12. 540 Principles of the Global Positioning System Lecture 04 Prof. Thomas Herring 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 1 12.540 Principles of the Global Positioning System Lecture 04 Prof. Thomas Herring
GPS Observables Today' s class we start discussing the nature of gs observables and the methods used to make range and phase measurements Start with idea of remotely measuring distances Introduce range measurement systems and concepts used in graphically representing electromagnetic signals Any questions on homework? 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 2 GPS Observables • Today’s class we start discussing the nature of GPS observables and the methods used to make range and phase measurements • Start with idea of remotely measuring distances • Introduce range measurement systems and concepts used in graphically representing electromagnetic signals • Any questions on homework?
Distance measurement What are some of the methods used to measure distance? We have talked about Direct measurement with a ruler ferred distances by measuring angles in triangles Distance measurement using the speed of light (light propagation time) GPS methods is related to measuring g propagation time but not directly 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 3 Distance measurement • What are some of the methods used to measure distance? • We have talked about: – Direct measurement with a “ruler” – Inferred distances by measuring angles in triangles – Distance measurement using the speed of light (light propagation time) • GPS methods is related to measuring light propagation time but not directly
Direct light propagation time Distance can be measured directly by sending a pulse and measuring how it takes to travel between two points Most common method is to reflect the signal and the time between when the pulse was transmitted and when the reflected signal returns System used in radar and satellite laser rangIng 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 4 Direct light propagation time • Distance can be measured directly by sending a pulse and measuring how it takes to travel between two points. • Most common method is to reflect the signal and the time between when the pulse was transmitted and when the reflected signal returns. • System used in radar and satellite laser ranging
Direct light propagation delay To measure a distance to 1 mm requires timing accuracy of 3x10-12 seconds(3 picoseconds) Timing accuracy needs to be maintained over the flight time. For satellite at 1000km distance, this is 3 millisecond Clock stability needed 3ps/3ms=10 A clock with this longtime stability would gain or lose 0.03 seconds in a year(10-9*86400"365) (Clock short term and long term stabilities are usually very different --Characterized by Allan Variance) 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 5 Direct light propagation delay • To measure a distance to 1 mm requires timing accuracy of 3x10-12 seconds (3 picoseconds) • Timing accuracy needs to be maintained over the “flight time”. For satellite at 1000km distance, this is 3 millisecond. • Clock stability needed 3ps/3ms = 10-9 • A clock with this longtime stability would gain or lose 0.03 seconds in a year (10-9*86400*365) • (Clock short term and long term stabilities are usually very different -- Characterized by Allan Variance)