draft-ietf-geopriv-uncertainty-01.txt   draft-ietf-geopriv-uncertainty-02.txt 
GEOPRIV M. Thomson GEOPRIV M. Thomson
Internet-Draft Mozilla Internet-Draft Mozilla
Intended status: Standards Track J. Winterbottom Intended status: Standards Track J. Winterbottom
Expires: January 5, 2015 Unaffiliated Expires: February 15, 2015 Unaffiliated
July 4, 2014 August 14, 2014
Representation of Uncertainty and Confidence in PIDF-LO Representation of Uncertainty and Confidence in PIDF-LO
draft-ietf-geopriv-uncertainty-01 draft-ietf-geopriv-uncertainty-02
Abstract Abstract
The key concepts of uncertainty and confidence as they pertain to The key concepts of uncertainty and confidence as they pertain to
location information are defined. Methods for the manipulation of location information are defined. Methods for the manipulation of
location estimates that include uncertainty information are outlined. location estimates that include uncertainty information are outlined.
Status of This Memo Status of This Memo
This Internet-Draft is submitted in full conformance with the This Internet-Draft is submitted in full conformance with the
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Internet-Drafts are working documents of the Internet Engineering Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet- working documents as Internet-Drafts. The list of current Internet-
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Internet-Drafts are draft documents valid for a maximum of six months Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress." material or to cite them other than as "work in progress."
This Internet-Draft will expire on January 5, 2015. This Internet-Draft will expire on February 15, 2015.
Copyright Notice Copyright Notice
Copyright (c) 2014 IETF Trust and the persons identified as the Copyright (c) 2014 IETF Trust and the persons identified as the
document authors. All rights reserved. document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of (http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents publication of this document. Please review these documents
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5. Manipulation of Uncertainty . . . . . . . . . . . . . . . . . 13 5. Manipulation of Uncertainty . . . . . . . . . . . . . . . . . 13
5.1. Reduction of a Location Estimate to a Point . . . . . . . 13 5.1. Reduction of a Location Estimate to a Point . . . . . . . 13
5.1.1. Centroid Calculation . . . . . . . . . . . . . . . . 14 5.1.1. Centroid Calculation . . . . . . . . . . . . . . . . 14
5.1.1.1. Arc-Band Centroid . . . . . . . . . . . . . . . . 14 5.1.1.1. Arc-Band Centroid . . . . . . . . . . . . . . . . 14
5.1.1.2. Polygon Centroid . . . . . . . . . . . . . . . . 15 5.1.1.2. Polygon Centroid . . . . . . . . . . . . . . . . 15
5.2. Conversion to Circle or Sphere . . . . . . . . . . . . . 17 5.2. Conversion to Circle or Sphere . . . . . . . . . . . . . 17
5.3. Three-Dimensional to Two-Dimensional Conversion . . . . . 18 5.3. Three-Dimensional to Two-Dimensional Conversion . . . . . 18
5.4. Increasing and Decreasing Uncertainty and Confidence . . 19 5.4. Increasing and Decreasing Uncertainty and Confidence . . 19
5.4.1. Rectangular Distributions . . . . . . . . . . . . . . 19 5.4.1. Rectangular Distributions . . . . . . . . . . . . . . 19
5.4.2. Normal Distributions . . . . . . . . . . . . . . . . 20 5.4.2. Normal Distributions . . . . . . . . . . . . . . . . 20
5.5. Determining Whether a Location is Within a Given Region . 21 5.5. Determining Whether a Location is Within a Given Region . 20
5.5.1. Determining the Area of Overlap for Two Circles . . . 22 5.5.1. Determining the Area of Overlap for Two Circles . . . 22
5.5.2. Determining the Area of Overlap for Two Polygons . . 23 5.5.2. Determining the Area of Overlap for Two Polygons . . 23
6. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.1. Reduction to a Point or Circle . . . . . . . . . . . . . 23 6.1. Reduction to a Point or Circle . . . . . . . . . . . . . 23
6.2. Increasing and Decreasing Confidence . . . . . . . . . . 27 6.2. Increasing and Decreasing Confidence . . . . . . . . . . 27
6.3. Matching Location Estimates to Regions of Interest . . . 27 6.3. Matching Location Estimates to Regions of Interest . . . 27
