Figure 2: True, Extended Kalman Filter and ℓ
∞
-Filter Esti-
mated Azimuth Angle -
˜
ψ versus t.
superiority of the induced ℓ
∞
filter over the Extended
Kalman Filter has been demonstrated, both in terms
of performance and simplicity of implementation.
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APPENDIX A - PROOF OF
LEMMA 1
Consider the system
x
k+1
=
¯
Ax
k
+
¯
Bw
k
, z
k
=
¯
Cx
k
+
¯
Dw
k
and define, following (Abedor et al., 1996),
ξ
k
= x
T
k+1
Px
k+1
−x
T
k
Px
k
+ λx
T
k
Px
k
−µw
T
k
w
k
.
Namely,
ξ
k
=(x
T
k
¯
A
T
+w
T
k
¯
B
T
)P(
¯
Ax
k
+
¯
Bw
k
)−x
T
k
Px
k
+λx
T
k
Px
k
−µw
T
k
w
k
.
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