Accuracy

For the user's benefit, the VisualeyezTM system accuracy is specified in terms of the 3D volume-accuracy (see definition below). The volume of space over which measurements are taken to specify the accuracy is:

from 0.6m to 2.2m in distance
± 40 degrees in the horizontal (yaw) angle, and
± 30 degrees in the vertical (pitch) angle.

The VisualeyezTM system's 3D volume accuracy is as specified in Specifications.

	Accuracy Definitions - General

Accuracy of a 3D sensing system can be specified in many ways. It is a function of the measurement direction(s), distance(s), and whether the measurements are taken over points at a fixed distance from the tracker or over a volume of the 3D operating space.

For marketing purposes, accuracy is often specified in terms of the best 1D value achievable at close to the shortest distance from a tracker. Such specification would be of little practical value to the users since a 3D sensing system is normally used for sensing over a 3D space of hopefully as large size as possible.

	3D vs. 1D Accuracy

A 3D accuracy specification is always larger than a 1D specification. It specifies the possible 3D position error between the system reading and the actual (theoretical) 3D position.

The relationship between a 3D and 1D accuracy specification is as follows:

A_3D = (A²_1x + A²_1y + A²_1z )^1/2

where

(.)^1/2 = the square-root of (.)
A_3D = the equivalent 3D accuracy
A_1x = 1D accuracy in the x-direction
A_1y = 1D accuracy in the y-direction
A_1z = 1D accuracy in the z-direction

Example
The 3D equivalent to a 1D accuracy specification of 0.32mm in x, 0.32mm in y and 0.48mm in z, is as follows:

(0.322 + 0.322 + 0.482)^1/2 = 0.66mm

Volume-Accuracy vs. Point-Accuracy

Volume-accuracy specifies the nominal position accuracy over a volume of the system?s operating space. Point-accuracy specifies the position accuracy at a point (only) within the operating space.
Volume-accuracy is roughly equal to the worst point-accuracy of a 3D optical position sensing system. This is because volume-accuracy is computed from accuracy values of points uniformly distributed over the operating space. An optical sensing system normally has a circular-conical or rectangular horn-shaped operating space that expands in proportion to distance from the trackers. Much more data have to be collected at the farthest distance, where the point-accuracy values are the worst, than from the nearest distance. After averaging, the computed volume-accuracy naturally becomes much closer to the worst point-accuracy value within the space.

Example:
Assume a system with a conical operating space has the following point-accuracy specifications:
At 1.2m distance (1 data point used) -- x = 0.12mm, y = 0.12mm, z = 0.18mm
At 2.4m distance (4 data points used) -- x = 0.32mm, y = 0.32mm, z = 0.48mm
At 3.6m distance (9 data points used) -- x = 0.80mm, y = 0.80mm, z = 1.20mm

The equivalent 3D volume-accuracy for this system would be:
[(1*(0.12²+ 0.12² + 0.18²) + 4*(0.32²+ 0.32² + 0.48²) + 9*(0.8²+ 0.8² + 1.2²))/14]^1/2 = 1.37mm
Thus, the 3D volume-accuracy for this system is actually worse than the worst 1D accuracy value within the specified sensing space!!!