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|Title={{PAGENAME}}
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|Authors=Rui Barradas Pereira
|Authors=GMV
|Level=Basic
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|YearOfPublication=2011
|YearOfPublication=2011
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Performance of a navigation system is most usually measured in terms of the solution error ([[Accuracy|accuracy]]) and of the portion of the time it can be used for the intended application ([[Availability|availability]]). However, other performance parameters can become important for some [[GNSS Applications|applications]]. For instance, when a navigation system is used for air or maritime navigation, an unwarned large solution error can seriously increase the risk of an accident, possibly causing damage of goods, injuries to people or even death. Such errors can occur without violating the [[Accuracy|accuracy]] specification, and this is why the civil aviation community has defined the concept of [[Integrity|integrity]] as a measure of the probability that such hazardous situations can take place. Also, since some flight phases (such as approach and landing) are of special criticality, it is important that the navigation system remains available without interruptions during such periods although actually all flight phases have certain needs at this respect. That is why the civil aviation community has defined a fourth performance parameter called [[Continuity|continuity]].


Accuracy is the degree of conformance between the estimated or measured position and/or velocity of a platform at a given time and its true position or velocity{{#tag:ref| This accuracy definition has been taken from the [http://www.navcen.uscg.gov/pdf/2008_Federal_Radionavigation_Plan.pdf 2008 US Federal Radionavigation Plan]<ref> [http://www.navcen.uscg.gov/pdf/2008_Federal_Radionavigation_Plan.pdf Federal Radionavigation Plan], DOT-VNTSC-RITA-08-02/DoD-4650.5, 2008</ref>|group="footnotes"}}.


==Performance Parameters==


==Measuring Accuracy==
The civil aviation community has put the greatest effort in the rationalization and standardization of positioning (navigation) performance parameters and requirements, thus specifying the so-called [[Wikipedia:Required navigation performance|Required Navigation Performance (RNP)]] that an airborne navigation system must accomplish<ref>Report of the Special Communications/Operations Divisional Meeting, [[Wikipedia:International Civil Aviation Organization|ICAO]] Doc. 9650, November 1995</ref>:


Although being very easily understood from a conceptual point of view, the way that accuracy is measured and what is measured is not always obvious. The accuracy concept is generally used to measure the accuracy of positioning but can be also be used to measure the accuracy of velocity and even the accuracy of timming. For positioning there are 3 variants depending on the number of dimensions being considered: unidimensional accuracy (used for vertical accuracy), bidimensional accuracy (used for horizontal accuracy) and tridimensional accuracy (combining horizontal and vertical accuracy)
:'''[[Wikipedia:Required navigation performance|RNP]]:''' A statement of the navigation performance [[Accuracy|accuracy]], [[Integrity|integrity]], [[Continuity|continuity]] and [[Availability|availability]] necessary for operations within a defined airspace.


In literature and in system/product specifications it can be found measurements of accuracy such as CEP, rms, Percentile 67%, Percentile 95%, 1 sigma, 2 sigma. Some of these accuracy measures are averages while others are counts of distribution<ref>[http://www.gpsworld.com/gnss-system/receiver-design/gnss-accuracy-lies-damn-lies-and-statistics-4142 GNSS Accuracy: Lies, Damn Lies, and Statistics], GPS World, Frank van Diggelen, January 2007</ref>:
* '''x% Percentile (x%):''' Means that x% of the positions calculated have an error lower or equal to the accuracy value obtained. Typical used values are 50%, 67%, 75% and 95%. Having an accuracy of 5m (95%) means that in 95% of the time the positioning error will be equal or below 5m.


* '''Circular Error Probable (CEP):''' Percentile 50%. Means that 50% of the positions returned calculated have an error lower or equal to the accuracy value obtained.


