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Map Building and SLAM Algorithms 347

ALGORITHM 9.2
ICNN
ICNN (E 1···m , F 1···n )
for i = 1to m do {measurement E i }
D 2 ← mahalanobis2 (E i , F 1 )
min
nearest ← 1
for j = 2to n do {feature F j }
2
D ← mahalanobis2 (E i , F j )
ij
2
if D < D 2 then
ij min
nearest ← j
D 2 ← D 2
min ij
end if
end for
if D 2 ≤ χ 2 then
min d i ,1−α
H i ← nearest
else
H i ← 0
end if
end for
return H

The IC considers individual compatibility between a measurement and
a feature. However, individually compatible pairings are not guaranteed to be
jointly compatible to form a consistent hypothesis. Thus, with ICNN there is a
high risk of obtaining an inconsistent hypothesis and thus updating the state vec-
tor with a set of incompatible measurements, which will cause EKF to diverge.
As vehicle error grows with respect to sensor error, the discriminant power of
IC decreases: the probability that a feature may be compatible with an unre-
lated (or spurious) sensor measurement increases. ICNN is a greedy algorithm,
and thus the decision to pair a measurement with its most compatible feature
is never reconsidered. As a result, spurious pairings may be included in the
hypothesis and integrated in the state estimation. This will lead to a reduction
in the uncertainty computed by the EKF with no reduction in the actual error,
that is, inconsistency.

9.3.2 Joint Compatibility
In order to limit the possibility of accepting a spurious pairing, reconsidera-
tion of the established pairings is necessary. The probability that a spurious

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c009” — 2006/3/31 — 16:43 — page 347 — #17