GNSS Errors

Dinesh Manandhar
Adjunct Associate Professor, RS/GIS, AIT
Project Associate Professor, Center for Spatial Information Science,
The University of Tokyo
Contact Information: dinesh@csis.u-tokyo.ac.jp
Homepage: https://home.csis.u-tokyo.ac.jp/~dinesh/
Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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GNSS Errors

Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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Background Information: Accuracy vs. Precision• Accuracy• Capable of providing a correct measurement• Measurement is compared with true value• Affected by systematic error• Precision• Capable of providing repeatable and reliable measurement• Statistical analysis of measurement provides the precision• Measure of random error• Systematic error has no effect

Neither Precise nor Accurate Precise but Not Accurate

Accurate but Not Precise

Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

Precise and Accurate
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GNSS Measurement Errors
MeasureAbbreviation

Definition

Root Mean SquareRMS

The square root of the average of the squared errors

Twice Distance RMS

2D RMS

Twice the RMS of the horizontal errors

Circular Error Probable

CEP

A circle's radius, centered at the true antenna position,
containing 50% of the points in the horizontal scatter plot

Horizontal 95%Accuracy

R95

A circle's radius, centered at the true antenna position,
containing 95% of the points in the horizontal scatter plot

SEP

A sphere’s radius centered at the true antenna position,
containing 50% of the points in the three dimensional scatter
plot

Spherical Error Probable

Source: GPS Accuracy: Lies, Damn Lies, and Statistics, GPS World, JAN 1998
https://www.gpsworld.com/gps-accuracy-lies-damn-lies-and-statistics/
Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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Commonly Used GNSS Performance Measurements• TTFF• True Time to First Fix• Parameter: Cold Start, Warm Start, Hot Start• Standard Accuracy• Accuracy attainable without any correction techniques• DGPS Accuracy• Accuracy attainable by differential correction data
• Code-phase correction• RTK Accuracy• Accuracy attainable by differential correction data
• Use both Code-Phase and Carrier Phase correction
Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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TTFF and Typical Example Values• TTFF• Cold Start : < 36 seconds• Time required to output first position data since the receiver power is on• No reference data like time or almanac are available• Warm Start : < 6 seconds• Time required to output first position data since the receiver power is onwith the latest satellite almanac data in the receiver’s memory• Time and almanac related reference data are already known• Hot Start : < 1 second• Receiver has already output position data
• Time to reacquire an already tracked satellite due to temporary blockage
by buildings or trees
Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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Performance Measurement of RTK Accuracy• A fix error and a variable error with respect to base-length is given• Such as : x cm + y ppm• Example: 2cm + 1ppm

• There is a fix error of 2cm plus 1ppm error due to base-length between the Base and Rover• 1ppm  1 parts per million•  1cm of error in 1 million centimeter distance between the Base and the Rover•  1cm of error in 1000000 centimeter distance between the Base and the Rover•  1cm of error in 10000 meter distance between the Base and the Rover•  1cm of error in 10 kilometer distance between the Base and the Rover•  1cm of error for every 10Km of distance between the Base and the Rover•  4cm of error for 40Km of distance between the Base and the Rover• Thus the total error is : 2cm + 4cm due to 40Km of base length• The longer the base-length, the larger the error• Do not assume that this error is linear• And it may not be valid for longer base-lines• Normally the recommended base-length for RTK for a Geodetic Receiver is 40Km
Dinesh Manandhar, CSIS, The University of Tokyo, dinesh@csis.u-tokyo.ac.jp

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