{"title":"关于飞机上排放源的识别","authors":"N.V. Arakelyan, Y. Kutoyants","doi":"10.46991/pysu:a/2019.53.2.075","DOIUrl":null,"url":null,"abstract":"We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $ K $ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"35 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"ON THE IDENTIFICATION OF THE SOURCE OF EMISSION ON THE PLANE\",\"authors\":\"N.V. Arakelyan, Y. Kutoyants\",\"doi\":\"10.46991/pysu:a/2019.53.2.075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $ K $ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2019.53.2.075\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2019.53.2.075","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE IDENTIFICATION OF THE SOURCE OF EMISSION ON THE PLANE
We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $ K $ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.