88
5 Higher Order Moment Robust Filtering …
Assuming the transition probability matrix is
[ i j ] 1≤i, j≤2 =
−0.5 0.5
0.3 −0.3
,
the initial conditions are given by x 0 =
0.1 0.3
, γ = 0.1, and the external noise is
ω(t) = 0.4 exp(−0.1t) sin(0.1πt)
To analyze the effect of the moment order p on the filtering performance for multimodel jumping system (5.1), the inequalities in Theorem 5.2 were solved with different p via MATLAB. Then, the filter parameters were derived as follows:
For p = 1,
A f 1 =
4.3741 4.4193
0.5418 −6.2403
, B f 1 =
−10.2634
0.4762
,
C f 1 =
0.5402 −0.1469
,
A f 2 =
−7.0889 −4.8135
−3.4392 −10.0682
, B f 2 =
−1.1304
1.1052
,
C f 2 =
−0.0153 0.9977
.
For p = 2,
A f 1 =
−21.5865 −0.3872
−0.5823 −10.2184
, B f 1 =
9.9764
0.0032
,
C f 1 =
0.3967 −0.1016
,
A f 2 =
−7.3713 −0.1187
0.40682 −22.01
, B f 2 =
1.2000
−1.0004
,
C f 2 =
−0.0038 1.0047
.
For p = 3,
A f 1 =
−287.2151 114.8757
108.8225 −660.8030
, B f 1 =
9.9764
0.0032
,
C f 1 =
0.5141 −0.1020
,
5 Higher Order Moment Robust Filtering …
Assuming the transition probability matrix is
[ i j ] 1≤i, j≤2 =
−0.5 0.5
0.3 −0.3
,
the initial conditions are given by x 0 =
0.1 0.3
, γ = 0.1, and the external noise is
ω(t) = 0.4 exp(−0.1t) sin(0.1πt)
To analyze the effect of the moment order p on the filtering performance for multimodel jumping system (5.1), the inequalities in Theorem 5.2 were solved with different p via MATLAB. Then, the filter parameters were derived as follows:
For p = 1,
A f 1 =
4.3741 4.4193
0.5418 −6.2403
, B f 1 =
−10.2634
0.4762
,
C f 1 =
0.5402 −0.1469
,
A f 2 =
−7.0889 −4.8135
−3.4392 −10.0682
, B f 2 =
−1.1304
1.1052
,
C f 2 =
−0.0153 0.9977
.
For p = 2,
A f 1 =
−21.5865 −0.3872
−0.5823 −10.2184
, B f 1 =
9.9764
0.0032
,
C f 1 =
0.3967 −0.1016
,
A f 2 =
−7.3713 −0.1187
0.40682 −22.01
, B f 2 =
1.2000
−1.0004
,
C f 2 =
−0.0038 1.0047
.
For p = 3,
A f 1 =
−287.2151 114.8757
108.8225 −660.8030
, B f 1 =
9.9764
0.0032
,
C f 1 =
0.5141 −0.1020
,