draft-ietf-geopriv-uncertainty-00.txt   draft-ietf-geopriv-uncertainty-01.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: July 26, 2014 Unaffiliated Expires: January 5, 2015 Unaffiliated
January 22, 2014 July 4, 2014
Representation of Uncertainty and Confidence in PIDF-LO Representation of Uncertainty and Confidence in PIDF-LO
draft-ietf-geopriv-uncertainty-00 draft-ietf-geopriv-uncertainty-01
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-
Drafts is at http://datatracker.ietf.org/drafts/current/. Drafts is at http://datatracker.ietf.org/drafts/current/.
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 July 26, 2014. This Internet-Draft will expire on January 5, 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 . 20 5.5. Determining Whether a Location is Within a Given Region . 21
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 . . 22 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 . . . . . . . . . . 26 6.2. Increasing and Decreasing Confidence . . . . . . . . . . 27
6.3. Matching Location Estimates to Regions of Interest . . . 26 6.3. Matching Location Estimates to Regions of Interest . . . 27
6.4. PIDF-LO With Confidence Example . . . . . . . . . . . . . 27 6.4. PIDF-LO With Confidence Example . . . . . . . . . . . . . 28
7. Confidence Schema . . . . . . . . . . . . . . . . . . . . . . 27 7. Confidence Schema . . . . . . . . . . . . . . . . . . . . . . 28
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 29 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 . . . . . . . . . . . 29 urn:ietf:params:xml:ns:geopriv:conf . . . . . . . . . . . 30
8.2. XML Schema Registration . . . . . . . . . . . . . . . . . 29 8.2. XML Schema Registration . . . . . . . . . . . . . . . . . 30
9. Security Considerations . . . . . . . . . . . . . . . . . . . 30 9. Security Considerations . . . . . . . . . . . . . . . . . . . 31
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 30 10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 31
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 30 11. References . . . . . . . . . . . . . . . . . . . . . . . . . 31
11.1. Normative References . . . . . . . . . . . . . . . . . . 30 11.1. Normative References . . . . . . . . . . . . . . . . . . 31
11.2. Informative References . . . . . . . . . . . . . . . . . 30 11.2. Informative References . . . . . . . . . . . . . . . . . 31
Appendix A. Conversion Between Cartesian and Geodetic Appendix A. Conversion Between Cartesian and Geodetic
Coordinates in WGS84 . . . . . . . . . . . . . . . . 32 Coordinates in WGS84 . . . . . . . . . . . . . . . . 33
Appendix B. Calculating the Upward Normal of a Polygon . . . . . 33 Appendix B. Calculating the Upward Normal of a Polygon . . . . . 34
B.1. Checking that a Polygon Upward Normal Points Up . . . . . 34 B.1. Checking that a Polygon Upward Normal Points Up . . . . . 35
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 34 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. Under ideal circumstances, a location estimate precisely Target [RFC6280]. Under ideal circumstances, a location estimate
reflects the actual location of the Target. In reality, there are precisely reflects the actual location of the Target. For automated
many factors that introduce errors into the measurements that are systems that determine location, there are many factors that
used to determine location estimates. introduce errors into the measurements that are used to determine
location estimates.
The process by which measurements are combined to generate a location The process by which measurements are combined to generate a location
estimate is outside of the scope of work within the IETF. However, estimate is outside of the scope of work within the IETF. However,
the results of such a process are carried in IETF data formats and the results of such a process are carried in IETF data formats and
protocols. This document outlines how uncertainty, and its protocols. This document outlines how uncertainty, and its
associated datum, confidence, are expressed and interpreted. associated datum, confidence, are expressed and interpreted.
This document provides a common nomenclature for discussing This document provides a common nomenclature for discussing
uncertainty and confidence as they relate to location information. uncertainty and confidence as they relate to location information.
This document also provides guidance on how to manage location This document also provides guidance on how to manage location
information that includes uncertainty. Methods for expanding or information that includes uncertainty. Methods for expanding or
reducing uncertainty to obtain a required level of confidence are reducing uncertainty to obtain a required level of confidence are
described. Methods for determining the probability that a Target is described. Methods for determining the probability that a Target is
within a specified region based on their location estimate are within a specified region based on their location estimate are
described. These methods are simplified by making certain described. These methods are simplified by making certain
assumptions about the location estimate and are designed to be assumptions about the location estimate and are designed to be
applicable to location estimates in a relatively small area. applicable to location estimates in a relatively small geographic
area.
A confidence extension for the Presence Information Data Format - A confidence extension for the Presence Information Data Format -
Location Object (PIDF-LO) [RFC4119] is described. Location Object (PIDF-LO) [RFC4119] is described.
This document describes methods that can be used in combination with
automatically determined location information. These are
statistically-based methods.
1.1. Conventions and Terminology 1.1. Conventions and Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119]. document are to be interpreted as described in [RFC2119].
This document assumes a basic understanding of the principles of This document assumes a basic understanding of the principles of
mathematics, particularly statistics and geometry. mathematics, particularly statistics and geometry.
Some terminology is borrowed from [RFC3693] and [RFC6280]. Some terminology is borrowed from [RFC3693] and [RFC6280], in
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)", error
function "erf(x)", and inverse error function "erfinv(x)". function "erf(x)", and inverse error function "erfinv(x)".
2. A General Definition of Uncertainty 2. A General Definition of Uncertainty
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possible values for the quantity. possible values for the quantity.
A probability distribution describing a measured quantity can be A probability distribution describing a measured quantity can be
arbitrarily complex and so it is desirable to find a simplified arbitrarily complex and so it is desirable to find a simplified
model. One approach commonly taken is to reduce the probability model. One approach commonly taken is to reduce the probability
distribution to a confidence interval. Many alternative models are distribution to a confidence interval. Many alternative models are
used in other areas, but study of those is not the focus of this used in other areas, but study of those is not the focus of this
document. document.
In addition to the central estimate of the observed quantity, a In addition to the central estimate of the observed quantity, a
confidence interval is succintly described by two values: an error confidence interval is succinctly described by two values: an error
range and a confidence. The error range describes an interval and range and a confidence. The error range describes an interval and
the confidence describes an estimated upper bound on the probability the confidence describes an estimated upper bound on the probability
that a "true" value is found within the extents defined by the error. that a "true" value is found within the extents defined by the error.
