*****
                           **:::::**
                         **:::::::::**
                        **:::::::::::**
                       *:::::::::::::::*
                      **:::::::::::::::**
                     **:::::::::::::::::**
                    *:::::::::::::::::::::*
                   *:::::::::::::::::::::::*
                  **:::::::::::::::::::::::**
                 *:::::::::::: c ::::::::::::*
                *:::::::::::::::::::::::::::::*
              **|:::::::::::::::::::::::::::::|**
            **  |:::::::::::::::::::::::::::::|  **
         ***    |:::::::::::::::::::::::::::::|    ***
     *****      |:::::::::::::::::::::::::::::|      *****
 .****..........!:::::::::::::::::::::::::::::!..........*****.
                |              |              |
              (m-u)            m            (m+u)

Figure 2: Confidence as the Integral of a PDF

In Section 5.4, methods are described for manipulating uncertainty if the shape of the PDF is known.

2.2. Deprecation of the Terms Precision and Resolution

The terms Precision and Resolution are defined in RFC 3693 [RFC3693]. These definitions were intended to provide a common nomenclature for discussing uncertainty; however, these particular terms have many different uses in other fields and their definitions are not sufficient to avoid confusion about their meaning. These terms are unsuitable for use in relation to quantitative concepts when discussing uncertainty and confidence in relation to location information.

2.3. Accuracy as a Qualitative Concept

Uncertainty is a quantitative concept. The term accuracy is useful in describing, qualitatively, the general concepts of location information. Accuracy is generally useful when describing qualitative aspects of location estimates. Accuracy is not a suitable term for use in a quantitative context.

For instance, it could be appropriate to say that a location estimate with uncertainty X is more accurate than a location estimate with uncertainty 2X at the same confidence. It is not appropriate to assign a number to "accuracy", nor is it appropriate to refer to any component of uncertainty or confidence as "accuracy". That is, to say that the "accuracy" for the first location estimate is X would be an erroneous use of this term.

3. Uncertainty in Location

A location estimate is the result of location determination. A location estimate is subject to uncertainty like any other observation. However, unlike a simple measure of a one dimensional property like length, a location estimate is specified in two or three dimensions.

Uncertainty in two or three dimensional locations can be described using confidence intervals. The confidence interval for a location estimate in two or three dimensional space is expressed as a subset of that space. This document uses the term region of uncertainty to refer to the area or volume that describes the confidence interval.

Areas or volumes that describe regions of uncertainty can be formed by the combination of two or three one-dimensional ranges, or more complex shapes could be described (for example, the shapes in [RFC5491]).

3.1. Targets as Points in Space

This document makes a simplifying assumption that the Target of the PIDF-LO occupies just a single point in space. While this is clearly false in virtually all scenarios with any practical application, it is often a reasonable simplifying assumption to make.

To a large extent, whether this simplification is valid depends on the size of the target relative to the size of the uncertainty region. When locating a personal device using contemporary location determination techniques, the space the device occupies relative to the uncertainty is proportionally quite small. Even where that device is used as a proxy for a person, the proportions change little.

This assumption is less useful as uncertainty becomes small relative to the size of the Target of the PIDF-LO (or conversely, as uncertainty becomes small relative to the Target). For instance, describing the location of a football stadium or small country would include a region of uncertainty that is infinitesimally larger than the Target itself. In these cases, much of the guidance in this document is not applicable. Indeed, as the accuracy of location 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

A set of shapes suitable for the expression of uncertainty in location estimates in the Presence Information Data Format - Location Object (PIDF-LO) are described in [GeoShape]. These shapes are the recommended form for the representation of uncertainty in PIDF-LO [RFC4119] documents.

The PIDF-LO can contain uncertainty, but does not include an indication of confidence. [RFC5491] defines a fixed value of 95%. Similarly, the PIDF-LO format does not provide an indication of the 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 indicate that there is no uncertainty in the location estimate. Uncertainty might not have been calculated for the estimate, or it may be withheld for privacy purposes.

If the Point shape is used, confidence and uncertainty are unknown; a receiver can either assume a confidence of 0% or infinite uncertainty. The same principle applies on the altitude axis for two-dimension shapes like the Circle.

3.3. Uncertainty and Confidence for Civic Addresses

Automatically determined civic addresses [RFC5139] inherently include uncertainty, based on the area of the most precise element that is specified. In this case, uncertainty is effectively described by the 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 unify the conceptual models of civic address with geodetic location information. This is particularly useful when considering civic addresses that are determined using reverse geocoding (that is, the process of translating geodetic information into civic addresses).

