GMM-Based Adaptive Extended Kalman Filter Design for Satellite Attitude Estimation under Thruster-Induced Disturbances

. 2023 Apr 23;23(9):4212. doi: 10.3390/s23094212

Algorithm 1: Thruster on-time setting algorithm

\begin{array}{l} Input : {\hat{τ}}_{cmd, x}, {\hat{τ}}_{cmd, y}, {\hat{τ}}_{cmd, z} \\ Compute the ratio of thruster 3, 4, 5, 6 using (19). \\ r r_{ratio, 6} = r_{ratio, 6} - r_{ratio, 3}; r r_{ratio, 3} = 0; \\ if (r r_{ratio, 6} < 0) r r_{ratio, 3} = r_{ratio, 3} - r_{ratio, 4}; r r_{ratio, 6} = 0; end \\ r r_{ratio, 4} = r_{ratio, 4} - r_{ratio, 5}; r r_{ratio, 5} = 0; \\ if (r r_{ratio, 4} < 0) r r_{ratio, 5} = r_{ratio, 5} - r_{ratio, 4}; r r_{ratio, 4} = 0; end \\ if ({\hat{τ}}_{cmd, y} > 0) r r_{ratio, 2} = {\hat{τ}}_{cmd, y}; r r_{ratio, 1} = 0; end \\ if ({\hat{τ}}_{cmd, y} < 0) r r_{ratio, 1} = Abs ({\hat{τ}}_{cmd, y}); r r_{ratio, 2} = 0; end \\ Output : r_{ratio, 1}, r_{ratio, 2}, r_{ratio, 3}, r_{ratio, 4}, r_{ratio, 5}, r_{ratio, 6} \\ [\begin{matrix} r_{ratio, 1} & r_{ratio, 2} & r_{ratio, 3} & r_{ratio, 4} & r_{ratio, 5} & r_{ratio, 6} \end{matrix}] = \\ [\begin{matrix} r r_{ratio, 1} & r r_{ratio, 2} & r r_{ratio, 3} & r r_{ratio, 4} & r r_{ratio, 5} & r r_{ratio, 6} \end{matrix}] \end{array}