Optimization of measurement schedules and sensor designs for linear dynamic systems

Abstract

This paper presents new results on the problem of measurement scheduling, sensor location and design for linear dynamic systems. Both time-invariant and timevarying systems are considered and different norms of the Observability and Information matrices are maximized with respect to the structural parameters of the system. A close connection is established between these problems and the Kiefer-Wolfowitz Theory of Experimental Design for Regression problems. Both randomized and nonrandomized designs are considered. It is shown that the optimal designs obey certain minmax properties that lead to rapidly convergent algorithms. The results are illustrated by an analytical and a numerical example.

A time-triggered object tracking subsystem for advanced driver assistance systems

“…In (Mehra, 1976), Mehra uses different norms of the observability and the Fisher information matrix (Spall, 2008) as criteria for the optimization of measurement scheduling and shows that it is preferable to cluster measurements around specific design points t k .…”

Value of measurement information: A simple case study on grade change decisions

“…[5][6][7][13][14][15][16][17]. In all these approaches the objective is to minimize a weighted state uncertainty matrix rather than the expected consequence of the action to be made on the basis of data obtained.…”

Optimal Sensor Network Design for Multirate Systems

“…Mellefont and Sargent [3] presented an implicit enumeration algorithm for the selection of sensors based on the minimization of an objective that includes both the measurement cost and a quadratic performance index (function of the covariance of the state prediction error) for optimal feedback control. The trace, norm or determinant of the state prediction error covariance matrix (SPECM) was considered by Mehra [4] to optimize the measurement schedules and sensor designs for linear dynamic systems. Recognizing the difficulty associated with the dynamic solution of the Riccati equation, Mehra [4] considered the inverse of the information matrix as an equivalent measure of SPECM.…”

“…The trace, norm or determinant of the state prediction error covariance matrix (SPECM) was considered by Mehra [4] to optimize the measurement schedules and sensor designs for linear dynamic systems. Recognizing the difficulty associated with the dynamic solution of the Riccati equation, Mehra [4] considered the inverse of the information matrix as an equivalent measure of SPECM. The work by Waldraff et al [5] used different metrics based on the observability matrix, observability gramian and Popov-Belevitch-Hautus rank test as criteria for sensor location in a tubular reactor.…”