Preprocessing observation vectors to increase attitude estimation accuracy

Abstract

The recently developed Vector Inertia Tensor Attitude Estimation, VITAE, method is enhanced by the addition of two different preprocessing algorithms that modify the observation vectors prior to attitude estimation. The first preprocessing algorithm is for use in cases that have one observation vector that is much more accurate than the other observation vectors. Such cases suffer numerical error caused by the large relative weight of the very accurate observation vector. Use of the preprocessing algorithm eliminates large variation in vector weights and resulting numerical error. The second preprocessing algorithm enables VITAE to generate results equivalent to a very accurate suboptimal attitude determination algorithm that produces results extremely close to the optimum solution. Preprocessing algorithms eliminate the need to select observation vector weights to remove eigenvalue degeneracy and allows the weights to be based solely on optimality, thereby improving estimation accuracy. When optimum weights are used, the inertia matrix is recognized as the information matrix, which links VITAE to other attitude estimation algorithms. The preprocessing algorithms used with VITAE were able to uncover erroneous results in a few published test cases. The VITAE solutions were validated analytically, through the inertia matrix’s inverse relationship to the error covariance matrix. A loss function comparison is also included to further validate the preprocessing algorithms and related VITAE solution.