Guaranteed Robust Performance of $\mathcal {H}_{\infty }$ Filters With Sparse and Low Precision Sensing

Abstract

The performance of estimation algorithms depends on the available sensors and their precisions. While higher precisions of sensors provide better estimation accuracy, it may lead to unnecessarily expensive designs and higher operational costs due to higher costs of high-precision sensing modalities. Also, higher precision can cause interference for other sensors in the environment, such as RADARS, resulting in degradation in the overall system's performance. This paper presents a framework for co-designing a sparse sensing network with the least precise sensors and the filter that guarantees the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> estimation accuracy. Convex optimization problems for minimizing sensor precisions are formulated for continuous and discrete-time linear time-invariant systems, with and without model uncertainties. Different heuristics for determining a sparse sensor set with the least precise sensors are discussed, and their performances are compared using numerical simulations. The application of the proposed framework is demonstrated using numerical examples.