Table 2: Classical implementation of the modified Riccati equation (cmRE).

Matrix operationMatrix dimensionsCalculation 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.