In the following example, a measurement result for a length is shown In the following example, a measurement result for a length is shown
as a nominal value with additional information on error range (0.0043 as a nominal value with additional information on error range (0.0043
meters) and confidence (95%). meters) and confidence (95%).
e.g. x = 1.00742 +/- 0.0043 meters at 95% confidence e.g. x = 1.00742 +/- 0.0043 meters at 95% confidence
This result indicates that the measurement indicates that the value This result indicates that the measurement indicates that the value
of "x" between 1.00312 and 1.01172 meters with 95% probability. No of "x" between 1.00312 and 1.01172 meters with 95% probability. No
other assertion is made: in particular, this does not assert that x other assertion is made: in particular, this does not assert that x
is 1.00742. is 1.00742.
This document uses the term _uncertainty_ to refer in general to the
concept as well as more specifically to refer to the error increment.
Uncertainty and confidence for location estimates can be derived in a Uncertainty and confidence for location estimates can be derived in a
number of ways. This document does not attempt to enumerate the many number of ways. This document does not attempt to enumerate the many
methods for determining uncertainty. [ISO.GUM] and [NIST.TN1297] methods for determining uncertainty. [ISO.GUM] and [NIST.TN1297]
provide a set of general guidelines for determining and manipulating provide a set of general guidelines for determining and manipulating
measurement uncertainty. This document applies that general guidance measurement uncertainty. This document applies that general guidance
for consumers of location information. for consumers of location information.
As a statistical measure, values determined for uncertainty are
determined based on information in the aggregate, across numerous
individual estimates. An individual estimate might be determined to
be "correct" - by using a survey to validate the result, for example
- without invalidating the statistical assertion.
This understanding of estimates in the statistical sense explains why
asserting a confidence of 100%, which might seem intuitively correct,
is rarely advisable.
2.1. Uncertainty as a Probability Distribution 2.1. Uncertainty as a Probability Distribution
The Probability Density Function (PDF) that is described by The Probability Density Function (PDF) that is described by
uncertainty indicates the probability that the "true" value lies at uncertainty indicates the probability that the "true" value lies at
any one point. The shape of the probability distribution can vary any one point. The shape of the probability distribution can vary
depending on the method that is used to determine the result. The depending on the method that is used to determine the result. The
two probability density functions most generally applicable most two probability density functions most generally applicable to
applicable to location information are considered in this document: location information are considered in this document:
o The normal PDF (also referred to as a Gaussian PDF) is used where o The normal PDF (also referred to as a Gaussian PDF) is used where
a large number of small random factors contribute to errors. The a large number of small random factors contribute to errors. The
value used for the error range in a normal PDF is related to the value used for the error range in a normal PDF is related to the
standard deviation of the distribution. standard deviation of the distribution.
o A rectangular PDF is used where the errors are known to be o A rectangular PDF is used where the errors are known to be
consistent across a limited range. A rectangular PDF can occur consistent across a limited range. A rectangular PDF can occur
where a single error source, such as a rounding error, is where a single error source, such as a rounding error, is
significantly larger than other errors. A rectangular PDF is significantly larger than other errors. A rectangular PDF is
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be an erroneous use of this term. be an erroneous use of this term.
3. Uncertainty in Location 3. Uncertainty in Location
A _location estimate_ is the result of location determination. A A _location estimate_ is the result of location determination. A
location estimate is subject to uncertainty like any other location estimate is subject to uncertainty like any other
observation. However, unlike a simple measure of a one dimensional observation. However, unlike a simple measure of a one dimensional
property like length, a location estimate is specified in two or property like length, a location estimate is specified in two or
three dimensions. three dimensions.
Uncertainty in 2- or 3-dimensional locations can be described using Uncertainty in two or three dimensional locations can be described
confidence intervals. The confidence interval for a location using confidence intervals. The confidence interval for a location
estimate in two or three dimensional space is expressed as a subset estimate in two or three dimensional space is expressed as a subset
of that space. This document uses the term _region of uncertainty_ of that space. This document uses the term _region of uncertainty_
to refer to the area or volume that describes the confidence to refer to the area or volume that describes the confidence
interval. interval.
Areas or volumes that describe regions of uncertainty can be formed Areas or volumes that describe regions of uncertainty can be formed
by the combination of two or three one-dimensional ranges, or more by the combination of two or three one-dimensional ranges, or more
complex shapes could be described. complex shapes could be described (for example, the shapes in
[RFC5491]).
3.1. Targets as Points in Space 3.1. Targets as Points in Space
This document makes a simplifying assumption that the Target of the This document makes a simplifying assumption that the Target of the
PIDF-LO occupies just a single point in space. While this is clearly PIDF-LO occupies just a single point in space. While this is clearly
false in virtually all scenarios with any practical application, it false in virtually all scenarios with any practical application, it
is often a reasonable assumption to make. is often a reasonable simplifying assumption to make.
To a large extent, whether this simplication is valid depends on the To a large extent, whether this simplification is valid depends on
size of the target relative to the size of the uncertainty region. the size of the target relative to the size of the uncertainty
When locating a personal device using contemporary location region. When locating a personal device using contemporary location
determination techniques, the space the device occupies relative to determination techniques, the space the device occupies relative to
the uncertainty is proportionally quite small. Even where that the uncertainty is proportionally quite small. Even where that
device is used as a proxy for a person, the proportions change device is used as a proxy for a person, the proportions change
little. little.
This assumption is less useful as the Target of the PIDF-LO becomes This assumption is less useful as uncertainty becomes small relative
large relative to the uncertainty region. For instance, describing to the size of the Target of the PIDF-LO (or conversely, as
the location of a football stadium or small country would include a uncertainty becomes small relative to the Target). For instance,
region of uncertainty that is infinitesimally larger than the Target describing the location of a football stadium or small country would
itself. In these cases, much of the guidance in this document is not include a region of uncertainty that is infinitesimally larger than
applicable. Indeed, as the accuracy of location determination the Target itself. In these cases, much of the guidance in this
technology improves, it could be that the advice this document document is not applicable. Indeed, as the accuracy of location
contains becomes less relevant by the same measure. determination technology improves, it could be that the advice this
document contains becomes less relevant by the same measure.
