Numerical Optimization of Multi-Sensor Estimation under Uncertain Measurement Constraints

Abstract

Multi-sensor state estimation becomes challenging when sensor measurements and physical constraints are affected by possibly incorrect information. This paper proposes a quantum-information-robust optimisation framework for constrained multi-sensor estimation under measurement uncertainty.The key novelty lies in the integration of the Bures uncertainty set over the density operator directly into the worst-case estimation formulation. This approach goes beyond simply using quantum information measures for sensor weighting or feature extraction.Each sensor is represented by a density operator along with an admissible quantum uncertainty region. This allows deviations in measurement information to be characterized geometrically.A variational quantum parameterisation is then used to represent the system state. Uncertain physical constraints are incorporated through a worst-case violation term.The resulting formulation jointly addresses estimation accuracy, quantum-information uncertainty and constraint robustness—all within an optimization framework.The analytical properties of the proposed estimator are investigated. This includes the existence of a solution, the convergenceof the optimization procedure and the sensitivity of the estimated state to changes in the uncertainty radius.Numerical experiments with nonlinear sensors compare the proposed method with conventional weighted least-squares, robust classicaloptimization and variational quantum estimation.The results show that the proposed framework has the potential to maintain estimation accuracy and constraint feasibility when measurement uncertainty increases.