* '''Root Mean Square Error (rms):''' The square root of the average of the squared error. This measurement is an average but assuming that the error follows a normal distribuition (which is close but not exactly true) it will correspond to the percentile 68% in unidimensional distribuitions (e.g. vertical error or timming error) and percentile 63% for bidimensional distributions (e.g. horizontal error). For the horizontal error this measurement is also refered as drms and can have variants such as 2rms or 2drms (2 times rms)
The four parameters on which [[Wikipedia:Required navigation performance|RNP]] specification is based are summarized hereafter<ref>Annex 10 (Aeronautical Telecommunications) To The Convention On International Civil Aviation, Volume I – Radio Navigation Aids, International Standards And Recommended Practices (SARPs), [[Wikipedia:International Civil Aviation Organization|ICAO]] Doc. AN10-1, 6<sup>th</sup> Edition, July 2006</ref>:


* '''x sigma:''' 1 sigma corresponds to one standard deviation and x sigma corresponds to x times 1 sigma. Assuming normal distribuitions 1 sigma corresponds to Percentile 68% in unidimentional distribuitions and Percentile 39% for bidimentional distribuitions.
:'''[[Accuracy]]{{#tag:ref| This [[Accuracy|accuracy]] definition was adapted from the [http://www.navcen.uscg.gov/pdf/2008_Federal_Radionavigation_Plan.pdf 2008 US Federal Radionavigation Plan]<ref> [http://www.navcen.uscg.gov/pdf/2008_Federal_Radionavigation_Plan.pdf Federal Radionavigation Plan], DOT-VNTSC-RITA-08-02/DoD-4650.5, 2008</ref>|group="footnotes"}}:''' is the degree of conformance between the estimated or measured position, velocity and/or time of a platform at a given time and its true position, velocity and/or time




Less used that the previous measurements are the:
:'''[[Availability]]:''' is the portion of time during which the system is to be used for navigation during which reliable navigation information is presented to the crew, autopilot, or other system managing the flight of the aircraft
* '''Mean Error:''' Average error. Corresponds Percentile 68% in unidimentional distribuitions and Percentile 54% for bidimentional distribuitions.


* '''Standard Deviation:''' Standard deviation of the error. Same as one sigma. Corresponds Percentile 58% in unidimentional distribuitions and Percentile 39% for bidimentional distribuitions.


The mean error and the standard deviation as less used accuracy measurements but assuming the normal distributions its use is as legitimate as the other mesurements usually used.
:'''[[Continuity]]:''' is the capability of the system to perform its function without unscheduled interruptions during the intended operation


==Relationship between Accuracy Measurements==


Assuming normal distribuitions these accuracy measurements can be converted between themselves. There is a correspondence between sigmas and percentiles. This correspondence can be used to convert between accuracy measurements since an accurary of 1m (1 sigma) corresponds to 2m (2 sigma) , 3m (3 sigma) and xm (x sigma).
:'''[[Integrity]]:''' is a measure of the trust which can be placed in the correctness of the information supplied by the total system. Integrity includes the ability of a system to provide timely and valid warnings to the user (alerts) when the system must not be used for the intended operation (or phase of flight)




For unidimensional distributions:
==Uses of GNSS Performance Parameters==
{| class="wikitable"
|-
! Sigma
! Percentile
|-
| 0,67
| 0,5 (CEP)
|-
| 0,80
| 0,58 (mean error)
|-
| 1
| 0,6827 (rms and std deviation)
|-
| 1,15
| 0,75
|-
| 1,96
| 0,95
|-
| 2
| 0,9545
|-
| 2,33
| 0,98
|-
| 2,57
| 0,99
|-
| 3
| 0,9973
|-
| 4
| 0,999936
|-
| 5
| 0,99999942
|-
| 6
| 0,999999998
|}


The performance parameters described above measure the performance of the GNSS system. These performance parameters can be used in different ways, with different purposes and in different conditions.