3.2. Representation of Uncertainty and Confidence in PIDF-LO 3.2. Representation of Uncertainty and Confidence in PIDF-LO
A set of shapes suitable for the expression of uncertainty in A set of shapes suitable for the expression of uncertainty in
location estimates in the Presence Information Data Format - Location location estimates in the Presence Information Data Format - Location
Object (PIDF-LO) are described in [GeoShape]. These shapes are the Object (PIDF-LO) are described in [GeoShape]. These shapes are the
recommended form for the representation of uncertainty in PIDF-LO recommended form for the representation of uncertainty in PIDF-LO
[RFC4119] documents. [RFC4119] documents.
The PIDF-LO does not include an indication of confidence, but that The PIDF-LO can contain uncertainty, but does not include an
confidence is 95%, by definition in [RFC5491]. Similarly, the PIDF- indication of confidence. [RFC5491] defines a fixed value of 95%.
LO format does not provide an indication of the shape of the PDF. Similarly, the PIDF-LO format does not provide an indication of the
Section 4 defines elements to convey this information. shape of the PDF. Section 4 defines elements to convey this
information in PIDF-LO.
Absence of uncertainty information in a PIDF-LO document does not Absence of uncertainty information in a PIDF-LO document does not
indicate that there is no uncertainty in the location estimate. indicate that there is no uncertainty in the location estimate.
Uncertainty might not have been calculated for the estimate, or it Uncertainty might not have been calculated for the estimate, or it
may be withheld for privacy purposes. may be withheld for privacy purposes.
If the Point shape is used, confidence and uncertainty are unknown; a If the Point shape is used, confidence and uncertainty are unknown; a
receiver can either assume a confidence of 0% or infinite receiver can either assume a confidence of 0% or infinite
uncertainty. The same principle applies on the altitude axis for uncertainty. The same principle applies on the altitude axis for
two-dimension shapes like the Circle. two-dimension shapes like the Circle.
3.3. Uncertainty and Confidence for Civic Addresses 3.3. Uncertainty and Confidence for Civic Addresses
Civic addresses [RFC5139] inherently include uncertainty, based on Automatically determined civic addresses [RFC5139] inherently include
the area of the most precise element that is specified. Uncertainty uncertainty, based on the area of the most precise element that is
is effectively defined by the presence or absence of elements -- specified. In this case, uncertainty is effectively described by the
elements that are not present are deemed to be uncertain. presence or absence of elements -- elements that are not present are
deemed to be uncertain.
To apply the concept of uncertainty to civic addresses, it is helpful To apply the concept of uncertainty to civic addresses, it is helpful
to unify the conceptual models of civic address with geodetic to unify the conceptual models of civic address with geodetic
location information. location information. This is particularly useful when considering
civic addresses that are determined using reverse geocoding (that is,
Note: This view is one perspective on the process of geo-coding - the process of translating geodetic information into civic
the translation of a civic address to a geodetic location. addresses).
In the unified view, a civic address defines a series of (sometimes In the unified view, a civic address defines a series of (sometimes
non-orthogonal) spatial partitions. The first is the implicit non-orthogonal) spatial partitions. The first is the implicit
partition that identifies the surface of the earth and the space near partition that identifies the surface of the earth and the space near
the surface. The second is the country. Each label that is included the surface. The second is the country. Each label that is included
in a civic address provides information about a different set of in a civic address provides information about a different set of
spatial partitions. Some partions require slight adjustments from a spatial partitions. Some partitions require slight adjustments from
standard interpretation: for instance, a road includes all properties a standard interpretation: for instance, a road includes all
that adjoin the street. Each label might need to be interpreted with properties that adjoin the street. Each label might need to be
other values to provide context. interpreted with other values to provide context.
As a value at each level is interpreted, one or more spatial As a value at each level is interpreted, one or more spatial
partitions at that level are selected, and all other partitions of partitions at that level are selected, and all other partitions of
that type are excluded. For non-orthogonal partitions, only the that type are excluded. For non-orthogonal partitions, only the
portion of the partition that fits within the existing space is portion of the partition that fits within the existing space is
selected. This is what distinguishes King Street in Sydney from King selected. This is what distinguishes King Street in Sydney from King
Street in Melbourne. Each defined element selects a partition of Street in Melbourne. Each defined element selects a partition of
space. The resulting location is the intersection of all selected space. The resulting location is the intersection of all selected
spaces. spaces.
The resulting spatial partition can be considered to represent a The resulting spatial partition can be considered as a region of
region of uncertainty. At no stage does this process select a point; uncertainty.
although, as spaces get smaller this distinction might have no
practical significance and an approximation if a point could be used. Note: This view is a potential perspective on the process of geo-
coding - the translation of a civic address to a geodetic
location.
Uncertainty in civic addresses can be increased by removing elements. Uncertainty in civic addresses can be increased by removing elements.
This doesn't necessarily improve confidence in the same way that This does not increase confidence unless additional information is
arbitrarily increasing uncertainty in a geodetic location doesn't used. Similarly, arbitrarily increasing uncertainty in a geodetic
increase confidence. location does not increase confidence.
3.4. DHCP Location Configuration Information and Uncertainty 3.4. DHCP Location Configuration Information and Uncertainty
Location information is often measured in two or three dimensions; Location information is often measured in two or three dimensions;
expressions of uncertainty in one dimension only are rare. The expressions of uncertainty in one dimension only are rare. The
"resolution" parameters in [RFC3825] provide an indication of "resolution" parameters in [RFC6225] provide an indication of how
uncertainty in one dimension. many bits of a number are valid, which could be interpreted as an
expression of uncertainty in one dimension.
[RFC3825] defines a means for representing uncertainty, but a value [RFC6225] defines a means for representing uncertainty, but a value
for confidence is not specified. A default value of 95% confidence for confidence is not specified. A default value of 95% confidence
can be assumed for the combination of the uncertainty on each axis. is assumed for the combination of the uncertainty on each axis. This
That is, the confidence of the resultant rectangular polygon or prism is consistent with the transformation of those forms into the
is 95%. uncertainty representations from [RFC5491]. That is, the confidence
of the resultant rectangular polygon or prism is assumed to be 95%.