6.4. PIDF-LO With Confidence Example . . . . . . . . . . . . . 28 6.4. PIDF-LO With Confidence Example . . . . . . . . . . . . . 28
7. Confidence Schema . . . . . . . . . . . . . . . . . . . . . . 28 7. Confidence Schema . . . . . . . . . . . . . . . . . . . . . . 28
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 30 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 30
8.1. URN Sub-Namespace Registration for 8.1. URN Sub-Namespace Registration for
urn:ietf:params:xml:ns:geopriv:conf . . . . . . . . . . . 30 urn:ietf:params:xml:ns:geopriv:conf . . . . . . . . . . . 30
8.2. XML Schema Registration . . . . . . . . . . . . . . . . . 30 8.2. XML Schema Registration . . . . . . . . . . . . . . . . . 30
9. Security Considerations . . . . . . . . . . . . . . . . . . . 31 9. Security Considerations . . . . . . . . . . . . . . . . . . . 31
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 31 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 31
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 31 11. References . . . . . . . . . . . . . . . . . . . . . . . . . 31
11.1. Normative References . . . . . . . . . . . . . . . . . . 31 11.1. Normative References . . . . . . . . . . . . . . . . . . 31
11.2. Informative References . . . . . . . . . . . . . . . . . 31 11.2. Informative References . . . . . . . . . . . . . . . . . 32
Appendix A. Conversion Between Cartesian and Geodetic Appendix A. Conversion Between Cartesian and Geodetic
Coordinates in WGS84 . . . . . . . . . . . . . . . . 33 Coordinates in WGS84 . . . . . . . . . . . . . . . . 33
Appendix B. Calculating the Upward Normal of a Polygon . . . . . 34 Appendix B. Calculating the Upward Normal of a Polygon . . . . . 34
B.1. Checking that a Polygon Upward Normal Points Up . . . . . 35 B.1. Checking that a Polygon Upward Normal Points Up . . . . . 35
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 35 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 35
1. Introduction 1. Introduction
Location information represents an estimation of the position of a Location information represents an estimation of the position of a
Target [RFC6280]. Under ideal circumstances, a location estimate Target [RFC6280]. Under ideal circumstances, a location estimate
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mathematics, particularly statistics and geometry. mathematics, particularly statistics and geometry.
Some terminology is borrowed from [RFC3693] and [RFC6280], in Some terminology is borrowed from [RFC3693] and [RFC6280], in
particular Target. particular Target.
Mathematical formulae are presented using the following notation: add Mathematical formulae are presented using the following notation: add
"+", subtract "-", multiply "*", divide "/", power "^" and absolute "+", subtract "-", multiply "*", divide "/", power "^" and absolute
value "|x|". Precedence is indicated using parentheses. value "|x|". Precedence is indicated using parentheses.
Mathematical functions are represented by common abbreviations: Mathematical functions are represented by common abbreviations:
square root "sqrt(x)", sine "sin(x)", cosine "cos(x)", inverse cosine square root "sqrt(x)", sine "sin(x)", cosine "cos(x)", inverse cosine
"acos(x)", tangent "tan(x)", inverse tangent "atan(x)", error "acos(x)", tangent "tan(x)", inverse tangent "atan(x)", two-argument
function "erf(x)", and inverse error function "erfinv(x)". inverse tangent "atan2(y,x)", error function "erf(x)", and inverse
error function "erfinv(x)".
2. A General Definition of Uncertainty 2. A General Definition of Uncertainty
Uncertainty results from the limitations of measurement. In Uncertainty results from the limitations of measurement. In
measuring any observable quantity, errors from a range of sources measuring any observable quantity, errors from a range of sources
affect the result. Uncertainty is a quantification of what is known affect the result. Uncertainty is a quantification of what is known
about the observed quantity, either through the limitations of about the observed quantity, either through the limitations of
measurement or through inherent variability of the quantity. measurement or through inherent variability of the quantity.
