Some Improvements on Relativistic Positioning Systems
We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2018-10-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.21042/AMNS.2018.1.00012 |
| _version_ | 1818744660530561024 |
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| author | Alfonso Màrius Josep Fullana i Milán Diego Pascual Sáez Córdoba Josep Vicent Arnau i Colmenero Neus Puchades |
| author_facet | Alfonso Màrius Josep Fullana i Milán Diego Pascual Sáez Córdoba Josep Vicent Arnau i Colmenero Neus Puchades |
| author_sort | Alfonso Màrius Josep Fullana i |
| collection | DOAJ |
| description | We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropriate set of four satellites which are not seen too close to the same circumference in the sky. Errors also increase as the user spacecraft separates from the emission satellite region, since the tetrahedron volume decreases.We propose a method to autonomously potion a user-spacecraft which can test our method. This positioning should be compared with those obtained by current methods. Finally, a proposal to position a user-spacecraft moving far from Earth, with suitable devices (autonomous), is presented. |
| first_indexed | 2024-12-18T02:47:50Z |
| format | Article |
| id | doaj.art-cfa9dbb63ede4de8984615dbca75cc54 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-18T02:47:50Z |
| publishDate | 2018-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-cfa9dbb63ede4de8984615dbca75cc542022-12-21T21:23:31ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562018-10-013116116610.21042/AMNS.2018.1.00012Some Improvements on Relativistic Positioning SystemsAlfonso Màrius Josep Fullana i0Milán Diego Pascual Sáez1Córdoba Josep Vicent Arnau i2Colmenero Neus Puchades3Institut de Matemàtica Multidisplinar, Universitat Politècnica de València, E-46022, València, SpainDepartament d’Astronomia i Astrofísica, Universitat de València, E-46100 Burjassot, València, SpainDepartament de Matemàtica Aplicada, Universitat de València, E-46100, Burjassot, València, SpainDepartament d’Astronomia i Astrofísica, Universitat de València, E-46100 Burjassot, València, SpainWe make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropriate set of four satellites which are not seen too close to the same circumference in the sky. Errors also increase as the user spacecraft separates from the emission satellite region, since the tetrahedron volume decreases.We propose a method to autonomously potion a user-spacecraft which can test our method. This positioning should be compared with those obtained by current methods. Finally, a proposal to position a user-spacecraft moving far from Earth, with suitable devices (autonomous), is presented.https://doi.org/10.21042/AMNS.2018.1.00012astronomy and astrophysicsmathematical physicsgeneral relativityrelativistic positioning systemsnumerical methods35q8537m9983c05 |
| spellingShingle | Alfonso Màrius Josep Fullana i Milán Diego Pascual Sáez Córdoba Josep Vicent Arnau i Colmenero Neus Puchades Some Improvements on Relativistic Positioning Systems Applied Mathematics and Nonlinear Sciences astronomy and astrophysics mathematical physics general relativity relativistic positioning systems numerical methods 35q85 37m99 83c05 |
| title | Some Improvements on Relativistic Positioning Systems |
| title_full | Some Improvements on Relativistic Positioning Systems |
| title_fullStr | Some Improvements on Relativistic Positioning Systems |
| title_full_unstemmed | Some Improvements on Relativistic Positioning Systems |
| title_short | Some Improvements on Relativistic Positioning Systems |
| title_sort | some improvements on relativistic positioning systems |
| topic | astronomy and astrophysics mathematical physics general relativity relativistic positioning systems numerical methods 35q85 37m99 83c05 |
| url | https://doi.org/10.21042/AMNS.2018.1.00012 |
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