# A Circuit-Theoretic Approach to State Estimation

arXiv: https://arxiv.org/abs/1911.05155 · HTML: https://mlsanity.com/paper/1911.05155/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2019.

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

- [Cyber-Resilient System Identification for Power Grid through Bayesian Integration](https://mlsanity.com/paper/2510.14043/) (2025)

## Abstract (arXiv)

Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from non-convergence and large residual errors. In this paper we propose an equivalent circuit formulation (ECF)-based SE approach that inherently considers the complete network topology and associated physical constraints. We analyze the mathematical differences between the two approaches and show that our approach produces a linear state-estimator that is mathematically a quadratic programming (QP) problem with closed-form solution. Furthermore, this formulation imposes additional topology-based constraints that provably shrink the feasible region and promote convergence to a more physically meaningful solution. From a probabilistic viewpoint, we show that our method applies prior knowledge into the estimate, thus converging to a more physics-based estimate than the traditional observation-driven maximum likelihood estimator (MLE). Importantly, incorporation of the entire system topology and underlying physics, while being linear, makes ECF-based SE advantageous for large-scale systems.