In the unified view, a civic address defines a series of (sometimes non-orthogonal) spatial partitions. The first is the implicit partition that identifies the surface of the earth and the space near the surface. The second is the country. Each label that is included in a civic address provides information about a different set of spatial partitions. Some partitions require slight adjustments from a standard interpretation: for instance, a road includes all properties that adjoin the street. Each label might need to be interpreted with other values to provide context.

As a value at each level is interpreted, one or more spatial partitions at that level are selected, and all other partitions of that type are excluded. For non-orthogonal partitions, only the portion of the partition that fits within the existing space is selected. This is what distinguishes King Street in Sydney from King Street in Melbourne. Each defined element selects a partition of space. The resulting location is the intersection of all selected spaces.

The resulting spatial partition can be considered as a region of uncertainty.

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. This does not increase confidence unless additional information is used. Similarly, arbitrarily increasing uncertainty in a geodetic location does not increase confidence.

3.4. DHCP Location Configuration Information and Uncertainty

Location information is often measured in two or three dimensions; expressions of uncertainty in one dimension only are rare. The "resolution" parameters in [RFC6225] provide an indication of how many bits of a number are valid, which could be interpreted as an expression of uncertainty in one dimension.

[RFC6225] defines a means for representing uncertainty, but a value for confidence is not specified. A default value of 95% confidence is assumed for the combination of the uncertainty on each axis. This is consistent with the transformation of those forms into the 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

On the whole, a fixed definition for confidence is preferable. Primarily because it ensures consistency between implementations. Location generators that are aware of this constraint can generate location information at the required confidence. Location recipients are able to make sensible assumptions about the quality of the information that they receive.

In some circumstances - particularly with pre-existing systems - location generators might unable to provide location information with consistent confidence. Existing systems sometimes specify confidence at 38%, 67% or 90%. Existing forms of expressing location information, such as that defined in [TS-3GPP-23_032], contain elements that express the confidence in the result.

The addition of a confidence element provides information that was previously unavailable to recipients of location information. Without this information, a location server or generator that has access to location information with a confidence lower than 95% has two options:

• The location server can scale regions of uncertainty in an attempt to acheive 95% confidence. This scaling process significantly degrades the quality of the information, because the location server might not have the necessary information to scale appropriately; the location server is forced to make assumptions that are likely to result in either an overly conservative estimate with high uncertainty or a overestimate of confidence.
• The location server can ignore the confidence entirely, which results in giving the recipient a false impression of its quality.

Both of these choices degrade the quality of the information provided.

The addition of a confidence element avoids this problem entirely if a location recipient supports and understands the element. A recipient that does not understand - and hence ignores - the confidence element is in no worse a position than if the location server ignored confidence.

4.1. The "confidence" Element

The confidence element MAY be added to the location-info element of the Presence Information Data Format - Location Object (PIDF-LO) [RFC4119] document. This element expresses the confidence in the 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 indicates the shape of the probability density function (PDF) of the associated region of uncertainty. Three values are possible: unknown, normal and rectangular.

Indicating a particular PDF only indicates that the distribution approximately fits the given shape based on the methods used to generate the location information. The PDF is normal if there are a large number of small, independent sources of error; rectangular if all points within the area have roughly equal probability of being the actual location of the Target; otherwise, the PDF MUST either be set to unknown or omitted.

If a PIDF-LO does not include the confidence element, the confidence of the location estimate is 95%, as defined in [RFC5491].

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

Location generators SHOULD attempt to ensure that confidence is equal in each dimension when generating location information. This restriction, while not always practical, allows for more accurate scaling, if scaling is necessary.

A confidence element MUST be included with all location information 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

The inclusion of confidence that is anything other than 95% presents a potentially difficult usability problem for applications that use location information. Effectively communicating the probability that a location is incorrect to a user can be difficult.

It is inadvisable to simply display locations of any confidence, or to display confidence in a separate or non-obvious fashion. If locations with different confidence levels are displayed such that the distinction is subtle or easy to overlook - such as using fine graduations of color or transparency for graphical uncertainty regions, or displaying uncertainty graphically, but providing confidence as supplementary text - a user could fail to notice a difference in the quality of the location information that might be significant.

Depending on the circumstances, different ways of handling confidence might be appropriate. Section 5 describes techniques that could be appropriate for consumers that use automated processing.

