Table 3: Proposed implementation of the modified Riccati equation (pmRE).

Matrix operationMatrix dimensionsCalculation 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.