Table 3:
Proposed implementation of the modified Riccati equation (pmRE).
Matrix operation
Matrix dimensions
Calculation burden
𝑃
−
1
𝑘
/
𝑘
−
1
(
𝑛
×
𝑛
)
(
1
/
6
)
(
1
6
𝑛
3
−
3
𝑛
2
−
𝑛
)
𝑀
≡
𝑃
−
1
𝑘
/
𝑘
−
1
+
𝐻
𝑇
𝑅
−
1
𝐻
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝑀
−
1
(
𝑛
×
𝑛
)
(
1
/
6
)
(
1
6
𝑛
3
−
3
𝑛
2
−
𝑛
)
𝐹
⋅
𝑀
−
1
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
2
𝑛
3
−
𝑛
2
𝐹
𝑀
−
1
⋅
𝐹
𝑇
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
∗
𝑛
3
+
(
1
/
2
)
(
𝑛
2
−
𝑛
)
Ω
≡
𝑄
+
𝐹
𝑀
−
1
𝐹
𝑇
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝑝
𝑑
⋅
Ω
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝐹
⋅
𝑃
𝑘
/
𝑘
−
1
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
2
𝑛
3
−
𝑛
2
𝐹
𝑃
𝑘
/
𝑘
−
1
⋅
𝐹
𝑇
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
∗
𝑛
3
+
(
1
/
2
)
(
𝑛
2
−
𝑛
)
Ψ
≡
𝑄
+
𝐹
𝑃
𝑘
/
𝑘
−
1
𝐹
𝑇
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
(
1
−
𝑝
𝑑
)
⋅
Ψ
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝑃
𝑘
+
1
/
𝑘
=
(
1
−
𝑝
𝑑
)
Ψ
+
𝑝
𝑑
Ω
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝐵
p
m
R
E
=
(
1
/
3
)
(
3
4
𝑛
3
+
3
𝑛
2
+
5
𝑛
)
^{ *}
Symmetric matrix.