IEEE Robotics & Automation Magazine - September 2017 - 68

where N L is the number of landmarks existing in the map,
N D the number of detectors, and N S the number of sensors.
Triplets construction is detailed in the "Perceptive Triplets"
section and takes into account the observability of the landmarks, the accuracy of the estimated position, the field of
view of the sensors, etc.
Triplet Selection Criterion
The most relevant triplet is the one that gives the best
compromise regarding our objectives, i.e., precision and
confidence. We have multiple objectives, so it is necessary to
weigh them appropriately. Indeed, we have to accept
deterioration of confidence to improve accuracy. This method
is called information driven and is widely used in the action
field of sensor management. In our approach, we tried to
formalize certain constraints that are naturally respected
by a human.
A Triplet Providing No New Information Is Not Selected
A triplet is considered to have completely new information
when the observation is not correlated with a previous one,
especially when it has not yet been selected. In this article,
CI k, denotes the event where the information provided by
the triplet is correlated, and the probability of this event is
determined by the following equation.

P (CIk) =

0
exp - c # D

if the triplet has never
been detected
,
otherwise.

(3)

A Triplet with Very Little Chance of Being Well
Detected Will Have a Low Criterion
Well detected means that the detector returns a result and
the data association is good. Using triplets with a good
probability to be well detected has a direct impact on the

CIk

Ok+

Figure 3. The BN at the time k. Yellow nodes are entries (their
probabilities are known). The green nodes implicate the
probabilities for which we are looking.

IEEE ROBOTICS & AUTOMATION MAGAZINE

SEPTEMBER 2017

Between Two Triplets, If the Only Difference Is the
Accuracy Value, the Triplet with the Higher Value Has
to Be Selected
To know what the expected accuracy is after triplet detection, we compute Pp (described in the "Objective" section).
For each triplet, the update due to this triplet is simulated thanks to an EKF, and the expected Pp after detection
is computed.
The criterion C used here mixes accuracy Pp given by the
triplet, the probability of detecting the landmark P(db) [in this
article, to simplify notations P (X = 1) (resp. P (X = 0)] is
noted P(X) [resp. P (Xr ) ]; every event is a binary event, so
there is no possible confusion) and the probability of new
information ( P ( CI k))
C = Pp # P (db) # P ( CI k).

(4)

Finally, we can compute for each triplet Ti the criterion
C (Ti). The best triplet Tb is chosen according to (5)
Tb = argmax (C (Ti)).

where D is the distance traveled since the last detection of this
triplet, and c is the parameter determining the forgetting
factor (fixed to 0.7 in our application).

Ok-

confidence. This event is noted db. The computation of this
event probability, realized thanks to a BN (see the "Illustration of the Process with an Example" section), takes into
account detector quality, occlusion phenomena, sensors
characteristics, etc.

(5)

Bayesian Modeling
BNs [19] are used to formalize the knowledge in an uncertain
environment and are therefore quite appropriate in our case.
To take the time into account, we used a dynamic BN that is a
copy of the static BN for every time.
Events Taken into Account
For a selected triplet Ti = {L i, S i, D i} (L i is the associated
landmark, S i the sensor, and D i the detector), events modeled in this BN (Figure 3) are
● O k : confidence of the localization before update
● zo: observability of the triplet landmark with the selected
sensor and detector
● A z : there is at least a landmark of the same type than L i in
the observed zone
● d k : a landmark has been detected
● db: a landmark has been detected and data association is
true
● CI k : the system already tried to detect this landmark
● d p : the landmark has previously been detected with this
sensor and this detector
+
● O k : confidence of the localization after localization
update.
This BN can take into account the detectors performances,
the occlusion of landmarks, the ambiguity between landmarks, the size of the search area, etc. The structure of our BN
is fixed and is the same for each triplet.

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2017