Resource Constrained Linear Estimation in Sensor Scheduling and Informative Path Planning

Abstract

This thesis studies problems in resource constrained linear estimation with a focus on sensor scheduling and informative path planning. Sensor scheduling concerns itself with the selection of the best subsets of sensors to activate in order to accurately monitor a linear dynamical system over a fixed time horizon. We consider two problems in this setting. First, we study the general version of sensor scheduling subject to resource constraints modeled as linear inequalities. This general form captures a variety of well-studied problems including sensor placement and linear quadratic control (LQG) control and sensing co-design. Second, we study a special case of sensor placement where only k measurements can be taken in a spatial field which finds applications in precision agriculture and environmental monitoring.

In informative path planning, an unknown target phenomena, modeled as a stochastic process, is estimated using a subset of measurements in a spatial field. We study two problems in this setting. First, we consider constraints on robot operation such as tour length or number of measurements with the goal of producing accurate estimates of the target phenomena. Second, we consider the dual version where robots must minimize resources used while ensuring the resulting estimates have low uncertainty or expected squared estimation error.

Our solution approaches exploit the problem structure at hand to give either exact formulations as integer programs, approximation algorithms, or well-designed heuristics that yield high quality solutions in practice. We develop algorithms that combine ideas from combinatorial optimization, stochastic processes, and estimation.