Lecture 5 – Differential Correction GPS Accuracy in General Recreational GPS – 5-15 meters Horizontal accuracy GeoXT – Submeter GeoXH – 30 cm Survey Grade GPS – Within Centimeter Updating is easy ArcGIS, AutoCad, Plotter, Printer, etc are all supporting the in house production of map and spatial analysis.

Differential Correction in Summary Base Station Rover Spatial Auto-correlation Similar errors from may factors –such as satellite clocks, ephemeris error, ionosphere, etc.

Thinking about Error Random Error Systematic Error

Averaging From one of my last year students’ report – coordinate difference (from real value) decreased from 6 feet to 4 feet, when he increased the averaging time from 30 seconds to 5 minutes. If you can stay at one point for several weeks to several months, your error should go down to 1-2 meters.

Sources of GPS Error For receivers of the Pathfinder Class: Satellite Clocks < 1 meter ephemeris Error < 1meter receiver error < 2 meter ionospheric < 2 meter tropospheric < 2 meter multipath varies

Clock Errors Each satellite has one board four atomic clocks and can keep time to within a billionth of a second or so GPS signal travels at about 3*10^8 meters/second Clock errors will be corrected by ground control stations The first accurate atomic clock, a cesium standard based on the transition of the cesium-133 atom, was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. http://en.wikipedia.org/wiki/Atomic_clock An atomic pie is a type of clock that uses an atomic resonance frequency standard to feed its counter. Early atomic clocks were masers with attached equipment. Today's best atomic frequency standards (or clocks) are based on absorption spectroscopy of cold atoms in atomic fountains. National standards agencies maintain an accuracy of 10-9 seconds per day, and a precision equal to the frequency of the radio transmitter pumping the maser.

Ephemeris Errors The receiver expects each satellite to be at a certain place at a particular given time. Every hour or so satellites send out info to receivers about where they are going to be at time “t” Predications can not be exactly the same as fact.

Receiver Errors Design – 6 channels vs. 12 channels (hardware) filtering bad/low quality signals or not (software) Calculation/rounding errors Receiver clock errors

Atmospheric Errors The ionosphere is the part of the atmosphere that is ionized by solar radiation. The Troposphere is the lowest portion of Earth's atmosphere. It is the densest layer of the atmosphere and contains approximately 75% of the mass of the atmosphere and almost all the water vapor and aerosol. Since the ionosphere affects the different frequencies differently a correction can be calculated. Some military and expensive survey-grade civilian receivers compare the different delays in the L1 and L2 frequencies to measure atmospheric dispersion, and apply a more precise correction. This can be done in civilian receivers without decrypting the P(Y) signal carried on L2, by tracking the carrier wave instead of the modulated code. To facilitate this on lower cost receivers, a new civilian code signal on L2, called L2C, was added to the Block IIR-M satellites, first launched in 2005. It allows a direct comparison of the L1 and L2 signals using the coded signal instead of the carrier wave. http://en.wikipedia.org/wiki/Ionosphere http://en.wikipedia.org/wiki/Earth%27s_atmosphere http://en.wikipedia.org/wiki/Troposphere

Multipath Errors http://www.trimble.com/gps/howgps-error2.shtml Multipath errors may occur if a given radio signal follows two paths to the receivers antenna. Many receivers are programmed to disregard the second signal.

Reducing Errors Most of these errors can be “calculated out” of the measurements by the process called differential correction. Real time differential correction Post-processing differential correction

An example of DC

From base station to rover The position of “T” The reading “O”, and The “difference” between “O” and “T” T = O - E An entity that has magnitude and direction is known as a vector. It is important to realize that none of these quantities are scalars.

O T E Base O T E Rover Known error vector applied to point observed by rover. E = O – T T=O-E

Making Differential Correction Work