Measurement partitioning and observational equivalence in state estimation

TL;DR

This paper explores how measurements in state estimation can be partitioned into two types based on graph theory, and how observational equivalence sets are characterized for each type, enhancing understanding of measurement importance.

Contribution

It introduces a novel partitioning of critical measurements into two categories, alpha and beta, based on graphical and algebraic methods, and defines their observational equivalence sets.

Findings

Partitioning of measurements into alpha and beta types.

Characterization of observational equivalence sets for each measurement type.

Application of graph-theoretic principles to state estimation measurement analysis.

Abstract

This letter studies measurement partitioning and equivalence in state estimation based on graph-theoretic principles. We show that a set of critical measurements (required to ensure LTI state-space observability) can be further partitioned into two types:~$\alpha$ and~$\beta$. This partitioning is driven by different graphical (or algebraic) methods used to define the corresponding measurements. Subsequently, we describe observational equivalence, i.e. given an~$\alpha$ (or~$\beta$) measurement, say~$y_i$, what is the set of measurements equivalent to~$y_i$, such that only one measurement in this set is required to ensure observability? Since~$\alpha$ and~$\beta$ measurements are cast using different algebraic and graphical characteristics, their equivalence sets are also derived using different algebraic and graph-theoretic principles. We illustrate the related concepts on an appropriate system digraph.