4. Representation of Confidence in PIDF-LO 4. Representation of Confidence in PIDF-LO
On the whole, a fixed definition for confidence is preferable. On the whole, a fixed definition for confidence is preferable.
Primarily because it ensures consistency between implementations. Primarily because it ensures consistency between implementations.
Location generators that are aware of this constraint can generate Location generators that are aware of this constraint can generate
location information at the required confidence. Location recipients location information at the required confidence. Location recipients
are able to make sensible assumptions about the quality of the are able to make sensible assumptions about the quality of the
information that they receive. information that they receive.
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previously unavailable to recipients of location information. previously unavailable to recipients of location information.
Without this information, a location server or generator that has Without this information, a location server or generator that has
access to location information with a confidence lower than 95% has access to location information with a confidence lower than 95% has
two options: two options:
o The location server can scale regions of uncertainty in an attempt o The location server can scale regions of uncertainty in an attempt
to acheive 95% confidence. This scaling process significantly to acheive 95% confidence. This scaling process significantly
degrades the quality of the information, because the location degrades the quality of the information, because the location
server might not have the necessary information to scale server might not have the necessary information to scale
appropriately; the location server is forced to make assumptions appropriately; the location server is forced to make assumptions
that are likely result in either an overly conservative estimate that are likely to result in either an overly conservative
with high uncertainty or a overestimate of confidence. estimate with high uncertainty or a overestimate of confidence.
o The location server can ignore the confidence entirely, which o The location server can ignore the confidence entirely, which
results in giving the recipient a false impression of its quality. results in giving the recipient a false impression of its quality.
Both of these choices degrade the quality of the information Both of these choices degrade the quality of the information
provided. provided.
The addition of a confidence element avoids this problem entirely if The addition of a confidence element avoids this problem entirely if
a location recipient supports and understands the element. A a location recipient supports and understands the element. A
recipient that does not understand, and hence ignores, the confidence recipient that does not understand - and hence ignores - the
element is in no worse a position than if the location server ignored confidence element is in no worse a position than if the location
confidence. server ignored confidence.
4.1. The "confidence" Element 4.1. The "confidence" Element
The confidence element MAY be added to the "location-info" element of The confidence element MAY be added to the "location-info" element of
the Presence Information Data Format - Location Object (PIDF-LO) the Presence Information Data Format - Location Object (PIDF-LO)
[RFC4119] document. This element expresses the confidence in the [RFC4119] document. This element expresses the confidence in the
associated location information as a percentage. associated location information as a percentage. A special "unknown"
value is reserved to indicate that confidence is supported, but not
known to the Location Generator.
The confidence element optionally includes an attribute that The confidence element optionally includes an attribute that
indicates the shape of the probability density function (PDF) of the indicates the shape of the probability density function (PDF) of the
associated region of uncertainty. Three values are possible: associated region of uncertainty. Three values are possible:
unknown, normal and rectangular. unknown, normal and rectangular.
Indicating a particular PDF only indicates that the distribution Indicating a particular PDF only indicates that the distribution
approximately fits the given shape based on the methods used to approximately fits the given shape based on the methods used to
generate the location information. The PDF is normal if there are a generate the location information. The PDF is normal if there are a
large number of small, independent sources of error; rectangular if large number of small, independent sources of error; rectangular if
all points within the area have roughly equal probability of being all points within the area have roughly equal probability of being
the actual location of the Target; otherwise, the PDF MUST either be the actual location of the Target; otherwise, the PDF MUST either be
set to unknown or omitted. set to unknown or omitted.
If a PIDF-LO does not include the confidence element, confidence is If a PIDF-LO does not include the confidence element, the confidence
95% [RFC5491]. A Point shape does not have uncertainty (or it has of the location estimate is 95%, as defined in [RFC5491].
infinite uncertainty), so confidence is meaningless for a point;
therefore, this element MUST be omitted if only a point is provided. A Point shape does not have uncertainty (or it has infinite
uncertainty), so confidence is meaningless for a point; therefore,
this element MUST be omitted if only a point is provided.
4.2. Generating Locations with Confidence 4.2. Generating Locations with Confidence
Location generators SHOULD attempt to ensure that confidence is equal Location generators SHOULD attempt to ensure that confidence is equal
in each dimension when generating location information. This in each dimension when generating location information. This
restriction, while not always practical, allows for more accurate restriction, while not always practical, allows for more accurate
scaling, if scaling is necessary. scaling, if scaling is necessary.
Confidence MUST NOT be included unless location information cannot be A confidence element MUST be included with all location information
acquired with 95% confidence. that includes uncertainty (that is, all forms other than a point). A
special "unknown" MAY be used if confidence is not known.
4.3. Consuming and Presenting Confidence 4.3. Consuming and Presenting Confidence
The inclusion of confidence that is anything other than 95% presents The inclusion of confidence that is anything other than 95% presents
a potentially difficult usability problem for applications that use a potentially difficult usability problem for applications that use
location information. Effectively communicating the probability that location information. Effectively communicating the probability that
a location is incorrect to a user can be difficult. a location is incorrect to a user can be difficult.
It is inadvisable to simply display locations of any confidence, or It is inadvisable to simply display locations of any confidence, or
to display confidence in a separate or non-obvious fashion. If to display confidence in a separate or non-obvious fashion. If
skipping to change at page 14, line 13 skipping to change at page 14, line 18
estimate to a point. Different methods each make a set of estimate to a point. Different methods each make a set of
assumptions about the properties of the PDF and the selected point; assumptions about the properties of the PDF and the selected point;
no one method is more "correct" than any other. For any given region no one method is more "correct" than any other. For any given region
of uncertainty, selecting an arbitrary point within the area could be of uncertainty, selecting an arbitrary point within the area could be
considered valid; however, given the aforementioned problems with considered valid; however, given the aforementioned problems with
point locations, a more rigorous approach is appropriate. point locations, a more rigorous approach is appropriate.
