

Experimental and mathematical model of the interactions in the mixed culture of links in the “producer–consumer” cycle

The paper presents a experimental and mathematical model of interactions between invertebrates (the ciliates Paramecium caudatum and the rotifers Brachionus plicatilis) in the “producer–consumer” aquatic biotic cycle with spatially separated components. The model describes the dynamics of the mixed culture of ciliates and rotifers in the “consumer” component, feeding on the mixed algal culture of the “producer” component. It has been found that metabolites of the algae Scenedesmus produce an adverse effect on the reproduction of the ciliates P. caudatum. Taking into account this effect, the results of investigation of the mathematical model were in qualitative agreement with the experimental results. In the “producer–consumer” biotic cycle it was shown that coexistence is impossible in the mixed culture of invertebrates of the “consumer” component. The ciliates P. caudatum are driven out by the rotifers B. plicatilis.