Convex Reformulation of Information Constrained Linear State Estimation with Mixed-Binary Variables for Outlier Accommodation

TL;DR

This paper introduces a convex reformulation of the RAPS state estimation approach with mixed-binary variables, enabling efficient outlier accommodation in linear state estimation.

Contribution

It transforms the non-convex RAPS optimization into a convex problem by linearizing binary variables, improving computational efficiency and practical applicability.

Findings

Convex reformulation allows efficient solving of RAPS problems.

Diag-RAPS outperforms Full-RAPS in speed and efficiency.

Diag-RAPS achieves lower risk than Kalman Filter and Threshold Decisions.

Abstract

This article considers the challenge of accommodating outlier measurements in state estimation. The Risk-Averse Performance-Specified (RAPS) state estimation approach addresses outliers as a measurement selection Bayesian risk minimization problem subject to an information accuracy constraint, which is a non-convex optimization problem. Prior explorations into RAPS rely on exhaustive search, which becomes computationally infeasible as the number of measurements increases. This paper derives a convex formulation for the RAPS optimization problems via transforming the mixed-binary variables into linear constraints. The convex reformulation herein can be solved by convex programming toolboxes, significantly enhancing computational efficiency. We explore two specifications: Full-RAPS, utilizing the full information matrix, and Diag-RAPS, focusing on diagonal elements only. The simulation comparison demonstrates that Diag-RAPS is faster and more efficient than Full-RAPS. In comparison with Kalman Filter (KF) and Threshold Decisions (TD), Diag-RAPS consistently achieves the lowest risk, while achieving the performance specification when it is feasible.