Operation Manual

88
9.5 System accuracy evaluation
1) Accuracy of distances measurement.
- Marvelmind navigation system can measure distances between beacons
with accuracy of +/- 2cm if it uses correct ultrasound speed in
measurements
- The ultrasound speed depends of many factors: temperature of air,
pressure, humidity and so on
- The main factor is temperature. In temperature range of -20…+50 °C the
speed of ultrasound changes on about 0.6 m/ (s* °C). It gives distance
error about (0.6 / 340) *100% ~ 0.17%/ °C. So caused by incorrect
temperature setting absolute error of distance measurement is 0.17% of
real distance between beacons. For example, with distance 30 meters and
5 °C error, this gives 0.85%*30 ~ 0.25 meters’ error. Marvelmind system
allows to setup temperature of air in the system settings
2) Accuracy of position measurement.
- Marvelmind system uses trilateration algorithm to calculate position by
distances. The inaccuracy of position calculation is related to inaccuracy
of distances measurement and to geometry of relative location of
stationary and mobile beacons
- Basic trilateration formulas are given in this article:
https://en.wikipedia.org/wiki/Trilateration
- As you see, the position of mobile beacons X, Y, Z is calculated from
positions of 3 stationary beacons which are set by values of d, i, j. One
of the beacons was shifted to (0,0) position to simplify formulas in the
article. In formulas for X, Y we see d and j in denominators. This means
that with low values of d and j small error of this value can cause large
position error
- Please see the picture of the beacons in the article - in more simple words,
in means that if one of three beacons is close to line connecting other two
beacons, it gives increased inaccuracy of locating mobile beacon
- For example:
- assume d= 10, i= 5, j= 0.1, r1= 7, r2= 7, r3= 4.8
- We get x= 5, y= 2.4375, z = 4.25
- If we suppose that j=0.101 (0.1 cm error), we receive x= 5, y= -0.06,
z= 4.89
- You see very large Y error
- Another example for Z. Assume mobile beacon is relative close to plane
of stationary beacons:
- d= 8, i= 4, j= 6, r1= 5.02, r2= 5.02, r3= 3.01
- This gives X=4, Y= 3.01169, Z= 0.36
- If we suppose r3= 3.0 (1 cm error), we receive X=4, Y= 3.016, Z=
0.44. Error on Z is about 8 cm
- Also, with r1= 5, r2= 5, r3= 3, Z will be 0. As you see, low change of
distances causes large change of Z value near the plane.