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Mathematical Problems in Engineering
Volume 2015, Article ID 946952, 6 pages
Research Article

New Viewpoints about Pseudo Measurements Method in Equality-Constrained State Estimation

College of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 4 October 2014; Revised 20 February 2015; Accepted 25 February 2015

Academic Editor: Elmetwally Elabbasy

Copyright © 2015 Bingjie Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss the pseudo measurement method which is one of the main approaches to equality-constrained state estimation for a dynamic system. We demonstrate by the fundamental theory of Kalman filtering that reviewing the equality constraint as a pseudo measurement seems questionable. The main reason is that the additional pseudo measurement is actually a constant here which cannot help to estimate the state. More specifically, when the states in an unconstrained dynamic system model have already satisfied the equality constraint, the extra constraint is obviously not necessary. When the true equality-constrained states do not satisfy the unconstrained dynamic process equation, the effect of pseudo measurement is projecting the estimate which is not optimal onto the constraint set. However, since the performance of a projected estimate is also certainly influenced by its original estimate, we show through a numerical example that the pseudo measurement method is not always a good choice, especially when the process equation mismatch is large.