# Measurement partitioning and observational equivalence in state estimation

arXiv: https://arxiv.org/abs/1412.5111 · HTML: https://mlsanity.com/paper/1412.5111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2014.

## Built on by (most cited first, 1 of 1)

- [Sensor-Conditioned Representation Learning via Scene-Relevant Observation Quotients](https://mlsanity.com/paper/2606.16210/) (2026)

## Abstract (arXiv)

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:~α and~β. 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~α (or~β) measurement, say~yi, what is the set of measurements equivalent to~yi, such that only one measurement in this set is required to ensure observability? Since~α and~β 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.