A conformal restriction measure is a probability measure which is used to describe the law of a random connected subset in a simply connected domain that satisfies a certain conformal restriction property. Usually the...A conformal restriction measure is a probability measure which is used to describe the law of a random connected subset in a simply connected domain that satisfies a certain conformal restriction property. Usually there are three kinds of conformal restriction measures: one (called the chordal restriction measure) has two given boundary points of the random set, the second (called the radial restriction measure) has one boundary point and one interior point in the random set, and the third (called the tri-chordal restriction measure) has three boundary points in the random set. In this article, we will define a new probability measure such that the random set associated to it contains one given interior point and does not intersect with the boundary. Furthermore, we will show that this measure can be characterized by one parameter;we will also construct this one-parameter family of measures in two ways and obtain several properties.展开更多
In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points...In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.展开更多
文摘A conformal restriction measure is a probability measure which is used to describe the law of a random connected subset in a simply connected domain that satisfies a certain conformal restriction property. Usually there are three kinds of conformal restriction measures: one (called the chordal restriction measure) has two given boundary points of the random set, the second (called the radial restriction measure) has one boundary point and one interior point in the random set, and the third (called the tri-chordal restriction measure) has three boundary points in the random set. In this article, we will define a new probability measure such that the random set associated to it contains one given interior point and does not intersect with the boundary. Furthermore, we will show that this measure can be characterized by one parameter;we will also construct this one-parameter family of measures in two ways and obtain several properties.
基金supported by the National Natural Science Foundation of China(Grant Nos.11773060,11973074,U1831137 and 11703070)National Key Basic Research and Development Program(2018YFA0404702)+1 种基金Shanghai Key Laboratory of Space Navigation and Positioning(3912DZ227330001)the Key Laboratory for Radio Astronomy of CAS。
文摘In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.