Providing that the full implications of any choice for the application are understood, some amount of automated processing could be appropriate. In a simple example, applications could choose to discard or suppress the display of location information if confidence does not meet a pre-determined threshold.

In settings where there is an opportunity for user training, some of these problems might be mitigated by defining different operational procedures for handling location information at different confidence levels.

5. Manipulation of Uncertainty

This section deals with manipulation of location information that contains uncertainty.

The following rules generally apply when manipulating location information:

• Where calculations are performed on coordinate information, these should be performed in Cartesian space and the results converted back to latitude, longitude and altitude. A method for converting to and from Cartesian coordinates is included in Appendix A.
  • While some approximation methods are useful in simplifying calculations, treating latitude and longitude as Cartesian axes is never advisable. The two axes are not orthogonal. Errors can arise from the curvature of the earth and from the convergence of longitude lines.

• Normal rounding rules do not apply when rounding uncertainty. When rounding, the region of uncertainty always increases (that is, errors are rounded up) and confidence is always rounded down (see [NIST.TN1297]). This means that any manipulation of uncertainty is a non-reversible operation; each manipulation can result in the loss of some information.

5.1. Reduction of a Location Estimate to a Point

Manipulating location estimates that include uncertainty information requires additional complexity in systems. In some cases, systems only operate on definitive values, that is, a single point.

This section describes algorithms for reducing location estimates to a simple form without uncertainty information. Having a consistent means for reducing location estimates allows for interaction between applications that are able to use uncertainty information and those that cannot.

Note:

Reduction of a location estimate to a point constitutes a reduction in information. Removing uncertainty information can degrade results in some applications. Also, there is a natural tendency to misinterpret a point location as representing a location without uncertainty. This could lead to more serious errors. Therefore, these algorithms should only be applied where necessary.

Several different approaches can be taken when reducing a location estimate to a point. Different methods each make a set of assumptions about the properties of the PDF and the selected point; no one method is more "correct" than any other. For any given region of uncertainty, selecting an arbitrary point within the area could be considered valid; however, given the aforementioned problems with point locations, a more rigorous approach is appropriate.

Given a result with a known distribution, selecting the point within the area that has the highest probability is a more rigorous method. Alternatively, a point could be selected that minimizes the overall error; that is, it minimizes the expected value of the difference between the selected point and the "true" value.

If a rectangular distribution is assumed, the centroid of the area or volume minimizes the overall error. Minimizing the error for a normal distribution is mathematically complex. Therefore, this document opts to select the centroid of the region of uncertainty when selecting a point.

5.1.1. Centroid Calculation

For regular shapes, such as Circle, Sphere, Ellipse and Ellipsoid, this approach equates to the center point of the region. For regions of uncertainty that are expressed as regular Polygons and Prisms the center point is also the most appropriate selection.

For the Arc-Band shape and non-regular Polygons and Prisms, selecting the centroid of the area or volume minimizes the overall error. This assumes that the PDF is rectangular.

Note:

The centroid of a concave Polygon or Arc-Band shape is not necessarily within the region of uncertainty.

5.1.1.1. Arc-Band Centroid

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 starting point of the arc-band (assuming an arc-band with an inner radius of r, outer radius R, start angle a, and opening angle o): a + (o/2).

• 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, the line at an angle of

5.1.1.2. Polygon Centroid

Calculating a centroid for the Polygon and Prism shapes is more complex. Polygons that are specified using geodetic coordinates are not necessarily coplanar. For Polygons that are specified without an altitude, choose a value for altitude before attempting this process; an altitude of 0 is acceptable.

• The method described in this section is simplified by assuming that the surface of the earth is locally flat. This method degrades as polygons become larger; see [GeoShape] for recommendations on polygon size.

The polygon is translated to a new coordinate system that has an x-y plane roughly parallel to the polygon. This enables the elimination of z-axis values and calculating a centroid can be done using only x and y coordinates. This requires that the upward normal for the polygon is known.

To translate the polygon coordinates, apply the process described in Appendix B to find the normal vector N = [Nx,Ny,Nz]. This value should be made a unit vector to ensure that the transformation matrix is a special orthogonal matrix. From this vector, select two vectors that are perpendicular to this vector and combine these into a transformation matrix.

If Nx and Ny are non-zero, the matrices in Figure 3 can be used, given p = sqrt(Nx^2 + Ny^2). More transformations are provided later in this section for cases where Nx or Ny are zero.