Given a result with a known distribution, selecting the point within Given a result with a known distribution, selecting the point within
the area that has the highest probability is a more rigorous method. the area that has the highest probability is a more rigorous method.
Alternatively, a point could be selected that minimizes the overall Alternatively, a point could be selected that minimizes the overall
error; that is, it minimises the expected value of the difference error; that is, it minimizes the expected value of the difference
between the selected point and the "true" value. between the selected point and the "true" value.
If a rectangular distribution is assumed, the centroid of the area or If a rectangular distribution is assumed, the centroid of the area or
volume minimizes the overall error. Minimizing the error for a volume minimizes the overall error. Minimizing the error for a
normal distribution is mathematically complex. Therefore, this normal distribution is mathematically complex. Therefore, this
document opts to select the centroid of the region of uncertainty document opts to select the centroid of the region of uncertainty
when selecting a point. when selecting a point.
5.1.1. Centroid Calculation 5.1.1. Centroid Calculation
skipping to change at page 14, line 47 skipping to change at page 15, line 6
The centroid of the Arc-Band shape is found along a line that bisects The centroid of the Arc-Band shape is found along a line that bisects
the arc. The centroid can be found at the following distance from the arc. The centroid can be found at the following distance from
the starting point of the arc-band (assuming an arc-band with an the starting point of the arc-band (assuming an arc-band with an
inner radius of "r", outer radius "R", start angle "a", and opening inner radius of "r", outer radius "R", start angle "a", and opening
angle "o"): angle "o"):
d = 4 * sin(o/2) * (R*R + R*r + r*r) / (3*o*(R + r)) d = 4 * sin(o/2) * (R*R + R*r + r*r) / (3*o*(R + r))
This point can be found along the line that bisects the arc; that is, This point can be found along the line that bisects the arc; that is,
the line at an angle of "a + (o/2)". Negative values are possible if the line at an angle of "a + (o/2)".
the angle of opening is greater than 180 degrees; negative values
indicate that the centroid is found along the angle "a + (o/
2) + 180".
5.1.1.2. Polygon Centroid 5.1.1.2. Polygon Centroid
Calculating a centroid for the Polygon and Prism shapes is more Calculating a centroid for the Polygon and Prism shapes is more
complex. Polygons that are specified using geodetic coordinates are complex. Polygons that are specified using geodetic coordinates are
not necessarily coplanar. For Polygons that are specified without an not necessarily coplanar. For Polygons that are specified without an
altitude, choose a value for altitude before attempting this process; altitude, choose a value for altitude before attempting this process;
an altitude of 0 is acceptable. an altitude of 0 is acceptable.
The method described in this section is simplified by assuming The method described in this section is simplified by assuming
skipping to change at page 19, line 14 skipping to change at page 19, line 14
"C[2d]" is the confidence of the two-dimensional shape and "C[3d]" is "C[2d]" is the confidence of the two-dimensional shape and "C[3d]" is
the confidence of the three-dimensional shape. For example, a Sphere the confidence of the three-dimensional shape. For example, a Sphere
with a confidence of 95% can be simplified to a Circle of equal with a confidence of 95% can be simplified to a Circle of equal
radius with confidence of 96.6%. radius with confidence of 96.6%.
5.4. Increasing and Decreasing Uncertainty and Confidence 5.4. Increasing and Decreasing Uncertainty and Confidence
The combination of uncertainty and confidence provide a great deal of The combination of uncertainty and confidence provide a great deal of
information about the nature of the data that is being measured. If information about the nature of the data that is being measured. If
both uncertainty, confidence and PDF are known, certain information uncertainty, confidence and PDF are known, certain information can be
can be extrapolated. In particular, the uncertainty can be scaled to extrapolated. In particular, the uncertainty can be scaled to meet a
meet a desired confidence or the confidence for a particular region desired confidence or the confidence for a particular region of
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 [I-D.thomson-geopriv-location-obscuring]), then the confidence
cannot be increased. cannot be increased.
skipping to change at page 19, line 44 skipping to change at page 19, line 44
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
dimension. This is not necessarily true in practice. If better dimension. This is not necessarily true in practice. If better
information is available, alternative methods might produce better information is available, alternative methods might produce better
results. results.
5.4.1. Rectangular Distributions 5.4.1. Rectangular Distributions
Uncertainty that follows a rectangular distribution can only be Uncertainty that follows a rectangular distribution can only be
decreased in size. Since the PDF is constant over the region of decreased in size. Increasing uncertainty has no value, since it has
uncertainty, the resulting confidence is determined by the following no effect on confidence. Since the PDF is constant over the region
formula: of uncertainty, the resulting confidence is determined by the
following formula:
Cr = Co * Ur / Uo Cr = Co * Ur / Uo
Where "Uo" and "Ur" are the sizes of the original and reduced regions Where "Uo" and "Ur" are the sizes of the original and reduced regions
of uncertainty (either the area or the volume of the region); "Co" of uncertainty (either the area or the volume of the region); "Co"
and "Cb" are the confidence values associated with each region. and "Cb" are the confidence values associated with each region.
Information is lost by decreasing the region of uncertainty for a Information is lost by decreasing the region of uncertainty for a
rectangular distribution. Once reduced in size, the uncertainty rectangular distribution. Once reduced in size, the uncertainty
region cannot subsequently be increased in size. region cannot subsequently be increased in size.
5.4.2. Normal Distributions 5.4.2. Normal Distributions
Uncertainty and confidence can be both increased and decreased for a Uncertainty and confidence can be both increased and decreased for a
normal distribution. However, the process is more complicated. normal distribution. This calculation depends on the number of
dimensions of the uncertainty region.
For a normal distribution, uncertainty and confidence are related to For a normal distribution, uncertainty and confidence are related to
the standard deviation of the function. The following function the standard deviation of the function. The following function
defines the relationship between standard deviation, uncertainty and defines the relationship between standard deviation, uncertainty, and
confidence along a single axis: confidence along a single axis:
S[x] = U[x] / ( sqrt(2) * erfinv(C[x]) ) S[x] = U[x] / ( sqrt(2) * erfinv(C[x]) )
Where "S[x]" is the standard deviation, "U[x]" is the uncertainty and Where "S[x]" is the standard deviation, "U[x]" is the uncertainty,
"C[x]" is the confidence along a single axis. "erfinv" is the and "C[x]" is the confidence along a single axis. "erfinv" is the
inverse error function. inverse error function.