For bidimensional distributions (Rayleigh distribution) :
One of the uses for the GNSS Performance Parameters is to define requirements that and GNSS System should have in specific conditions. All GNSS systems had such requirements during the specification phase of the development of the system. These requirements are one of the drivers of the system design and development. During the operational phase these requirements are kept and sometimes updated as operational requirements against which actual performance will be verified. Such [[GALILEO Performances|performance]] requirements for [[GALILEO|Galileo]] can be found in the [http://ec.europa.eu/dgs/energy_transport/galileo/doc/galileo_hld_v3_23_09_02.pdf Galileo Mission High Level Definition] coming from the Galileo System Requirement Document<ref> [http://ec.europa.eu/dgs/energy_transport/galileo/doc/galileo_hld_v3_23_09_02.pdf Galileo Mission High Level Definition], v3, September 2002.</ref><ref> Galileo System Requirement Document, ESA-APPNS-REQ-00011, issue 3.0, June 20 2003</ref>. The GPS Performance requirements can be found in the [http://www.gps.gov/technical/ps/ GPS Performance Requirements Documents]<ref> [http://www.pnt.gov/public/docs/2008/spsps2008.pdf GPS Standard Positioning Service (SPS) Performance Standard], 4<sup>th</sup> Edition, September 2008.</ref><ref> [http://www.pnt.gov/public/docs/2007/ppsps2007.pdf GPS Precision Positioning Service (PPS) Performance Standard], 1<sup>st</sup> Edition, February 2007.</ref>.
{| class="wikitable"
|-
! Sigma
! Percentile
|-
| 1
| 0,394 (std deviation)
|-
| 1,18
| 0,5 (CEP)
|-
| 1,25
| 0,544 (mean error)
|-
| 1,414
| 0,632 (rms)
|-
| 1,67
| 0,75
|-
| 2
| 0,865
|-
| 2,45
| 0,95
|-
| 2,818
| 0,982 (2rms)
|-
| 3
| 0,989
|-
| 3,03
| 0,99
|-
| 4
| 0,9997
|-
| 5
| 0,999997
|-
| 6
| 0,999999985
|}


In a similar way this kind of performance requirements can be used also to define the performance that an [[GNSS Applications|application]] will need from a GNSS system in order to be able to perform its functionality adequately.


In the same way that these parameters are used for the definition of requirements of a GNSS system they are use to evaluate its actual performance under typical and well defined conditions. The actual [[GPS Perfomance|performance of GPS]] is monitored by several entities such as the [[Wikipedia:Federal Aviation Administration|US Federal Aviation Adminstration]] in its GPS Performance Analysis Reports><ref> [http://www.nstb.tc.faa.gov/reports/PAN72_0111.pdf FAA Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report], Report 72, January 2011.</ref>.


In the same way that space-based GNSS Systems ([[GALILEO Perfomances|GALILEO]], [[GPS Performances|GPS]], [[GLONASS Performances|GLONASS]], [[COMPASS Performances|COMPASS]]) are evaluated in terms of performance using these parameters also the increase in performance given by space-based augmentations systems ([[EGNOS Perfomances|EGNOS]], [[WAAS Performances|WAAS]], [[MSAS Performances|MSAS]]) and of other [[GNSS Augmentations]] are measured using these parameters.
Besides being used to evaluate the performance of the GNSS systems and its augmentation systems and technologies these performance parameters are used to measure the performance of the receivers that use these systems. This performance evaluation can be made for generic conditions (such as open sky locations) or for the evaluation of the receiver on specific conditions since the receiver performance can be influenced by local factors such as:
* '''Location of the user''' - Different locations yield different performances since different satellites will be visible at different positions in the sky.
* '''Time of day''' - Despite the fact that different views of constellation will be visible at different times of day, some errors (such as the errors caused by [[Ionospheric Delay]]) have different impacts during different times of the day.
* '''Surrounding environment''' - Surrounding buildings and vegetation can lead to masking of the sky leading to less visible satellites, signal attenuation effects coming from tree foliage and multi-path effects coming from the reflection of the GNSS signal on buildings or other landmarks.


==Notes==
==Notes==

Revision as of 16:49, 28 March 2011


FundamentalsFundamentals
Title Accuracy
Author(s) GMV
Level Basic
Year of Publication 2011
Logo GMV.png


Performance of a navigation system is most usually measured in terms of the solution error (accuracy) and of the portion of the time it can be used for the intended application (availability). However, other performance parameters can become important for some applications. For instance, when a navigation system is used for air or maritime navigation, an unwarned large solution error can seriously increase the risk of an accident, possibly causing damage of goods, injuries to people or even death. Such errors can occur without violating the accuracy specification, and this is why the civil aviation community has defined the concept of integrity as a measure of the probability that such hazardous situations can take place. Also, since some flight phases (such as approach and landing) are of special criticality, it is important that the navigation system remains available without interruptions during such periods although actually all flight phases have certain needs at this respect. That is why the civil aviation community has defined a fourth performance parameter called continuity.