       [   -Ny/p     Nx/p     0  ]         [ -Ny/p  -Nx*Nz/p  Nx ]
   T = [ -Nx*Nz/p  -Ny*Nz/p   p  ]    T' = [  Nx/p  -Ny*Nz/p  Ny ]
       [    Nx        Ny      Nz ]         [   0      p       Nz ]
              (Transform)                    (Reverse Transform)

   [   -Ny/p     Nx/p     0  ]   [ x[1]  x[2]  x[3]  ...  x[n] ]
   [ -Nx*Nz/p  -Ny*Nz/p   p  ] * [ y[1]  y[2]  y[3]  ...  y[n] ]
   [    Nx        Ny      Nz ]   [ z[1]  z[2]  z[3]  ...  z[n] ]

       [ x'[1]  x'[2]  x'[3]  ... x'[n] ]
     = [ y'[1]  y'[2]  y'[3]  ... y'[n] ]
       [ z'[1]  z'[2]  z'[3]  ... z'[n] ]

   [ -Ny/p  -Nx*Nz/p  Nx ]     [       Cx'        ]   [ Cx ]
   [  Nx/p  -Ny*Nz/p  Ny ]  *  [       Cy'        ] = [ Cy ]
   [   0        p     Nz ]     [ sum of z'[i] / n ]   [ Cz ]

 if Nx == 0:                              | if Ny == 0:
     [ 0  -Nz  Ny ]       [  0   1  0  ]  |            [ -Nz  0  Nx ]
 T = [ 1   0   0  ]  T' = [ -Nz  0  Ny ]  |   T = T' = [  0   1  0  ]
     [ 0   Ny  Nz ]       [  Ny  0  Nz ]  |            [  Nx  0  Nz ]

                 _.-""""-._
               .'          `.    _ Region of
              /              \  /  Uncertainty
           ..+-"""--..        |
        .-'  | :::::: `-.     |
      ,'     | :: Ao ::: `.   |
     /        \ :::::::::: \ /
    /          `._ :::::: _.X
   |              `-....-'   |
   |                         |
   |                         |
    \                       /
     `.                   .'  \_ Region of
       `._             _.'       Interest
          `--..___..--'

  <gp:geopriv>
    <gp:location-info>
      <gs:Ellipsoid srsName="urn:ogc:def:crs:EPSG::4979">
        <gml:pos>-34.407242 150.882518 34</gml:pos>
        <gs:semiMajorAxis uom="urn:ogc:def:uom:EPSG::9001">
          7.7156
        </gs:semiMajorAxis>
        <gs:semiMinorAxis uom="urn:ogc:def:uom:EPSG::9001">
          3.31
        </gs:semiMinorAxis>
        <gs:verticalAxis uom="urn:ogc:def:uom:EPSG::9001">
          28.7
        </gs:verticalAxis>
        <gs:orientation uom="urn:ogc:def:uom:EPSG::9102">
          43
        </gs:orientation>
      </gs:Ellipsoid>
    </gp:location-info>
    <gp:usage-rules/>
  </gp:geopriv>

  <gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326">
    <gml:exterior>
      <gml:LinearRing>
        <gml:posList>
          -33.856625 151.215906 -33.856299 151.215343
          -33.856326 151.214731 -33.857533 151.214495
          -33.857720 151.214613 -33.857369 151.215375
          -33.856625 151.215906
        </gml:posList>
      </gml:LinearRing>
    </gml:exterior>
  </gml:Polygon>

Polygon in ECEF coordinate space
   (repeated point omitted and transposed to fit):
         [ -4.6470e+06  2.5530e+06  -3.5333e+06 ]
         [ -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  -3.5334e+06 ]
         [ -4.6469e+06  2.5531e+06  -3.5333e+06 ]

Normal Vector: n = [ -0.72782  0.39987  -0.55712 ]

Transformation Matrix:
     [ -0.48152  -0.87643   0.00000 ]
 t = [ -0.48828   0.26827   0.83043 ]
     [ -0.72782   0.39987  -0.55712 ]

Transformed Coordinates:
          [  8.3206e+01  1.9809e+04  6.3715e+06 ]
          [  3.1107e+01  1.9845e+04  6.3715e+06 ]
 pecef' = [ -2.5528e+01  1.9842e+04  6.3715e+06 ]
          [ -4.7367e+01  1.9708e+04  6.3715e+06 ]
          [ -3.6447e+01  1.9687e+04  6.3715e+06 ]
          [  3.4068e+01  1.9726e+04  6.3715e+06 ]

