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 | |||

skipping to change at page 1, line 33 | skipping to change at page 1, line 33 | |||

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 | |||

skipping to change at page 2, line 32 | skipping to change at page 2, line 32 | |||

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 | |||

skipping to change at page 4, line 27 | skipping to change at page 4, line 36 | |||

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 | |||

skipping to change at page 8, line 16 | skipping to change at page 8, line 16 | |||

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. | |||

skipping to change at page 11, line 16 | skipping to change at page 11, line 19 | |||

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 | |||

End of changes. 66 change blocks. | ||||

163 lines changed or deleted | | 196 lines changed or added | ||

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