Uncertainty is most completely described by a probability Uncertainty is most completely described by a probability
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extrapolated. In particular, the uncertainty can be scaled to meet a extrapolated. In particular, the uncertainty can be scaled to meet a
desired confidence or the confidence for a particular region of desired confidence or the confidence for a particular region of
uncertainty can be found. uncertainty can be found.
In general, confidence decreases as the region of uncertainty In general, confidence decreases as the region of uncertainty
decreases in size and confidence increases as the region of decreases in size and confidence increases as the region of
uncertainty increases in size. However, this depends on the PDF; uncertainty increases in size. However, this depends on the PDF;
expanding the region of uncertainty for a rectangular distribution expanding the region of uncertainty for a rectangular distribution
has no effect on confidence without additional information. If the has no effect on confidence without additional information. If the
region of uncertainty is increased during the process of obfuscation region of uncertainty is increased during the process of obfuscation
(see [I-D.thomson-geopriv-location-obscuring]), then the confidence (see [RFC6772]), then the confidence cannot be increased.
cannot be increased.
A region of uncertainty that is reduced in size always has a lower A region of uncertainty that is reduced in size always has a lower
confidence. confidence.
A region of uncertainty that has an unknown PDF shape cannot be A region of uncertainty that has an unknown PDF shape cannot be
reduced in size reliably. The region of uncertainty can be expanded, reduced in size reliably. The region of uncertainty can be expanded,
but only if confidence is not increased. but only if confidence is not increased.
This section makes the simplifying assumption that location This section makes the simplifying assumption that location
information is symmetrically and evenly distributed in each information is symmetrically and evenly distributed in each
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</xs:appinfo> </xs:appinfo>
<xs:documentation source="http://www.ietf.org/rfc/rfcXXXX.txt"> <xs:documentation source="http://www.ietf.org/rfc/rfcXXXX.txt">
<!-- [[NOTE TO RFC-EDITOR: Please replace above URL with URL of <!-- [[NOTE TO RFC-EDITOR: Please replace above URL with URL of
published RFC and remove this note.]] --> published RFC and remove this note.]] -->
This schema defines an element that is used for indicating This schema defines an element that is used for indicating
confidence in PIDF-LO documents. confidence in PIDF-LO documents.
</xs:documentation> </xs:documentation>
</xs:annotation> </xs:annotation>
<xs:element name="confidence" type="conf:confidenceType"/> <xs:element name="confidence" type="conf:confidenceType"/>
<xs:complexType name="confidenceType"> <xs:complexType name="confidenceType">
<xs:simpleContent> <xs:simpleContent>
<xs:extension base="conf:confidenceBase"> <xs:extension base="conf:confidenceBase">
<xs:attribute name="pdf" type="conf:pdfType" <xs:attribute name="pdf" type="conf:pdfType"
default="unknown"/> default="unknown"/>
</xs:extension> </xs:extension>
</xs:simpleContent> </xs:simpleContent>
</xs:complexType> </xs:complexType>
<xs:simpleType name="confidenceBase"> <xs:simpleType name="confidenceBase">
<xs:union> <xs:union>
<xs:restriction base="xs:decimal"> <xs:simpleType>
<xs:minInclusive value="0.0"/> <xs:restriction base="xs:decimal">
<xs:maxInclusive value="100.0"/> <xs:minExclusive value="0.0"/>
</xs:restriction> <xs:maxExclusive value="100.0"/>
<xs:restriction base="xs:token"> </xs:restriction>
<xs:enumeration value="unknown"/> </xs:simpleType>
</xs:restriction> <xs:simpleType>
<xs:restriction base="xs:token">
<xs:enumeration value="unknown"/>
</xs:restriction>
</xs:simpleType>
</xs:union>
</xs:simpleType> </xs:simpleType>
<xs:simpleType name="pdfType"> <xs:simpleType name="pdfType">
<xs:restriction base="xs:token"> <xs:restriction base="xs:token">
<xs:enumeration value="unknown"/> <xs:enumeration value="unknown"/>
<xs:enumeration value="normal"/> <xs:enumeration value="normal"/>
<xs:enumeration value="rectangular"/> <xs:enumeration value="rectangular"/>
</xs:restriction> </xs:restriction>
</xs:simpleType> </xs:simpleType>
</xs:schema> </xs:schema>
8. IANA Considerations 8. IANA Considerations
8.1. URN Sub-Namespace Registration for 8.1. URN Sub-Namespace Registration for
urn:ietf:params:xml:ns:geopriv:conf urn:ietf:params:xml:ns:geopriv:conf
This section registers a new XML namespace, This section registers a new XML namespace,
"urn:ietf:params:xml:ns:geopriv:conf", as per the guidelines in "urn:ietf:params:xml:ns:geopriv:conf", as per the guidelines in
[RFC3688]. [RFC3688].