Two dimensional polygon area: A = 12600 m^2
Two-dimensional polygon centroid: C' = [ 8.8184e+00  1.9775e+04 ]

Average of pecef' z coordinates: 6.3715e+06

Reverse Transformation Matrix:
      [ -0.48152  -0.48828  -0.72782 ]
 t' = [ -0.87643   0.26827   0.39987 ]
      [  0.00000   0.83043  -0.55712 ]

Polygon centroid (ECEF): C = [ -4.6470e+06  2.5531e+06  -3.5333e+06 ]
Polygon centroid (Geo): Cg = [ -33.856926  151.215102  -4.9537e-04 ]

  <pidf:presence
      xmlns:pidf="urn:ietf:params:xml:ns:pidf"
      xmlns:dm="urn:ietf:params:xml:ns:pidf:data-model"
      xmlns:gp="urn:ietf:params:xml:ns:pidf:geopriv10"
      xmlns:gs="http://www.opengis.net/pidflo/1.0"
      xmlns:gml="http://www.opengis.net/gml"
      xmlns:con="urn:ietf:params:xml:ns:pidf:geopriv:conf"
      entity="pres:alice@example.com">
    <dm:device id="sg89ab">
      <pidf:status>
        <gp:geopriv>
          <gp:location-info>
            <gs:Circle srsName="urn:ogc:def:crs:EPSG::4326">
              <gml:pos>42.5463 -73.2512</gml:pos>
              <gs:radius uom="urn:ogc:def:uom:EPSG::9001">
                850.24
              </gs:radius>
            </gs:Circle>
<!-- c -->  <con:confidence pdf="normal">67</con:confidence>
          </gp:location-info>
          <gp:usage-rules/>
        </gp:geopriv>
      </pidf:status>
      <dm:deviceID>mac:010203040506</dm:deviceID>
    </dm:device>
  </pidf:presence>

<?xml version="1.0"?>
<xs:schema
    xmlns:conf="urn:ietf:params:xml:ns:geopriv:conf"
    xmlns:xs="http://www.w3.org/2001/XMLSchema"
    targetNamespace="urn:ietf:params:xml:ns:geopriv:conf"
    elementFormDefault="qualified"
    attributeFormDefault="unqualified">

  <xs:annotation>
    <xs:appinfo
        source="urn:ietf:params:xml:schema:geopriv:conf">
      PIDF-LO Confidence
    </xs:appinfo>
    <xs:documentation source="http://www.ietf.org/rfc/rfcXXXX.txt">
      <!-- [[NOTE TO RFC-EDITOR: Please replace above URL with URL of
           published RFC and remove this note.]] -->
      This schema defines an element that is used for indicating
      confidence in PIDF-LO documents.
    </xs:documentation>
  </xs:annotation>

  <xs:element name="confidence" type="conf:confidenceType"/>
  <xs:complexType name="confidenceType">
    <xs:simpleContent>
      <xs:extension base="conf:confidenceBase">
        <xs:attribute name="pdf" type="conf:pdfType"
                      default="unknown"/>
      </xs:extension>
    </xs:simpleContent>
  </xs:complexType>
  <xs:simpleType name="confidenceBase">
  <xs:union>
    <xs:restriction base="xs:decimal">
      <xs:minInclusive value="0.0"/>
      <xs:maxInclusive value="100.0"/>
    </xs:restriction>
    <xs:restriction base="xs:token">
      <xs:enumeration value="unknown"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="pdfType">
    <xs:restriction base="xs:token">
      <xs:enumeration value="unknown"/>
      <xs:enumeration value="normal"/>
      <xs:enumeration value="rectangular"/>
    </xs:restriction>
  </xs:simpleType>
</xs:schema>

      BEGIN
        <?xml version="1.0"?>
        <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
          "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
        <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
          <head>
            <title>PIDF-LO Confidence Attribute</title>
          </head>
          <body>
            <h1>Namespace for PIDF-LO Confidence Attribute</h1>
            <h2>urn:ietf:params:xml:ns:geopriv:conf</h2>
[[NOTE TO IANA/RFC-EDITOR: Please update RFC URL and replace XXXX
    with the RFC number for this specification.]]
            <p>See <a href="[[RFC URL]]">RFCXXXX</a>.</p>
          </body>
        </html>
      END