Scaling a normal distribution in two dimensions requires several Scaling a normal distribution in two dimensions requires several
assumptions. Firstly, it is assumed that the distribution along each assumptions. Firstly, it is assumed that the distribution along each
axis is independent. Secondly, the confidence for each axis is the axis is independent. Secondly, the confidence for each axis is
same. Therefore, the confidence along each axis can be assumed to assumed to be the same. Therefore, the confidence along each axis
be: can be assumed to be:
C[x] = Co ^ (1/n) C[x] = Co ^ (1/n)
Where "C[x]" is the confidence along a single axis and "Co" is the Where "C[x]" is the confidence along a single axis and "Co" is the
overall confidence and "n" is the number of dimensions in the overall confidence and "n" is the number of dimensions in the
uncertainty. uncertainty.
Therefore, to find the uncertainty for each axis at a desired Therefore, to find the uncertainty for each axis at a desired
confidence, "Cd", apply the following formula: confidence, "Cd", apply the following formula:
Ud[x] <= U[x] * (erfinv(Cd ^ (1/n)) / erfinv(Co ^ (1/n))) Ud[x] <= U[x] * (erfinv(Cd ^ (1/n)) / erfinv(Co ^ (1/n)))
For regular shapes, this formula can be applied as a scaling factor For regular shapes, this formula can be applied as a scaling factor
in each dimension to reach a required confidence. in each dimension to reach a required confidence.
5.5. Determining Whether a Location is Within a Given Region 5.5. Determining Whether a Location is Within a Given Region
A number of applications require that a judgement be made about A number of applications require that a judgment be made about
whether a Target is within a given region of interest. Given a whether a Target is within a given region of interest. Given a
location estimate with uncertainty, this judgement can be difficult. location estimate with uncertainty, this judgment can be difficult.
A location estimate represents a probability distribution, and the A location estimate represents a probability distribution, and the
true location of the Target cannot be definitively known. Therefore, true location of the Target cannot be definitively known. Therefore,
the judgement relies on determining the probability that the Target the judgment relies on determining the probability that the Target is
is within the region. within the region.
The probability that the Target is within a particular region is The probability that the Target is within a particular region is
found by integrating the PDF over the region. For a normal found by integrating the PDF over the region. For a normal
distribution, there are no analytical methods that can be used to distribution, there are no analytical methods that can be used to
determine the integral of the two or three dimensional PDF over an determine the integral of the two or three dimensional PDF over an
arbitrary region. The complexity of numerical methods is also too arbitrary region. The complexity of numerical methods is also too
great to be useful in many applications; for example, finding the great to be useful in many applications; for example, finding the
integral of the PDF in two or three dimensions across the overlap integral of the PDF in two or three dimensions across the overlap
between the uncertainty region and the target region. If the PDF is between the uncertainty region and the target region. If the PDF is
unknown, no determination can be made. When judging whether a unknown, no determination can be made without a simplifying
location is within a given region, uncertainties using these PDFs can assumption.
be assumed to be rectangular. If this assumption is made, the
confidence should be scaled to 95%, if possible.
Note: The selection of confidence has a significant impact on the When judging whether a location is within a given region, this
document assumes that uncertainties are rectangular. This introduces
errors, but simplifies the calculations significantly. Prior to
applying this assumption, confidence should be scaled to 95%.
Note: The selection of confidence has a significant impact on the
final result. Only use a different confidence if an uncertainty final result. Only use a different confidence if an uncertainty
value for 95% confidence cannot be found. value for 95% confidence cannot be found.
Given the assumption of a rectangular distribution, the probability Given the assumption of a rectangular distribution, the probability
that a Target is found within a given region is found by first that a Target is found within a given region is found by first
finding the area (or volume) of overlap between the uncertainty finding the area (or volume) of overlap between the uncertainty
region and the region of interest. This is multiplied by the region and the region of interest. This is multiplied by the
confidence of the location estimate to determine the probability. confidence of the location estimate to determine the probability.
Figure 7 shows an example of finding the area of overlap between the Figure 7 shows an example of finding the area of overlap between the
region of uncertainty and the region of interest. region of uncertainty and the region of interest.
skipping to change at page 23, line 23 skipping to change at page 23, line 45
contained within the smaller polygon. Where the entire area of the contained within the smaller polygon. Where the entire area of the
larger polygon is of interest, geodesic interpolation is necessary. larger polygon is of interest, geodesic interpolation is necessary.
6. Examples 6. Examples
This section presents some examples of how to apply the methods This section presents some examples of how to apply the methods
described in Section 5. described in Section 5.
6.1. Reduction to a Point or Circle 6.1. Reduction to a Point or Circle
Alice receives a location estimate from her LIS that contains a Alice receives a location estimate from her LIS that contains an
ellipsoidal region of uncertainty. This information is provided at ellipsoidal region of uncertainty. This information is provided at
19% confidence with a normal PDF. A PIDF-LO extract for this 19% confidence with a normal PDF. A PIDF-LO extract for this
information is shown in Figure 8. information is shown in Figure 8.
<gp:geopriv> <gp:geopriv>
<gp:location-info> <gp:location-info>
<gs:Ellipsoid srsName="urn:ogc:def:crs:EPSG::4979"> <gs:Ellipsoid srsName="urn:ogc:def:crs:EPSG::4979">
<gml:pos>-34.407242 150.882518 34</gml:pos> <gml:pos>-34.407242 150.882518 34</gml:pos>
<gs:semiMajorAxis uom="urn:ogc:def:uom:EPSG::9001"> <gs:semiMajorAxis uom="urn:ogc:def:uom:EPSG::9001">
7.7156 7.7156
skipping to change at page 24, line 39 skipping to change at page 25, line 23
</gml:posList> </gml:posList>
</gml:LinearRing> </gml:LinearRing>
</gml:exterior> </gml:exterior>
</gml:Polygon> </gml:Polygon>
Figure 9 Figure 9
To convert this to a polygon, each point is firstly assigned an To convert this to a polygon, each point is firstly assigned an
altitude of zero and converted to ECEF coordinates (see Appendix A). altitude of zero and converted to ECEF coordinates (see Appendix A).
