An alternative methodology for the mathematical treatment of GPS positioning
The basic operation of GPS involves the detection and measurement, with a GPS receiver, of data carried on electromagnetic signals transmitted by the earth-orbiting GPS satellite constellation and the computation of the travel time of these received signals. The time measurements are converted to di...
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| Format: | Article |
| Language: | English |
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Elsevier
2011-12-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016811000470 |
| _version_ | 1818671169110278144 |
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| author | Aly M. El-naggar |
| author_facet | Aly M. El-naggar |
| author_sort | Aly M. El-naggar |
| collection | DOAJ |
| description | The basic operation of GPS involves the detection and measurement, with a GPS receiver, of data carried on electromagnetic signals transmitted by the earth-orbiting GPS satellite constellation and the computation of the travel time of these received signals. The time measurements are converted to distance measurements, which can then be used to compute the unknown position and time of the receiver from the known positions of the satellite transmitters and signal transit times. To solve the problem, at least four satellite’s measurements are needed to find user position and receiver time offset. A set of nonlinear navigation equations are formed. These nonlinear equations can be solved using iterative techniques based on linearization by Taylor model. This method is approximate since only the first term of Taylor model is used.
In this paper a simple alternative method is developed to solve the GPS navigation equations directly without linearization and iteration. A practical study was done to evaluate the new model. Performance analysis was conducted using data collected by Trimble 4000SSE dual frequency receiver. The results indicated that the alternative methodology is simple, fast, and accurate as compared to Taylor method. |
| first_indexed | 2024-12-17T07:19:43Z |
| format | Article |
| id | doaj.art-ae4b43e85e7e48418455310977228c11 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-17T07:19:43Z |
| publishDate | 2011-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-ae4b43e85e7e48418455310977228c112022-12-21T21:58:48ZengElsevierAlexandria Engineering Journal1110-01682011-12-0150435936610.1016/j.aej.2011.07.002An alternative methodology for the mathematical treatment of GPS positioningAly M. El-naggarThe basic operation of GPS involves the detection and measurement, with a GPS receiver, of data carried on electromagnetic signals transmitted by the earth-orbiting GPS satellite constellation and the computation of the travel time of these received signals. The time measurements are converted to distance measurements, which can then be used to compute the unknown position and time of the receiver from the known positions of the satellite transmitters and signal transit times. To solve the problem, at least four satellite’s measurements are needed to find user position and receiver time offset. A set of nonlinear navigation equations are formed. These nonlinear equations can be solved using iterative techniques based on linearization by Taylor model. This method is approximate since only the first term of Taylor model is used. In this paper a simple alternative method is developed to solve the GPS navigation equations directly without linearization and iteration. A practical study was done to evaluate the new model. Performance analysis was conducted using data collected by Trimble 4000SSE dual frequency receiver. The results indicated that the alternative methodology is simple, fast, and accurate as compared to Taylor method.http://www.sciencedirect.com/science/article/pii/S1110016811000470GPSNavigation equationsTaylor modelLinearization |
| spellingShingle | Aly M. El-naggar An alternative methodology for the mathematical treatment of GPS positioning Alexandria Engineering Journal GPS Navigation equations Taylor model Linearization |
| title | An alternative methodology for the mathematical treatment of GPS positioning |
| title_full | An alternative methodology for the mathematical treatment of GPS positioning |
| title_fullStr | An alternative methodology for the mathematical treatment of GPS positioning |
| title_full_unstemmed | An alternative methodology for the mathematical treatment of GPS positioning |
| title_short | An alternative methodology for the mathematical treatment of GPS positioning |
| title_sort | alternative methodology for the mathematical treatment of gps positioning |
| topic | GPS Navigation equations Taylor model Linearization |
| url | http://www.sciencedirect.com/science/article/pii/S1110016811000470 |
| work_keys_str_mv | AT alymelnaggar analternativemethodologyforthemathematicaltreatmentofgpspositioning AT alymelnaggar alternativemethodologyforthemathematicaltreatmentofgpspositioning |