An adaptive Gaussian sum filter for the spacecraft attitude estimation problem

The present paper is concerned with improving the attitude estimation accuracy by using a finite Gaussian-mixture approximation for the conditional probability density function (pdf). A novel method is discussed to update the weights corresponding to different components of the Gaussian mixture model by constraining the Gaussian sum approximation to satisfy the Fokker-Planck- Kolmogorov equation. Updating the weights not only provides us with better estimates but also with a more accurate pdf. The numerical results show that updating the weights in the propagation step not only gives better estimates between the observations but also provides superior estimator performance where the measurements are ambiguous.