==Proposed algorithm
When providing a new location, randomize the point to expand uncertainty to the required distance.
Only provide a new location when the centroid of the known location moves outside a trigger circle.
Trigger circle is defined at the same time as a new location, it has a radius of the required distance and its centre is up to half that distance from the centroid of the known location at that time.
==Weaknesses
(1)
Scenario:
The Target visits the same location multiple times over time.
Assumptions required by recipient:
The Target is visiting the same location.
Constraints on scenario:
Each time, location is only reported while at that location, not on the approach to, or leaving from the location. This requires that the Target be unable to located on approach to or exodus from the location. This constraint is met by having the means of location disabled while in transit - e.g. by turning off their phone.
Weakness:
Multiple samples can be combined over time to determine the location that is visited. For example, this might be the location of the Target's home.
(2)
Scenario:
The algorithm randomly produces two subsequent locations where the two centres of uncertainty are 2.5 times the distance (or approaching that number) apart.
Assumptions required by recipient:
The recipient must know the obscuring distance; a recipient might be able to assume this value by observing that previous reported locations have the same uncertainty.
Constraints on scenario:
The obscuring distance must have been revealed previously. This is possible if the uncertainty of the known location does not exceed the obscuring distance.
The location must be known with low (or very low) uncertainty at the time that each of the subsequent obscured locations are produced.
Random chance determines that this scenario is unlikely.
Weakness:
At the time that the location is produced, the recipient knows that there is a point within the new reported location that is 1.5 times the obscuring distance from a point within the last reported location.
Given that the distance between the two locations is such that there is only a small region within each location that meets this constraint, the location of the Target is known with uncertainty approaching that of the known location.
(3)
Scenario:
Movement.
Assumptions required by recipient:
Approximately straight line travel over the interval, or
Travel along an identified route. Even a relatively large obscuring distance might not prevent a recipient from identifying that the Target is travelling along a particular highway over time.
Constraints on scenario:
Constant or relatively constant travel speed.
Weakness:
Average speed of travel can be estimated. The longer the distance between two locations, the less uncertainty present in the estimate.
An upper or lower bound on speed might be determined. If, as in the previous scenario, two locations are produced with significant distance between them, it might be possible place a lower bound on speed over an interval. From this, it might be possible to identify that the Target is exceeding a speed limit.
These need not be consecutive reported locations.
There may be other flaws, but these are the ones that I've been able to identify so far.
--Martin
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