## Tuesday, May 11, 2010

### GPS Fundamentals

The Global Positioning System is vast, expensive and involves a lot of technical ingenuity, but the fundamental concepts at work are quite simple and intuitive.

The Global Positioning System (GPS) is a constellation of about 30 Earth-orbiting satellites (24 in operation and extras in case one fails). The U.S. military originally developed this satellite network as a military navigation system but has made it available for civilian use.

• Each satellite weighs 3,000- to 4,000-pounds

• They are solar-powered

• Each satellite orbits the globe at about 12,000 miles (19,300 km), making two complete rotations every day.

##### Trilateration

A GPS receiver must locate four or more of satellites and calculate the distance to each. Using this information the satellite can determine its own location. This operation is based on a simple mathematical principle called trilateration.

Trilateration is defined as a method for determining the intersections of spherical surfaces given the centers and radii of the three spheres.

We can visualize this concept on a map by using three known positions. For this example (see Figure 1.) we will use the city centers of Albuquerque, Santa Fe, and Las Cruces. If a distance is determined from each city center to our unknown point, one could calculate a location for the “unknown” by finding the intersection of each city center radius. By plotting three circles, representing the determined distances, it would be easy to visually see that they all are likely to intersect at the city center of Roswell. A fourth distance from the city center of Carlsbad is used as a check, confirming the “unknown” location is in Roswell.

##### 3D-Trilateration

Based on the principals of Trilateration the GPS receiver has to know two things:

1. The location of at least three satellites above you

2. The distance between you and each of those satellites

The GPS receiver calculates these by analyzing high-frequency, low-power radio signals from the GPS satellites. The GPS receiver can figure out how far the signal has traveled by timing how long it took the signal to arrive. A position can be determined by three satellites, and verified by a fourth satellite. Precise survey receivers may require 5-6 satellites for a “fixed” position.

##### Timing

A GPS receiver calculates the distance to GPS satellites by timing a signal's journey from satellite to receiver.

A satellite begins transmitting a long, digital pattern called a pseudo-random code. The receiver begins running the same digital pattern at the same time as the satellite. When the satellite's signal reaches the receiver, its transmission of the pattern will lag a bit behind the receiver's playing of the pattern.

When you measure the distance to four located satellites, you can draw four spheres that all intersect at one point. Three spheres will intersect even if your numbers are way off, but four spheres will not intersect at one point if you've measured incorrectly. Since the receiver makes all its distance measurements using its own built-in clock, the distances will all be proportionally incorrect.

The receiver can easily calculate the necessary adjustment that will cause the four spheres to intersect at one point. Based on this, it resets its clock to be in sync with the satellite's atomic clock.

##### GPS Almanac

In order for the distance information to be of any use, the receiver also has to know where the satellites actually are. This isn't particularly difficult because the satellites travel in very high and predictable orbits. The GPS receiver simply stores an almanac that tells it where every satellite should be at any given time. Things like the pull of the moon and the sun do change the satellites' orbits very slightly, but the Department of Defense constantly monitors their exact positions and transmits any adjustments to all GPS receivers as part of the satellites' signals.

##### Differential GPS

A GPS receiver calculates its position on earth based on the information it receives from four located satellites. This method assumes the radio signals will make their way through the atmosphere at a consistent speed (the speed of light). However, the Earth's atmosphere slows the electromagnetic energy down, particularly as it goes through the ionosphere and troposphere. The delay varies depending on where you are on Earth, which means it's difficult to accurately factor this into the distance calculations. Problems can also occur when radio signals bounce off large objects, such as buildings, giving a receiver the impression that a satellite is farther away than it actually is.

On top of all that, satellites sometimes just send out bad almanac data, misreporting their own position.

Differential GPS (DGPS) helps correct these errors. The basic idea is to gauge GPS inaccuracy at a stationary receiver station with a known location. Since the DGPS hardware at the station already knows its own position, it can easily calculate its receiver's inaccuracy. Differential GPS is what we use when we post process static data. By using a receiver that is collecting static data at the same time as the receiver at the unknown position we can have post processing software, such as Topcon Tools, process the data and correct the unknown position.

Differential GPS involves the cooperation of at least two receivers. One receiver must be stationary and ideally with a known coordinate. The other receiver will be “roving” and occupying the unknown stations. The stationary receiver will be used to correct the roving receiver to the known reference system or control network.

GPS receivers use timing signals from the GPS satellites to calculate a position. Timing signals will have error or delay due to atmospheric conditions, multi-path, or other obstacles that the signals will have to travel through.

Without corrections the receivers will only be able to calculate an “autonomous position”.

##### Types of Post Processed GPS Surveys

Post Processed Surveys

GPS surveys fall into two main types, post processed and real-time. With post proceed surveys the only thing that is actually done in the field is data collection. The GPS receivers are left to collect data for different lengths of time, depending on the requirements of the project. Once the data is collected it is taken back to the office and is uploaded in to a computer. The computer then makes all of the necessary calculations, allowing the information to be used.

There are three types of post processed surveys, static, fast static/rapid static, and kinematic. In static surveys one receiver is set up as a base or reference point. Another receiver, called a rover, is set up on another point to be surveyed. The receivers are left on the first set of points for a period of time ranging for 30 minutes up to several hours. After the data has been collected at the first set of points, the rover is then moved to the next point, and the process is repeated until all of the points to be surveyed have been occupied.

A fast static/rapid static survey also requires a receiver to be set up as a reference point, but generally use multiple rovers. The rovers are set up on the points to be surveyed and left to collect data. The rovers are left for upwards of 20 minutes, but generally not as long as with static surveys. The rovers are then moved to another set of points. In rapid static surveys, the points are occupied a number of different times, but in different configurations, which allows for a number of different base lines to be established. Rapid static works best with shorter base lines.

Post-processed kinematic (PPK) survey methods provide the surveyor with a technique for high production measurements and can be used in areas with minimal obstructions of the satellites. PPK uses significantly reduced observation times (i.e. 0.5 to 3 minutes, usually 10-30 seconds per point) compared to static or fast static/rapid static observations.

This method requires a least squares adjustment or other multiple baseline statistical analysis capable of producing a weighted mean average of the observations.