Optimal Sensor Precision for Multi-Rate Sensing for Bounded Estimation Error

TL;DR

This paper develops a convex optimization approach within the Kalman filtering framework to determine optimal sensor precisions that ensure bounded estimation errors, promoting sparse sensor configurations for linear time-varying systems.

Contribution

It introduces a method to optimize sensor precisions via convex programming, ensuring error bounds and promoting sensor sparsity, applicable to complex engineering systems.

Findings

Successfully applied to flight mechanics and astrodynamics problems.

Enabled sparse sensor configurations while maintaining error bounds.

Optimized sensor scheduling for linear time-varying systems.

Abstract

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the l1 norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to a) determine redundant sensing architectures for linear time invariant systems, b) accurately estimate states with low-cost sensors, and c) optimally schedule sensors for linear time-varying systems.