An Adaptive Extended Kalman Filter Incorporating State Model Uncertainty for Localizing a High Heat Flux Spot Source Using an Ultrasonic Sensor Array

An adaptive extended Kalman filter is developed and investigated for a transient heat transfer problem in which a high heat flux spot source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. The novel approach is based on the uncertainty in the state model covariance and leverages trends in the extended Kalman filter covariance to drive changes to the state model covariance during convergence. This work is an integral part of an effort to develop a system capable of locating the boundary layer transition region on a hypersonic vehicle aeroshell. Results from thermal conduction experiments involving oneway ultrasonic pulse time of flight measurements are presented. Comparisons between the adaptive extended Kalman filter and a non-adaptive extended Kalman filter are presented. Heating source localization results and convergence behavior are compared for the two filters. This work provides evidence that, for the subject heating source localization problem, the state model covariance and measurement covariance in the extended Kalman filter are correlated in an inversely proportional manner. Modifications to either the state model covariance or the measurement covariance effects the convergence behavior of the Kalman filter. The extended Kalman filter variance was observed to increase until convergence and to decrease rapidly after convergence. The variance was used to drive modifications to the state model covariance in a manner designed to affect convergence behavior. The adaptive extended Kalman filter developed in this work produces faster and smoother convergence than the non-adaptive form of the extended Kalman filter. This performance boost is accomplished by tailoring the state model covariance during each iteration instead of retaining the assumed state model covariance throughout the convergence process. 1 Vanderbilt University, Nashville, TN, USA. 2 Federal University of Itajubá, Itajubá, MG, Brazil. 3 Industrial Measurement Systems, Inc., Aurora, IL, USA. 222 Copyright © 2012 Tech Science Press CMES, vol.83, no.3, pp.221-248, 2012