Observability Analysis for Orthogonal Transformation Based State Estimation

Recently a triangular-factorization based observability analysis has been proposed. The method uses subroutines already existing in a state estimation software using the standard normal equations approach. The normal equations approach works well in most applications. However, occasional numerical ill-conditioning of the gain matrix has been observed in practice. Orthogonal transformation methods have been suggested to alleviate this problem. A hybrid approach combining the sparsity of the normal equations method and the numerical robustness of the orthogonal transformation methods has recently been developed. The method solves the normal equations using the orghogonal transformation of the Jacobian matrix. This paper extends the basic idea of the triangular-factorization based observability analysis to orthogonal transformation and hybrid state estimators. The observability analysis is performed during the process or orthogonal transformation (Householder or Givens) of the Jacobian matrix. The deailed algorithm is given. Test results are presented.