Representation of Uncertainty and Confidence in the Presence Information Data Format Location Object (PIDF-LO)
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Extracted elements (30)
A fixed default confidence (95%) is preferred for PIDF-LO because it ensures consistency across implementations. Without a fixed value, location servers faced a dilemma: either scale uncertainty without sufficient information (degrading quality) or silently ignore confidence (creating false impressions). The optional confidence element is added to handle legacy systems that cannot meet 95%.
The document simplifies calculations by assuming Targets occupy a single point in space and that rectangular PDF distributions apply when determining overlap with regions of interest. While not always accurate, this assumption greatly simplifies computations and is reasonable when device size is small relative to uncertainty.
The term 'accuracy' is deliberately treated as qualitative only. Assigning a number to 'accuracy' or using it as a synonym for uncertainty conflates a quantitative measure with a qualitative descriptor, which leads to incorrect usage. Uncertainty (quantitative) and accuracy (qualitative) serve distinct purposes.
Calculations on coordinate information should be performed in Cartesian (ECEF) space, not by treating latitude/longitude as Cartesian axes. The axes are not orthogonal, and treating them as such causes errors from earth curvature and convergence of longitude lines.
RFC 5491 defines a fixed confidence of 95% for PIDF-LO, while this document introduces a 'confidence' element permitting other values. Recipients that ignore the confidence element are no worse off than if the server had ignored confidence, but misinterpretation (e.g., by systems reducing confidence) is a noted risk.
The 'Precision' and 'Resolution' terms defined in RFC 3693 are deprecated by this document. Those terms have many conflicting uses in other fields and are unsuitable for quantitative discussion of uncertainty and confidence in location information.
A confidence element MUST be included with all location information that includes uncertainty (i.e., all forms other than a Point). If confidence is not known, the special value 'unknown' MUST be used.
A default value of 95% confidence SHOULD be assumed for DHCP LCI (RFC 6225) 'resolution' parameters, applied to the combination of the uncertainty on each axis, consistent with transformation to RFC 5491 uncertainty shapes.
If a PIDF-LO does not include the confidence element, the confidence of the location estimate is 95%, as defined in RFC 5491. This default ensures consistent interoperability with systems unaware of the confidence element.
Location generators SHOULD attempt to ensure that confidence is equal in each dimension when generating location information. This restriction allows for more accurate scaling if scaling is necessary.
The confidence element MUST be omitted if only a Point shape is provided, because a Point has no uncertainty (or infinite uncertainty), making confidence meaningless for that shape.
The PDF attribute MUST either be set to 'unknown' or omitted if the distribution does not approximately fit normal or rectangular shapes. Indicating a particular PDF only signifies an approximate fit based on the generation method.
When judging whether a location is within a given region, a probability threshold of 50% or greater is recommended before deciding that an uncertain value is within the region. If selecting among multiple regions, the region with the highest probability can be selected.
When rounding uncertainty, the region of uncertainty always increases (errors rounded up) and confidence is always rounded down, per NIST guidelines. Manipulation of uncertainty is therefore non-reversible.
Adding confidence to location information risks misinterpretation by consumers who do not understand the element. This could be exploited when reducing confidence, causing the recipient to assume a larger or more likely region than intended.
Altering uncertainty is not an effective privacy mechanism. Increasing the uncertainty region does not necessarily reduce the information conveyed by the location object, as noted in RFC 6772 Section 13.5.
A 3D shape can be converted to a 2D shape by removing altitude. Confidence of the resulting 2D shape is higher; the approximate formula is C[2d] >= C[3d]^(2/3) assuming equal per-axis confidence.
Absence of uncertainty information in a PIDF-LO does not mean the location is certain; uncertainty may simply be uncalculated or withheld. A Point shape implies either 0% confidence or infinite uncertainty, not a precise location.
For a normal distribution, uncertainty can be scaled to a desired confidence Cd using: Ud[x] <= U[x] * (erfinv(Cd^(1/n)) / erfinv(Co^(1/n))), where n is the number of dimensions and standard deviation is derived as S[x] = U[x] / (sqrt(2) * erfinv(C[x])).
For a rectangular distribution, reducing the region of uncertainty scales confidence proportionally: Cr = Co * Ur / Uo (areas or volumes). Increasing the region size has no effect on confidence. The operation is irreversible.
The Arc-Band centroid distance from the inner arc starting point is: d = 4 * sin(o/2) * (R^2 + R*r + r^2) / (3*o*(R + r)), along the bisecting angle a + o/2, where r is inner radius, R is outer radius, a is start angle, and o is opening angle.
The centroid of a region of uncertainty is used as the canonical point when reducing a location estimate to a single point. For regular shapes (Circle, Sphere, Ellipse, Ellipsoid) this is the center point; for Arc-Band and irregular Polygons/Prisms, explicit centroid formulas are defined.
The 'confidence' element MAY be added to the 'location-info' element of a PIDF-LO document to express confidence in the associated location information as a percentage (exclusive range 0–100) or the special value 'unknown'. An optional 'pdf' attribute indicates the shape of the probability distribution: unknown, normal, or rectangular.
The probability Pi that a Target lies within a region of interest is Pi = Co * Ao / Au, where Ao is the area of overlap between the uncertainty region and the region of interest and Au is the area of the uncertainty region. This assumes a rectangular PDF; confidence should be scaled to 95% before applying.
The XML schema (namespace urn:ietf:params:xml:ns:geopriv:conf) defines the 'confidence' element as a 'confidenceType' complex type containing a decimal in (0.0, 100.0) or the token 'unknown', with an optional 'pdf' attribute of type pdfType (unknown | normal | rectangular).
To convert a location estimate to a Circle or Sphere, take the centroid as center and the maximum distance from the centroid to any point in the region of uncertainty as the radius. Specific formulas are given for each shape type (Ellipse, Polygon, Arc-Band).
Two probability density function (PDF) shapes are recognized for location uncertainty: normal (Gaussian, applicable when many small independent errors contribute) and rectangular (applicable when a single dominant error source spans a limited, uniform range). The pdf attribute on the confidence element conveys which shape applies.
A new XML namespace 'urn:ietf:params:xml:ns:geopriv:conf' is registered per RFC 3688 to identify the PIDF-LO confidence element defined in this document.
An XML schema is registered under URI 'urn:ietf:params:xml:schema:geopriv:conf' per RFC 3688. The full schema is given in Section 7 and defines the confidenceType and pdfType for the confidence element.
Providing uncertainty and confidence information can reveal details about the location generation process — for example, inferring use of GPS or a specific network-based service. Rule Makers may choose to strip uncertainty fields, but location obfuscation is imperfect; increasing uncertainty does not reliably reduce information conveyed.