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)
Direct light propagation measurement The noise in measuring the time will be proportional the duration of the pulse For mm-level measurements, need a pulse of the duration equivalent of a few millimeters Pulse strength also enters you need to be able to detect the return pulse) In general, direct time measurement needs expensive equipment a laser system capable of mm-level ranging to satellites costs - $1M 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 6 Direct light propagation measurement • The noise in measuring the time will be proportional the duration of the pulse • For mm-level measurements, need a pulse of the duration equivalent of a few millimeters. • Pulse strength also enters (you need to be able to detect the return pulse). • In general, direct time measurement needs expensive equipment. • A laser system capable of mm-level ranging to satellites costs ~$1M
Reflecting the signal back With optical (laser) systems you want to reflect signal back: a plain mirror wont do this unless perfectly normal to ray ·Usea" corner cube” reflector.n2 D shown on next page For satellites, need to"spoil the cube (i.e corner not exactly 90 degrees because station not where it was when signal transmitted) 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 7 Reflecting the signal back • With optical (laser) systems you want to reflect signal back: a plain mirror won’t do this unless perfectly normal to ray. • Use a “corner cube” reflector. In 2-D shown on next page • For satellites, need to “spoil” the cube (i.e., corner not exactly 90 degrees because station not where it was when signal transmitted)
Corner cube reflector Corner Cube reflector The return angle is twice the coming and outgoing rays are parallel corner angle For go degree 90- corner. return Is 180 degrees 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 8 Corner cube reflector Corner Cube Reflector Incoming and outgoing rays are parallel i i 90-i 90-i The return angle is twice the corner angle For 90 degree corner, return is 180 degrees
Alternative way to measure distance Instead of generating a short pulse and measuring round trip propagation time(also requires return pulse be detected), you can measure phase ditterence between outgoing and incoming continuous wave Schematic shown on next page Basic method used by interferometer 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 9 Alternative way to measure distance • Instead of generating a short pulse and measuring round trip propagation time (also requires return pulse be detected), you can measure phase difference between outgoing and incoming continuous wave • Schematic shown on next page • Basic method used by interferometer
Difference measurement(stays constant with time and depends on distance) 1.00 Outgoing Incoming 0.00 Outgoing + coming+△t 0.4 .8 4 Distance 02/25/02 12.540Lec06
02/25/02 12.540 Lec 06 10 Difference measurement (stays constant with time and depends on distance) -1.00 -0.50 0.00 0.50 1.00 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Outgoing Incoming Outgoing + ∆t Incoming + ∆t Signal voltage Distance
