IEEE Systems, Man and Cybernetics Magazine - October 2020 - 31

E59

C

B

D

Convergence
Point
R10

RSSI Positioning
Using the models developed in the example, suppose the
following arbitrarily produced measurement matrix
i s ut i l i z e d : p br = 6 p r (- 44), p r (- 83), p r (- 30), p r (- 40)@T
in decibels.
Each model is parsed for a value that is within ±1.5 dB
of the desired value for each BSSID's RSSI. This is accomplished with a straightforward systematic search of values
through the rows and columns of the model. Any value
that is not within the desired band is assigned a value of
NaN. Desired values can then be normalized about the
measurement value for each RSSI to allow for the comparison of values to determine regions of model intersection.
Much like the validity matrix, this leads to bands of valid
regions in the six intersections of the four models.
Figure 8 displays the bands of validity for each model in
addition to the intersections of the models. The bands of
validity are given on the upper and left edge of the matrix.
The diagonal is presented as a zero matrix for clarity. The

intersections of the models represent the sum of the normalized values and are shown above and below the diagonal. An inspection of the figure reveals a small valid
region where all the models converge to the selected RSSI

POV

zero. This region is of specific interest because the ensemble
of models would have a nonunique solution when all four
models have zero difference. Overlaying the difference of the
ensembles provides a means to confirm that the solution for
position, based off of an RSSI model, does not suffer from a
singularity in solution.

E53

E51

A
Figure 9. The final convergence point is actually a

range of possible points based upon the sum of the
six RSSI location-band differences.

Frame Number 1 of 455, t = 0

10

50

20
100

Possible
Locations

30
150

40
50

200

60

250

70
300
80
350

90
100

400
50

100

(a)

150

200

10

20

30
(b)

40

50

Figure 10. Data frame 1, depicting (a) the model's convergence bands and (b) the RSSI position solution with

GPS ground truth.

O c tob e r 2020

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE

31



IEEE Systems, Man and Cybernetics Magazine - October 2020

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