1. Dr Andy H. Kemp A.H.Kemp@leeds.ac.uk
08/05/2018
Tracking Technology
Dr Andy H. Kemp
08/05/2018

2. On-going position estimates
08/05/2018
Tracking Technology
Localization data
Position estimate
Initial
position estimate
On-going position estimates
User input
Localization data
Time-based Methods: ToA/ToF, TDoA
Angle of Arrival: AoA
Signal strength: RSSI
Obtain position estimate
Trilateration,
Triangulation,
Statistical Technique
Connectivity
Tracking algorithm
Tracking Algorithm
Tracking algorithms, e.g. Kalman fitlers, particle filters…

3. Basic localization methodologyr1 r0 1 r2 2
So where are we?
08/05/2018

4. Basic localization methodology
So how do we actually do this?
Trilateration (cf. triangulation).
Assume:
3 anchors Ai i.e. 3 devices at known positions (xi, yi, i = 0..2).
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} i x y s
(xi,, yi)
(xs,, ys) ri
(xs – xi)
(ys – yi)
08/05/2018

5. 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)
08/05/2018

6. Analytical methodology
This can be expressed in matrix form as:
(r02 – r22) - (x02 – x22) - (y02 – y22) = x2 – x0 y2 – y xs
(r12 – r22) - (x12 – x22) - (y12 – y22) x2 – x1 y2 – y ys
In matrix form this is: [b] = [A][s]
With [b] = 1 (r02 – r22) - (x02 – x22) - (y02 – y22)
2 (r12 – r22) - (x12 – x22) - (y12 – y22)
[A] = x2 – x0 y2 – y and [s] = xs
x2 – x1 y2 – y ys
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7. (xs, ys) = (2, 5) Practice Time for an exercise:
08/05/2018
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?
So what do you think is the best way to learn how to use this maths? Practice it right?
(Answer should not be on student slides…
And should only come up here after a key press…
x, y of subject is 6.25, 6.25
Probably useful to draw this on an x, y coordinate system.)
(xs, ys) = (2, 5)
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8. 08/05/2018
Problem
What happens if we can’t get an accurate range measurement from our satellite?
There will always be PDP on range ESTIMATES.
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9. Ambiguity r1 r0 r2 1 So where are we?
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Ambiguity r1 1 r0
Range estimate: most probable position. r2 2
So where are we?
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10. GDOP
08/05/2018

11. 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

12. Resolution of some current technologies

13. 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

14. (Source: Da Zhang, Localization Technologies for Indoor Human Tracking,2010, IEEE)