Mathematical Problems in Engineering

Research Article

Highly Efficient Sigma Point Filter for Spacecraft Attitude and Rate Estimation

Table 1

Simplex base sets for 3-dimensional space.
Sigma set 𝖀 ∈ ℝ 𝑛 × 𝑚 for 𝑛 = 3
√ 𝖀 = ( 0 . 5 / 𝑊 𝑚 ) [ √ 0 , − 1 / √ 2 , 1 / √ 2 , 0 , 0 0 , − 1 / √ 6 , − 1 / √ 6 , 2 / √ 6 , 0 0 , − 1 / √ 1 2 , − 1 / √ 1 2 , − 1 / √ 1 2 , 3 / 1 2 ]
Spherical simplex
𝑚 = 5 0 < 𝑊 0 < 1 , 𝑊 𝑚 = ( 1 − 𝑊 0 ) / ( 𝑛 + 1 )
√ 𝖀 = ( 1 / 𝑊 ) [ √ 1 / √ 2 , − 1 / √ 2 , 0 , 0 1 / √ 6 , 1 / √ 6 , − 1 / √ 3 / 2 , 0 1 / √ 1 2 , 1 / √ 1 2 , 1 / √ 1 2 , − 1 / 4 / 3 ]
Schmidt orthogonal
𝑚 = 4 𝑊 = 1 / ( 𝑛 + 1 ) = 1 / 4
𝖀 = [ + 1 , + 1 − 1 − 1 + 1 , − 1 − 1 + 1 + 1 , − 1 + 1 − 1 ]
Geometric simplex
𝑚 = 4 𝑊 = 1 / ( 𝑛 + 1 ) = 1 / 4