An Efficient Nonlinear Filter for Spacecraft Attitude Estimation

Algorithm 1

TP model transformation algorithm [20].

Step  1. Determine the bounded domain Ω where the parameter 𝑝 varying on;

Step  2. Set the transformation space Ω into 𝑁 uniformly distributed grid: Ω=𝑎₁,𝑏₁×⋯×[𝑎_𝑁,𝑏_𝑁];

Step  3. Sample the functions 𝐹(𝑝) over the hyper rectangular grid and store the sample

matrixes in the tensor 𝐅;

Step  4. Execute the higher order singular value decomposition (HOSVD) on tensor 𝐅 and

extract the minimal basis, the result of this step is 𝐅≈𝐕⊗_𝑚𝑈_𝑚;

Step  5. Normalize the basis matrix 𝑈_𝑚, one can obtain 𝐹(𝑝)≈𝐕⊗_𝑚𝑈_𝑚;

Step  6. Extract the vertexes of the polytopic linear model (49) from 𝐕.