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Beginning with the definition of autonomous time reference and its generation principle, the relativistic effects on the essential factors including satellite clock relativity and crosslink measurements relativity are analyzed in this paper, and calculated by taking GPS and BDS constellations for examples. The following conclusions are reached: 1) the satellite clock relativity effect has a constant part and a periodic part, and the constant part is compensated by terrestrial frequency adjustment, while the periodic clock error is corrected in real time according to the ephemeris; on the basis of the adjustment of the satellite clock, 2) the crosslink pseudo-range (PR) measurement relativity effect between satellites inview is mainly the relativity effect on the light time delay, and can reach cm-level for medium and high orbits satellite; 3) the crosslink Doppler measurement relativity effect is due to the period part of clock frequency offset, and its effect on radial velocity is around 1cm/s for medium and high orbits satellite with small eccentricity. The above-mentioned analyses can help to improve the accuracy of autonomous time reference, and provide certain reference significance for the research of deep-space measurement and space-based time reference establishment. [ABSTRACT FROM AUTHOR]

• To study Δ -Choquets integral on time scales with respect to non-additive measure, more precisely, a distorted Lebesgue Δ -measure. That is also aspecial case of Choquet integral with respect to abstract fuzzy measure. • This integral unifies both continuous and discrete Choquet integral. Further, results unify and extend the results reported in the literature. • A short note on Δ -Choquet integral on time scale and Caputo-Fabrizio fractional derivative on time scale is discussed. • Stieltjes distorted type-I and II Lebesgue measures on time scales are provided to present another special Choquet integral. • Various examples are given to illustrate the outcomes. The fundamental purpose of this work is to analyze Δ -Choquet integrals on time scales which is a special case of Choquet integral on abstract fuzzy (non-additive) measure space. We first present a Δ -Choquet integral with respect to non-additive Δ -measure or more precisely a distorted Lebesgue Δ -measure on an arbitrary time scale. Consequently, we come up with a more general integral than the standard Choquet integral of continuous and discrete calculus. Its use can be seen as convenient in economics, decision making, artificial intelligence, and many more. Particularly, in economics, most of the models are dynamic models (continuous and/or discrete), and those can be easily studied on time scales. Further, some basic essential results and properties of the general integral are studied. For instance, we discuss translation, homogeneity, linearity, and many more with respect to the functions and measures of the integral. Then, after that, we present some theorems for computing the integral. The findings agree to unify and extend a number of well-known results reported in the literature to a broader calculus, including continuous, discrete, and quantum calculus, among others. We also evaluate the integral on an invariant under the translation of time scales. Besides, a short note on Δ -Choquet integral with the Caputo-Fabrizio fractional derivative on the time scales is given. The significance of the outcomes is also further enhanced by a variety of interesting examples. Moreover, eventually, we stop findings after discussing an another way to calculate the Δ -Choquet integral on the time scales. To do this, we define Stieltjes distorted types-I and II Lebesgue Δ -measures on time scales which are accomplished with the help of distorted Lebesgue Δ -measure. [ABSTRACT FROM AUTHOR]