GPS notes

Global Navigation Satellite System (GNSS) or Global Positioning System (GPS) is a power tool for positioning and applying to Geophysical usages. There are typical 2-kinds of positioning methods:(1)code range (2) phase range.

(1)C/A code: For common user (i.e. car or phone), GPS receives the C/A code from satellite.

C/A code directly carry the time information, by simple calculation:

C1=c*dt1

(c=speed of light; dt1=transition time from satellite to receiver)

Receiver's location (X,Y,Z) can easily be resolved by simultaneous equation. (* Satellite's positions are known and provide in signal (https://igscb.jpl.nasa.gov/)).

This accuracy of code positioning could satisfy most of the users, however, for the Geophysical usage, we cannot use the positioning results in a uncertainty of meter-level.

Thus, the phase positioning is required.

(2)L1 & L2 phase: In order to transfer information, GPS satellite carrier the information by "carrier wave".

The wave is a periodic function with frequency:L1=1575.42 MHz; L2=1227.60 MHz which equivalent to λL1=19 cm; λL2=24 cm. By measuring the "phase" of the wave, we could calculate the position as a mm-level.

But, the most difficult of phase positioning is to determine the number of "whole phase", for example:

(1+pi/4)=(10+pi/4)=(100+pi/4)=(10000+pi/4)=N+pi/4

All the "phase" observations show exactly the same result of pi/4, the most important thing is to find out what is the value of N or Ambiguity. (Strategics including fix/free ambiguity, or code range). As ambiguity been solved, the positioning results could be greatly improved.

SIGNAL NOISE

Any inconsiderable noise can be significant magnified because the speed of transition radiowave is nearly 300000000 m/s, that is, to evaluate the positioning in mm-level, the uncertainty of time should not greater than 3*10^-11 sec. Thus, the time and range information should be perfectly controlled. The most common error in signal are caused by Atmosphere (=Ionosphere effect+Troposphere effect), clock error (=satellite+receiver) and multi-path effect. Others reduction are depended on the object of research (e.g. tide effect).

Atmosphere effect

When signal transmits throughout Ionosphere, the interaction between radiowave and the charged ions can delay the radiowave. The time of delay depends on the density of ions and the frequency of radiowave (this also called wave dispersion). For a dual-frequency receiver (receives both L1 and L2), delay time can be calculated by simultaneous equation (http://www.navipedia.net/index.php/Ionospheric_Delay).This also called Ionosphere-free measurement.

Not only Ionosphere but also Troposphere could cause the signal delay. However for radiowave of frequency smaller than 15 GHz do not have dispersion effect. Thus, Troposphere delay can only be corrected by troposphere model (e.g. Vienna Mapping Functions (VMF1)).

Clock bias

The clock bias plays an important role in GPS positioning, which including the error from satellite (dt_s) & receiver (dt_r). Clock bias can be corrected by differential GPS method by more than 4 observations.

Assuming unknowns are [X,Y,Z,dt(=dt_s+dt_r)], (this also provides the key that why we need at least 4-satellite for positioning) by single different the signal from same satellite in 2-stations, the common clock error from satellite can be removed (single difference in satellite). By this conception, we can single different the signal from 2-satellites in the same station to eliminate the receiver clock error (single difference in station). Combine these two single difference, we can eliminate all the clock bias (double difference method), which is the conception of relatively positioning (e.g. GAMIT/GLOBOK). Another methodology uses single difference in station only to eliminate the dominant clock bias from receiver clock and speed up calculation, which called PPP (Precise Point Positioning; e.g. GIPSY/OASIS).

Multi-path effect

The multi-path effect occurs when signal be reflected by surrounding object then transmit into receiver. This effect is hard to model because the reflection time depend on the environment of station. We can only reduce the signal from reflecting object by cutoff the signal from satellite which lower than 15 degree in common.