Then a normal vector for this polygon is found (see Appendix B). The Then a normal vector for this polygon is found (see Appendix B). The
results of each of these stages is shown in Figure 10. Note that the result of each of these stages is shown in Figure 10. Note that the
numbers shown are all rounded; no rounding is possible during this numbers shown are all rounded; no rounding is possible during this
process since rounding would contribute significant errors. process since rounding would contribute significant errors.
Polygon in ECEF coordinate space Polygon in ECEF coordinate space
(repeated point omitted and transposed to fit): (repeated point omitted and transposed to fit):
[ -4.6470e+06 2.5530e+06 -3.5333e+06 ] [ -4.6470e+06 2.5530e+06 -3.5333e+06 ]
[ -4.6470e+06 2.5531e+06 -3.5332e+06 ] [ -4.6470e+06 2.5531e+06 -3.5332e+06 ]
pecef = [ -4.6470e+06 2.5531e+06 -3.5332e+06 ] pecef = [ -4.6470e+06 2.5531e+06 -3.5332e+06 ]
[ -4.6469e+06 2.5531e+06 -3.5333e+06 ] [ -4.6469e+06 2.5531e+06 -3.5333e+06 ]
[ -4.6469e+06 2.5531e+06 -3.5334e+06 ] [ -4.6469e+06 2.5531e+06 -3.5334e+06 ]
skipping to change at page 26, line 8 skipping to change at page 27, line 8
ignoring the altitude since the original shape did not include ignoring the altitude since the original shape did not include
altitude. altitude.
To convert this to a circle, take the maximum distance in ECEF To convert this to a circle, take the maximum distance in ECEF
coordinates from the center point to each of the points. This coordinates from the center point to each of the points. This
results in a radius of 99.1 meters. Confidence is unchanged. results in a radius of 99.1 meters. Confidence is unchanged.
6.2. Increasing and Decreasing Confidence 6.2. Increasing and Decreasing Confidence
Assuming that confidence is known to be 19% for Alice's location Assuming that confidence is known to be 19% for Alice's location
information. This is typical value for a three-dimensional ellipsoid information. This is a typical value for a three-dimensional
uncertainty of normal distribution where the standard deviation is ellipsoid uncertainty of normal distribution where the standard
supplied in each dimension. The confidence associated with Alice's deviation is used directly for uncertainty in each dimension. The
location estimate is quite low for many applications. Since the confidence associated with Alice's location estimate is quite low for
estimate is known to follow a normal distribution, the method in many applications. Since the estimate is known to follow a normal
Section 5.4.2 can be used. Each axis can be scaled by: distribution, the method in Section 5.4.2 can be used. Each axis can
be scaled by:
scale = erfinv(0.95^(1/3)) / erfinv(0.19^(1/3)) = 2.9937 scale = erfinv(0.95^(1/3)) / erfinv(0.19^(1/3)) = 2.9937
Ensuring that rounding always increases uncertainty, the location Ensuring that rounding always increases uncertainty, the location
estimate at 95% includes a semi-major axis of 23.1, a semi-minor axis estimate at 95% includes a semi-major axis of 23.1, a semi-minor axis
of 10 and a vertical axis of 86. of 10 and a vertical axis of 86.
Bob's location estimate covers an area of approximately 12600 square Bob's location estimate (from the previous example) covers an area of
meters. If the estimate follows a rectangular distribution, the approximately 12600 square meters. If the estimate follows a
region of uncertainty can be reduced in size. To find the confidence rectangular distribution, the region of uncertainty can be reduced in
that he is within the smaller area of the concert hall, given by the size. Here we find the confidence that Bob is within the smaller
polygon [-33.856473, 151.215257; -33.856322, 151.214973; area of the concert hall. For the concert hall, the polygon
[-33.856473, 151.215257; -33.856322, 151.214973;
-33.856424, 151.21471; -33.857248, 151.214753; -33.856424, 151.21471; -33.857248, 151.214753;
-33.857413, 151.214941; -33.857311, 151.215128]. To use this new -33.857413, 151.214941; -33.857311, 151.215128] is used. To use this
region of uncertainty, find its area using the same translation new region of uncertainty, find its area using the same translation
method described in Section 5.1.1.2, which is 4566.2 square meters. method described in Section 5.1.1.2, which produces 4566.2 square
The confidence associated with the smaller area is therefore 95% * meters. Given that the concert hall is entirely within Bob's
4566.2 / 12600 = 34%. original location estimate, the confidence associated with the
smaller area is therefore 95% * 4566.2 / 12600 = 34%.
6.3. Matching Location Estimates to Regions of Interest 6.3. Matching Location Estimates to Regions of Interest
Suppose than a circular area is defined centered at Suppose that a circular area is defined centered at
[-33.872754, 151.20683] with a radius of 1950 meters. To determine [-33.872754, 151.20683] with a radius of 1950 meters. To determine
whether Bob is found within this area, we apply the method in whether Bob is found within this area - given that Bob is at
Section 5.5. Using the converted Circle shape for Bob's location, [-34.407242, 150.882518] with an uncertainty radius 7.7156 meters -
the distance between these points is found to be 1915.26 meters. The we apply the method in Section 5.5. Using the converted Circle shape
area of overlap between Bob's location estimate and the region of for Bob's location, the distance between these points is found to be
interest is therefore 2209 square meters and the area of Bob's 1915.26 meters. The area of overlap between Bob's location estimate
location estimate is 30853 square meters. This gives the probability and the region of interest is therefore 2209 square meters and the
that Bob is less than 1950 meters from the selected point as 67.8%. area of Bob's location estimate is 30853 square meters. This gives
the estimated probability that Bob is less than 1950 meters from the
selected point as 67.8%.