Performance Parameters

The civil aviation community has put the greatest effort in the rationalization and standardization of positioning (navigation) performance parameters and requirements, thus specifying the so-called Required Navigation Performance (RNP) that an airborne navigation system must accomplish[1]:

RNP: A statement of the navigation performance accuracy, integrity, continuity and availability necessary for operations within a defined airspace.


The four parameters on which RNP specification is based are summarized hereafter[2]:

Accuracy[footnotes 1]: is the degree of conformance between the estimated or measured position, velocity and/or time of a platform at a given time and its true position, velocity and/or time


Availability: is the portion of time during which the system is to be used for navigation during which reliable navigation information is presented to the crew, autopilot, or other system managing the flight of the aircraft


Continuity: is the capability of the system to perform its function without unscheduled interruptions during the intended operation


Integrity: is a measure of the trust which can be placed in the correctness of the information supplied by the total system. Integrity includes the ability of a system to provide timely and valid warnings to the user (alerts) when the system must not be used for the intended operation (or phase of flight)


Uses of GNSS Performance Parameters

The performance parameters described above measure the performance of the GNSS system. These performance parameters can be used in different ways, with different purposes and in different conditions.

One of the uses for the GNSS Performance Parameters is to define requirements that and GNSS System should have in specific conditions. All GNSS systems had such requirements during the specification phase of the development of the system. These requirements are one of the drivers of the system design and development. During the operational phase these requirements are kept and sometimes updated as operational requirements against which actual performance will be verified. Such performance requirements for Galileo can be found in the Galileo Mission High Level Definition coming from the Galileo System Requirement Document[4][5]. The GPS Performance requirements can be found in the GPS Performance Requirements Documents[6][7].

In a similar way this kind of performance requirements can be used also to define the performance that an application will need from a GNSS system in order to be able to perform its functionality adequately.

In the same way that these parameters are used for the definition of requirements of a GNSS system they are use to evaluate its actual performance under typical and well defined conditions. The actual performance of GPS is monitored by several entities such as the US Federal Aviation Adminstration in its GPS Performance Analysis Reports>[8].

In the same way that space-based GNSS Systems (GALILEO, GPS, GLONASS, COMPASS) are evaluated in terms of performance using these parameters also the increase in performance given by space-based augmentations systems (EGNOS, WAAS, MSAS) and of other GNSS Augmentations are measured using these parameters.

Besides being used to evaluate the performance of the GNSS systems and its augmentation systems and technologies these performance parameters are used to measure the performance of the receivers that use these systems. This performance evaluation can be made for generic conditions (such as open sky locations) or for the evaluation of the receiver on specific conditions since the receiver performance can be influenced by local factors such as:

  • Location of the user - Different locations yield different performances since different satellites will be visible at different positions in the sky.
  • Time of day - Despite the fact that different views of constellation will be visible at different times of day, some errors (such as the errors caused by Ionospheric Delay) have different impacts during different times of the day.
  • Surrounding environment - Surrounding buildings and vegetation can lead to masking of the sky leading to less visible satellites, signal attenuation effects coming from tree foliage and multi-path effects coming from the reflection of the GNSS signal on buildings or other landmarks.

Notes

  1. ^ This accuracy definition was adapted from the 2008 US Federal Radionavigation Plan[3]

References

  1. ^ Report of the Special Communications/Operations Divisional Meeting, ICAO Doc. 9650, November 1995
  2. ^ Annex 10 (Aeronautical Telecommunications) To The Convention On International Civil Aviation, Volume I – Radio Navigation Aids, International Standards And Recommended Practices (SARPs), ICAO Doc. AN10-1, 6th Edition, July 2006
  3. ^ Federal Radionavigation Plan, DOT-VNTSC-RITA-08-02/DoD-4650.5, 2008
  4. ^ Galileo Mission High Level Definition, v3, September 2002.
  5. ^ Galileo System Requirement Document, ESA-APPNS-REQ-00011, issue 3.0, June 20 2003
  6. ^ GPS Standard Positioning Service (SPS) Performance Standard, 4th Edition, September 2008.
  7. ^ GPS Precision Positioning Service (PPS) Performance Standard, 1st Edition, February 2007.
  8. ^ FAA Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report, Report 72, January 2011.