Making Every Bit Count for $A$-Optimal State Estimation

TL;DR

This paper develops efficient optimization methods for allocating limited communication bits across sensors to minimize the error covariance in linear state estimation, with applications to power grid monitoring.

Contribution

It derives a gradient formula simplifying the optimization of bit allocation under a nonconvex constraint, enabling effective use of Frank-Wolfe and interior point methods.

Findings

Gradient computation reduces to a single Cholesky factorization.

Proposed rounding procedure bounds solution quality.

Numerical experiments show efficiency and improved performance over uniform allocation.

Abstract

We study the problem of controlling how a limited communication bandwidth budget is allocated across heterogeneously quantized sensor measurements. The performance criterion is the trace of the error covariance matrix of the linear minimum mean square error (LMMSE) state estimator, i.e., an $A$-optimal design criterion. Minimizing this criterion with a bit budget constraint yields a nonconvex optimization problem. We derive a formula that reduces each evaluation of the gradient to a single Cholesky factorization. This enables efficient optimization by both a projection-free Frank-Wolfe method (with a computable convergence certificate) and an interior point method with L-BFGS Hessian approximation over the problem's continuous relaxation. A largest remainder rounding procedure recovers integer bit allocations with a bound on the quality of the rounded solution. Numerical experiments in IEEE power grid test cases with up to 300 buses compare both solvers and demonstrate that the analytic gradient is the key computational enabler for both methods. Additionally, the heterogeneous bit allocation is compared to standard uniform bit allocation on the 500 bus IEEE power grid test case.