Note that if 1920 meters were chosen for the distance from the Note that if 1920 meters were chosen for the distance from the
selected point, the area of overlap is only 16196 square meters and selected point, the area of overlap is only 16196 square meters and
the confidence is 49.8%. Therefore, it is marginally more likely the confidence is 49.8%. Therefore, it is marginally more likely
that Bob is outside the region of interest, despite the center point that Bob is outside the region of interest, despite the center point
of his location estimate being within the region. of his location estimate being within the region.
6.4. PIDF-LO With Confidence Example 6.4. PIDF-LO With Confidence Example
The PIDF-LO document in Figure 11 includes a representation of The PIDF-LO document in Figure 11 includes a representation of
skipping to change at page 28, line 35 skipping to change at page 29, line 35
<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:restriction base="xs:decimal"> <xs:restriction base="xs:decimal">
<xs:minExclusive value="0.0"/> <xs:minInclusive value="0.0"/>
<xs:maxExclusive value="100.0"/> <xs:maxInclusive value="100.0"/>
</xs:restriction>
<xs:restriction base="xs:token">
<xs:enumeration value="unknown"/>
</xs:restriction> </xs:restriction>
</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].
URI: urn:ietf:params:xml:ns:geopriv:conf URI: urn:ietf:params:xml:ns:geopriv:conf
Registrant Contact: IETF, GEOPRIV working group, Registrant Contact: IETF, GEOPRIV working group, (geopriv@ietf.org),
(geopriv@ietf.org), Martin Thomson (martin.thomson@andrew.com). Martin Thomson (martin.thomson@gmail.com).
XML: XML:
BEGIN BEGIN
<?xml version="1.0"?> <?xml version="1.0"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head> <head>
<title>PIDF-LO Confidence Attribute</title> <title>PIDF-LO Confidence Attribute</title>
</head> </head>
<body> <body>
skipping to change at page 29, line 47 skipping to change at page 30, line 47
END END
8.2. XML Schema Registration 8.2. XML Schema Registration
This section registers an XML schema as per the guidelines in This section registers an XML schema as per the guidelines in
[RFC3688]. [RFC3688].
URI: urn:ietf:params:xml:schema:geopriv:conf URI: urn:ietf:params:xml:schema:geopriv:conf
Registrant Contact: IETF, GEOPRIV working group, (geopriv@ietf.org), Registrant Contact: IETF, GEOPRIV working group, (geopriv@ietf.org),
Martin Thomson (martin.thomson@andrew.com). Martin Thomson (martin.thomson@gmail.com).
Schema: The XML for this schema can be found as the entirety of Schema: The XML for this schema can be found as the entirety of
Section 7 of this document. Section 7 of this document.
9. Security Considerations 9. Security Considerations
This document describes methods for managing and manipulating This document describes methods for managing and manipulating
uncertainty in location. No specific security concerns arise from uncertainty in location. No specific security concerns arise from
most of the information provided. most of the information provided.
skipping to change at page 31, line 16 skipping to change at page 32, line 16
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 [RFC3693] Cuellar, J., Morris, J., Mulligan, D., Peterson, J., and
J. Polk, "Geopriv Requirements", RFC 3693, February 2004. J. Polk, "Geopriv Requirements", RFC 3693, February 2004.
[RFC3694] Danley, M., Mulligan, D., Morris, J., and J. Peterson,
"Threat Analysis of the Geopriv Protocol", RFC 3694,
February 2004.
[RFC3825] Polk, J., Schnizlein, J., and M. Linsner, "Dynamic Host
Configuration Protocol Option for Coordinate-based
Location Configuration Information", RFC 3825, July 2004.
[RFC5139] Thomson, M. and J. Winterbottom, "Revised Civic Location [RFC5139] Thomson, M. and J. Winterbottom, "Revised Civic Location
Format for Presence Information Data Format Location Format for Presence Information Data Format Location
Object (PIDF-LO)", RFC 5139, February 2008. 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 [RFC5491] Winterbottom, J., Thomson, M., and H. Tschofenig, "GEOPRIV
Presence Information Data Format Location Object (PIDF-LO) Presence Information Data Format Location Object (PIDF-LO)
Usage Clarification, Considerations, and Recommendations", Usage Clarification, Considerations, and Recommendations",
RFC 5491, March 2009. 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., [RFC6280] Barnes, R., Lepinski, M., Cooper, A., Morris, J.,
Tschofenig, H., and H. Schulzrinne, "An Architecture for Tschofenig, H., and H. Schulzrinne, "An Architecture for
Location and Location Privacy in Internet Applications", Location and Location Privacy in Internet Applications",
BCP 160, RFC 6280, July 2011. 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/>.
skipping to change at page 33, line 4 skipping to change at page 33, line 49
methods introduce some error in latitude and altitude. A range of methods introduce some error in latitude and altitude. A range of
techniques are described in [Convert]. A variant on the method techniques are described in [Convert]. A variant on the method
originally proposed by Bowring, which results in an acceptably small originally proposed by Bowring, which results in an acceptably small
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) /
(p - e^2 * R * cos(u)^3))
latitude = atan((Z + e'^2 * (1-f) * R * sin(u)^3)
/ (p - e^2 * R * cos(u)^3))
longitude = atan(Y / X) longitude = atan(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)
skipping to change at page 34, line 37 skipping to change at page 35, line 36
Up = [ cos(lat) * cos(lng) ; cos(lat) * sin(lng) ; sin(lat) ] Up = [ cos(lat) * cos(lng) ; cos(lat) * sin(lng) ; sin(lat) ]
For polygons that span less than half the globe, any point in the For polygons that span less than half the globe, any point in the
polygon - including the centroid - can be selected to generate an polygon - including the centroid - can be selected to generate an
approximate up vector for comparison with the upward normal. approximate up vector for comparison with the upward normal.
Authors' Addresses Authors' Addresses
Martin Thomson Martin Thomson
Mozilla Mozilla
Suite 300 331 E Evelyn Street
650 Castro Street
Mountain View, CA 94041 Mountain View, CA 94041
US US
Email: martin.thomson@gmail.com Email: martin.thomson@gmail.com
James Winterbottom James Winterbottom
Unaffiliated Unaffiliated
AU AU
Email: a.james.winterbottom@gmail.com Email: a.james.winterbottom@gmail.com
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