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11. References 11. References
11.1. Normative References 11.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997. Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC3688] Mealling, M., "The IETF XML Registry", BCP 81, RFC 3688, [RFC3688] Mealling, M., "The IETF XML Registry", BCP 81, RFC 3688,
January 2004. January 2004.
[RFC3693] Cuellar, J., Morris, J., Mulligan, D., Peterson, J., and
J. Polk, "Geopriv Requirements", RFC 3693, February 2004.
[RFC4119] Peterson, J., "A Presence-based GEOPRIV Location Object [RFC4119] Peterson, J., "A Presence-based GEOPRIV Location Object
Format", RFC 4119, December 2005. Format", RFC 4119, December 2005.
[RFC5139] Thomson, M. and J. Winterbottom, "Revised Civic Location
Format for Presence Information Data Format Location
Object (PIDF-LO)", RFC 5139, February 2008.
[RFC5491] Winterbottom, J., Thomson, M., and H. Tschofenig, "GEOPRIV
Presence Information Data Format Location Object (PIDF-LO)
Usage Clarification, Considerations, and Recommendations",
RFC 5491, March 2009.
[RFC6225] Polk, J., Linsner, M., Thomson, M., and B. Aboba, "Dynamic
Host Configuration Protocol Options for Coordinate-Based
Location Configuration Information", RFC 6225, July 2011.
[RFC6280] Barnes, R., Lepinski, M., Cooper, A., Morris, J.,
Tschofenig, H., and H. Schulzrinne, "An Architecture for
Location and Location Privacy in Internet Applications",
BCP 160, RFC 6280, July 2011.
11.2. Informative References 11.2. Informative References
[Convert] Burtch, R., "A Comparison of Methods Used in Rectangular [Convert] Burtch, R., "A Comparison of Methods Used in Rectangular
to Geodetic Coordinate Transformations", April 2006. to Geodetic Coordinate Transformations", April 2006.
[GeoShape] [GeoShape]
Thomson, M. and C. Reed, "GML 3.1.1 PIDF-LO Shape Thomson, M. and C. Reed, "GML 3.1.1 PIDF-LO Shape
Application Schema for use by the Internet Engineering Application Schema for use by the Internet Engineering
Task Force (IETF)", Candidate OpenGIS Implementation Task Force (IETF)", Candidate OpenGIS Implementation
Specification 06-142r1, Version: 1.0, April 2007. Specification 06-142r1, Version: 1.0, April 2007.
[I-D.thomson-geopriv-location-obscuring]
Thomson, M., "Obscuring Location", draft-thomson-geopriv-
location-obscuring-03 (work in progress), June 2011.
[ISO.GUM] ISO/IEC, "Guide to the expression of uncertainty in [ISO.GUM] ISO/IEC, "Guide to the expression of uncertainty in
measurement (GUM)", Guide 98:1995, 1995. measurement (GUM)", Guide 98:1995, 1995.
[NIST.TN1297] [NIST.TN1297]
Taylor, B. and C. Kuyatt, "Guidelines for Evaluating and Taylor, B. and C. Kuyatt, "Guidelines for Evaluating and
Expressing the Uncertainty of NIST Measurement Results", Expressing the Uncertainty of NIST Measurement Results",
Technical Note 1297, Sep 1994. Technical Note 1297, Sep 1994.
