**What is GPS**

- A highly accurate positioning system
- Created and managed by the Ministry of Defense
- Born to military requirements
- Developed in anticipation of potential civilian applications
- Based on a constellation of satellites

**Histories of the GPS**

- The system is constantly evolving from 1973
- The first satellite was launched in 1978
- The constellation was completed in 1994
- A new generation of satellites (Block IIR) is replacing those of the block I and II
- Everything is managed by the DoD (Department of Defense)

**The GPS System**

It consists of three parts

- The space segment
- The control segment
- The USER segment

**The space segment**

- 24 orbiting satellites
- Circular orbits on 6 orbital planes of inclined parallel 55° compared to the Equatorial plan.
- 4 satellites equally spaced on each orbital plane very high orbits height 20, 200 11 hours 58 minutes revolution period the height provides greater accuracy and safety

**The control segment**

- 4 ground monitoring stations
- Diego Garci
- Ascention Island Island
- Kwajalein
- Hawaii

Transmit the new ephemeris, the fix for watches, etc.

**The User segment**

- Users for the purposes of air navigation, sea and land
- Geodetic and topographic applications users
- GPS flashlights here.

**Signal structure**

- Two L-band frequencies:
- L1 1575.42 Mhz-
- L2-1227.60 Mhz

- Three modulations (codes):
- Two codes for the distance determination
- Code (c/a): only on L1, freq. 1023 Mhz, l. (29.3 m)
- Code (P): P1 onto L1 and P2 onto L2, freq. 10.23 Mhz length.(29.3 m)

A message code (NAVDATA) on both frequencies:

- Correction data (orbits and clock)
- Satellite status (orbits and health)

**How accurate is it?**

- Depends on some variables
- Time taken to the extent
- Type of receivers used
- Correction algorithm applied to measures

- From 30 to 100 metres for any receiver used independently
- From 1 to 5 meters For differential mode DGPS receivers
- More sophisticated systems < 1 cm accuracy

**How does that work?**

The 5 points on which is based the system

- The trilateration from satellites is the basis of GPS system
- The GPS measures the distance from the satellites by knowing the time taken and the speed of the signal
- In order to measure the distance from the satellites you need a good watch and a fourth satellite
- The satellites transmit their position and knowing the distance, you can calculate the position of the receiver
- Finally, we analyze the various errors due to signal propagation in the atmosphere and the geometry of the satellites

**Trilateration with GPS**

One measure of distance from a point (1 satellite) identifies our location anywhere on the surface of a sphere

We are in any point on the surface of the sphere

The intersection of two balls is a circle

A second measure indicates our location on the intersection of two spheres

A third measure identifies only two points

Points identified by the intersection of two spheres

A fourth measure removes any doubt

Quttaro measures identify a single point

**Trilateration with GPS**

- In theory the three measures are sufficient
- One of the two points could be deleted because absurd (located somewhere in space and moves at high speed)
- We still need the fourth satellite because there are 4 unknowns to be solved:

- Latitude
- Longitude
- Quota
- Time!

**Distance from the satellites**

Distance measurement from a satellite

- You measure the time it takes for the signal to take the Satellite-Receiver path
- You multiply the time taken for the speed of light:

Time (sec) x 300,000 (km/s) = distance - It is necessary to know exactly when the signal has been transmitted
- It is imperative to have a great clock

How do you know when the signal is gone?

- You use the same code (sequence of pulses) on the satellite and receiver
- Synchronizes the receiver’s clock with that of the satellites
- In this way the satellites and receivers generate the same code at the same time
- It is now possible to compare the code received with that generated and measure the time difference between the two (i.e. the time difference between the time of signal reception and the time on the ground)

**The importance of the clock**

- To measure distance Satellite-Receiver requires a highly accurate clock

Ensures that the satellites and receivers are synchronized - Most satellites have atomic clocks on board

Accurate, but quite expensive - For a stable clock receivers

Thanks for the information of the fourth satellite we can synchronize the clock in the receiver and fix the unknown time

**Situation with sketchy clock**

Wrong location due to the error of watches

**Three sizes with inaccurate clock**

Wrong location due to the error of watches

The third measure does not intersect with the other two in the same location

**The satellites**

- Are about 20,000 km altitude
- The satellite itself broadcasts its location to that of all other satellites (the Almanac)
- Very high orbit:

-Makes the bike very stable satellites

-Absence of atmospheric friction

-Terrestrial coverage - Controlled by the DoD (Department of Defense)

-Their orbit carries them over to American territory at least once a day

-DoD transmits corrections to orbit satellites

**Source of the errors**

The GPS does not work in a vacuum

- Ionosphere (80-500 km)

Portion of the dense atmosphere of electrically charged particles deflect radio waves - Troposphere (0-10 km)

Portion of the atmosphere where you create the main meteorological phenomena

Characterized by a strong presence of water varies widely from area to area

- Errors in the satellite clock and orbit

-Very small and mostly fixed by DoD - Receiver errors

-Problems due to instability of the oscillator (clock)

-Noise in measures introduced by the receiver itself - Multipath (multiple locations)

