Phoenix Technologies
  Phoenix Technologies  
System Structure Tracker Models Features Accessories Software Brochures  

  Accuracy

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

  Accuracy Definitions - General

Accuracy of a 3D motion measurement device (sensor) can be specified in many ways. In general it is a function of the angles and distances of the measurement points from the sensor.

For marketing purposes, accuracy is often specified in terms of the best 1D value achievable at the shortest operating distance from a sensor. Such specification would be of little practical value to the user since a 3D sensor is normally applied to sense points over a large 3D space.

  3D vs. 1D Accuracy

A 3D accuracy specification is always larger (i.e., worse) than a 1D specification. It specifies the possible 3D position error between a sensor reading and the actual (theoretical) 3D position of a point relative to the sensor.

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

A3D = (A21x + A21y + A21z )1/2
where

(.)1/2 = the square-root of (.)
A3D = the equivalent 3D accuracy
A1x = 1D accuracy in the x-direction
A1y = 1D accuracy in the y-direction
A1z = 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 sensor operating space. Point-accuracy specifies the position accuracy at a specific point (only) within the operating space.

Volume-accuracy is roughly equal to the worst point-accuracy of a 3D optical position sensor. This is because volume-accuracy is computed from accuracy values of points uniformly distributed over the sensor operating space. An optical sensor normally has a round-conical or rectangular horn-shaped operating space that expands in proportion to distance from the sensor. Much more data are collected at the farthest distance, where the point-accuracy values are the worst, than from near the sensor. After averaging, the computed volume-accuracy naturally becomes much closer to the worst point-accuracy value within the space.

Example:
Assume a sensor 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 sensor is actually worse than the worst 1D accuracy value (1.20mm) within the specified sensing space!