[RFC3693] Cuellar, J., Morris, J., Mulligan, D., Peterson, J., and
J. Polk, "Geopriv Requirements", RFC 3693, February 2004.
[RFC5139] Thomson, M. and J. Winterbottom, "Revised Civic Location
Format for Presence Information Data Format Location
Object (PIDF-LO)", RFC 5139, February 2008.
[RFC5222] Hardie, T., Newton, A., Schulzrinne, H., and H. [RFC5222] Hardie, T., Newton, A., Schulzrinne, H., and H.
Tschofenig, "LoST: A Location-to-Service Translation Tschofenig, "LoST: A Location-to-Service Translation
Protocol", RFC 5222, August 2008. Protocol", RFC 5222, August 2008.
[RFC5491] Winterbottom, J., Thomson, M., and H. Tschofenig, "GEOPRIV [RFC6772] Schulzrinne, H., Tschofenig, H., Cuellar, J., Polk, J.,
Presence Information Data Format Location Object (PIDF-LO) Morris, J., and M. Thomson, "Geolocation Policy: A
Usage Clarification, Considerations, and Recommendations", Document Format for Expressing Privacy Preferences for
RFC 5491, March 2009. Location Information", RFC 6772, January 2013.
[RFC6225] Polk, J., Linsner, M., Thomson, M., and B. Aboba, "Dynamic
Host Configuration Protocol Options for Coordinate-Based
Location Configuration Information", RFC 6225, July 2011.
[RFC6280] Barnes, R., Lepinski, M., Cooper, A., Morris, J.,
Tschofenig, H., and H. Schulzrinne, "An Architecture for
Location and Location Privacy in Internet Applications",
BCP 160, RFC 6280, July 2011.
[Sunday02] [Sunday02]
Sunday, D., "Fast polygon area and Newell normal Sunday, D., "Fast polygon area and Newell normal
computation", Journal of Graphics Tools JGT, computation", Journal of Graphics Tools JGT,
7(2):9-13,2002, 2002, 7(2):9-13,2002, 2002,
<http://www.acm.org/jgt/papers/Sunday02/>. <http://www.acm.org/jgt/papers/Sunday02/>.
[TS-3GPP-23_032] [TS-3GPP-23_032]
3GPP, "Universal Geographic Area Description (GAD)", 3GPP 3GPP, "Universal Geographic Area Description (GAD)", 3GPP
TS 23.032 11.0.0, September 2012. TS 23.032 11.0.0, September 2012.
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error, is described by the following: error, is described by the following:
p = sqrt(X^2 + Y^2) p = sqrt(X^2 + Y^2)
r = sqrt(X^2 + Y^2 + Z^2) r = sqrt(X^2 + Y^2 + Z^2)
u = atan((1-f) * Z * (1 + e'^2 * (1-f) * R / r) / p) u = atan((1-f) * Z * (1 + e'^2 * (1-f) * R / r) / p)
latitude = atan((Z + e'^2 * (1-f) * R * sin(u)^3) latitude = atan((Z + e'^2 * (1-f) * R * sin(u)^3)
/ (p - e^2 * R * cos(u)^3)) / (p - e^2 * R * cos(u)^3))
longitude = atan(Y / X) longitude = atan2(Y, X)
altitude = sqrt((p - R * cos(u))^2 + (Z - (1-f) * R * sin(u))^2) altitude = sqrt((p - R * cos(u))^2 + (Z - (1-f) * R * sin(u))^2)
If the point is near the poles, that is "p < 1", the value for If the point is near the poles, that is "p < 1", the value for
altitude that this method produces is unstable. A simpler method for altitude that this method produces is unstable. A simpler method for
determining the altitude of a point near the poles is: determining the altitude of a point near the poles is:
altitude = |Z| - R * (1 - f) altitude = |Z| - R * (1 - f)
Appendix B. Calculating the Upward Normal of a Polygon Appendix B. Calculating the Upward Normal of a Polygon
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