Table 2:
Classical implementation of the modified Riccati equation (cmRE).
Matrix operation
Matrix dimensions
Calculation burden
𝐻
⋅
𝑃
𝑘
/
𝑘
−
1
(
𝑚
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
2
𝑛
2
𝑚
−
𝑛
𝑚
𝐻
𝑃
𝑘
/
𝑘
−
1
⋅
𝐻
𝑇
(
𝑚
×
𝑛
)
⋅
(
𝑛
×
𝑚
)
∗
𝑛
𝑚
2
+
𝑛
𝑚
−
(
1
/
2
)
(
𝑚
2
+
𝑚
)
𝑂
𝑘
≡
𝐻
𝑃
𝑘
/
𝑘
−
1
𝐻
𝑇
+
𝑅
(
𝑚
×
𝑚
)
+
(
𝑚
×
𝑚
)
∗
(
1
/
2
)
(
𝑚
2
+
𝑚
)
𝑂
𝑘
−
1
(
𝑚
×
𝑚
)
(
1
/
6
)
(
1
6
𝑚
3
−
3
𝑚
2
−
𝑚
)
𝐾
𝑘
≡
𝑂
𝑘
−
1
⋅
𝐻
𝑃
𝑘
/
𝑘
−
1
(
𝑚
×
𝑚
)
⋅
(
𝑚
×
𝑛
)
2
𝑛
𝑚
2
−
𝑛
𝑚
𝑊
≡
𝑃
𝑘
/
𝑘
−
1
𝐻
𝑇
⋅
𝐾
𝑘
(
𝑛
×
𝑚
)
⋅
(
𝑚
×
𝑛
)
∗
𝑛
2
𝑚
+
𝑛
𝑚
−
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝑝
𝑑
⋅
𝑊
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
Π
1
≡
𝑃
𝑘
/
𝑘
−
1
−
𝑝
𝑑
⋅
𝑊
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝐹
⋅
Π
1
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
2
𝑛
3
−
𝑛
2
Π
2
≡
𝐹
Π
1
⋅
𝐹
𝑇
(
𝑛
×
𝑛
)
⋅
(
𝑛
×
𝑛
)
∗
𝑛
3
+
(
1
/
2
)
(
𝑛
2
−
𝑛
)
𝑃
𝑘
+
1
/
𝑘
=
𝑄
+
Π
2
(
𝑛
×
𝑛
)
+
(
𝑛
×
𝑛
)
∗
(
1
/
2
)
(
𝑛
2
+
𝑛
)
𝐵
c
m
R
E
=
(
1
/
2
)
(
6
𝑛
3
+
𝑛
2
+
𝑛
)
+
3
𝑛
2
𝑚
+
3
𝑛
𝑚
2
+
(
1
/
6
)
(
1
6
𝑚
3
−
3
𝑚
2
−
𝑚
)
^{ *}
Symmetric matrix.