State estimator condition number analysis

Abstract

Abstract-This paper develops formulas for the condition number of the state estimation problem as a function of the different types and number of measurements. We present empirical results using the IEEE RTS-96 and IEEE 118 bus systems that validate the formulas.

An efficient algebraic approach to observability analysis in state estimation

“…Note that the zero identification problem plagues all algebraic procedures to check observability. However, this problem can be mitigated by selecting the right number and type of measurements, as suggested in [23,24].…”

Vehicle state estimation for anti-lock control with nonlinear observer

“…Additionally, the inverse of the Jacobian matrix condition number as used in Stéphant, Charara, and Meizel (2007) is introduced as an observability indicator, which gives a measure of the sensitivity of the solution to the observation problem. The condition number of a matrix is defined as the ratio of the largest singular value to the smallest one (Ebrahimian & Baldick, 2001).…”

Power System State Estimation Under Incomplete PMU Observability—A Reduced-Order Approach

“…Similarly, the two-stage approach described in [12] also requires more computational effort than the proposed method because it involves the QR factorization of an matrix followed by backward substitutions in the first stage as well as the inversion of a matrix in the second stage. 2) Improved Numerical Stability: Numerical stability depends critically on the condition number of the gain matrix of the Gauss-Newton iterations [26], [27]. The condition number of a matrix is the ratio of its largest eigenvalue to its smallest eigenvalue.…”