-The signal bounces off reflective surfaces and interferes with the direct signal

-Well-made receivers and antennas are capable of reducing the problem - DOP

The geometry of the satellites affect accuracy

**Source of the errors
Selective Availability (S/A)**

- The U.S. Government can introduce an artificial error on the watch of satellites and their orbits to degrade the accuracy of the system:

-Prevents hostile Nations to use the GPS for military purposes

-When enabled, is the major source of error - The S/A is the sum of two errors:

-Epsilon: maniolazione ephemeris data are biased (per hour)

-Dither: variations repetitively to watches (each 4-15 minutes)

**Source of the errors
Geometry of the satellites (PDO)**

The error increases if the satellites formed between their acute angles

It is expressed through these values

- Gdop-Geometric Diluition Of Precision
- Pdop-Position Diluition Of Precision
- Hdop-Horizontal Diluition Of Precision
- Vdop-Vertical Diluition Of Precision
- Edop-East Diluition Of Precision
- Ndop-North Diluition Of Precision
- Tdop-Time Diluition Of Precision
- Gdop
^{2 = }^{2}+^{2}Tpod Pdop - Pdop
^{2 = }^{2}+^{2}Vpod Hdop - Hdop
^{2 = }^{2}+^{2}Npod Edop

- Gdop

Summary

Typical errors:

- Satellite clock 0.5 m
- Ephemeris 0.5 m
- Receiver 1.0 m
- Iono/troposphere 3.5 m
- Total (rms) 5-10 m

Multiplying by the HDOP you causes a about 8-30 m

With S/A enable 100 m

**Summary**

- The trilateration from satellites is the basis of GPS system
- The GPS measures the distance from the satellites using the signals traveling at the speed of light
- To measure the distance from the satellites you need a good watch and a fourth satellite
- In addition to measuring the distance you need to know the position of the satellites
- For the location we analyze the various errors due to the ionosphere, troposphere and geometry of the satellites

**The GPS in topography**

- Sources of error affect equally on all receivers who see the same satellites
- The relative position of two or more GPS receivers can be known with great precision
- The analysis of received signals simultaneously from 2 door tools in precision of even a few millimeters
- GPS can measure long vectors (even hundreds of km)
- It works 24 hours a day and in any weather condition
- The GPS is used in topography because it does not require intervisibilità of the points to be noted

**Differential correction**

- Data logging at a point is error-prone
- Each of these errors is identified by GPS time
- At the same time the same error affects all receivers operating nearby
- To eliminate errors DGPS differential measurement is used

With differential calculus you eliminate errors that affect two measurements made at the same time - Differential calculus can be made:

-a posteriori in “post-processing”

-immediately in the measure phase in “Real time”

**Sources of error**

- Geometry of the satellites (PDOP)
- Ephemeris——> removed from DGPS
- Watch satellites——> removed from DGPS
- Ionospheric delay——> removed from DGPS
- Tropospheric delay——> removed from DGPS
- Selective Availability——> removed from DGPS
- Multipath
- Receiver clock drift
- Noise receiver
- Satellite (unhealty)——> not used

**Errors**

**Significant topographic techniques**

- Static
- Fast static
- Kinematic

**Static**

- It is the most accurate (< 5 mm + 1 ppm)
- It’s the slowest (> 1 hour parking brake)
- It is the most reliable (hardly mistaken)
- It is the simplest (fieldwork = 0)

**Fast Static**

- Similar to static holding time much smaller (5-30 min.) (requires at least 5 satellites)
- Possible thanks to more powerful SW and HW
- The static “really fast” you get with dual-frequency receivers or dual constellation.

-A lot more information than the single frequency: L1, L2, L1 + L2, L1-L2

-The static fast in single frequency relies exclusively to SW

- The same simplicity of static
- Same accuracy of static (?!?)
- Same reliability of static (?!?)

* Mathematical level is all true. Actually the accuracy is slightly lower.The reliability depends on the sensitivity of field representative (DOP, number of satellites, signal-to-noise ratio …)

**Kinematic**

- It’s the fastest (just 1 second per point)
- It is the most difficult (we must not lose the signal from the satellites)
- Should have the same precision of static but compared to this is much more influenced by DOP (we get about 3-10 cm)
- Requires initialization when starting the survey and a new initialization whenever you have fewer than 4 satellites
- Initialization with only L1—-static
- Initializing with L1 + L2—Static, static-fast, O.T.F. (On The Fly) (on the fly)
- Data can be captured in constant motion (kinematic) or moving from one point to another Pausing an instant (STOP and GO)

Initializing with only L1

- Antenna Swap (Exchange of antennas)
- Fast static/Static (at least 20 minutes)
- Initialization using vectors (or points) Note
- Initialization always standing still

Initializing with L1 + L2

- Antenna Swap (Exchange of antennas)
- Fast static/Static (2-3 minutes)
- O.T.F. on the fly (the fly)
- Initialization using vectors (or points) Note
- 2-3 minutes of data, even on the go
- The data can be acquired while walking toward the point to be noted
- It’s the most productive technique ever