School of Electronic & Electrical Engineering
FACULTY OF ENGINEERING
Tracking Technology
Dr Andy H. Kemp
[email protected]
31/07/2017
1
Tracking Technology
Localization data
User input
Initial
position
estimate
On-going
position
estimates
o Localization data
•
Time-based Methods: ToA/ToF, TDoA
•
Angle of Arrival: AoA
•
Signal strength: RSSI
Tracking Algorithm
o Obtain position estimate
•
Trilateration,
•
Triangulation,
•
Statistical Technique
•
Connectivity
o Tracking algorithm
2
Basic localization methodology
r1
1
r0
0
r2
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2
So where are we?
3
Basic localization methodology
• So how do we actually do this?
y
• Trilateration (cf. triangulation).
• Assume:
• We have some way of
determining the distance/range,
ri, from the anchors to our
unknown position (xs, ys).
• From Pythagoras’ theorem we
can readily see that:
• (ri)2 = {(xs – xi)2 + (ys – yi)2}
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s
(xs,, ys)
(ys – yi)
• 3 anchors Ai i.e. 3 devices at
known positions (xi, yi, i = 0..2).
ri
i
x
(xi,, yi)
(xs – xi)
4
Analytical methodology
Solve system of equations (using Pythagoras!)
• (xi, yi) : coordinates of anchor point Ai, ri distance to anchor Ai from s
which is at (xs, ys).
• (ri)2 = {(xs – xi)2 + (ys – yi)2} for i = 0..2
• We now construct 3 equations with 2 unknowns (xs, ys).
• By subtracting 3rd equation from 1st & 2nd we make the equations linear
in our unknowns:
(r02 – r22) - (x02 – x22) - (y02 – y22) = 2xs(x2 – x0) +2ys(y2 – y0)
(r12 – r22) - (x12 – x22) - (y12 – y22) = 2xs(x2 – x1) +2ys(y2 – y1)
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5
Analytical methodology
• This can be expressed in matrix form as:
(r02 – r22) - (x02 – x22) - (y02 – y22) = 2 x2 – x0 y2 – y0
(r12 – r22) - (x12 – x22) - (y12 – y22)
x2 – x1 y2 – y1
• In matrix form this is:
xs
ys
[b] = [A][s]
• With [b] = 1 (r02 – r22) - (x02 – x22) - (y02 – y22)
2 (r 2 – r 2) - (x 2 – x 2) - (y 2 – y 2)
1
2
1
2
1
2
[A] =
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x2 – x0 y2 – y0
and [s] = xs
x2 – x1 y2 – y1
ys
6
Practice
Time for an exercise:
We have 3 anchors A0..A2 on a flat x, y, grid measured
out in metres, at: A0(10, 5), A1(2, 10) and A2(10, 15).
The range from each anchor to the subject is r0 = 8m,
r1= 5m, and r2 = 12.8m.
Where is the subject?
(xs, ys) = (2, 5)
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Problem
What happens if we can’t
get an accurate range
measurement from our
satellite?
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8
Ambiguity
r1
1
r0
0
r2
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2
So where are we?
9
GDOP
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10
Probabilistic ranges
• From our ranging mechanism we obtain a range estimate
• Provided this is unbiased, estimates will have a mean of the correct range
• Each estimate will have a random error
11
Resolution of some current
technologies
Conclusion
• The tracking methodology relies on some kind of
positioning method
• The positioning method inherently displays probabilistic
inaccuracy
• Averaging will enhance an unbiased system
• Tracking algorithms can enhance positioning performance
13
(Source: Da Zhang, Localization Technologies for Indoor Human Tracking,2