A comparison of extended Kalman filter,particle filter,and least squares localization methods for a high heat flux concentrated source

State estimation procedures using the extended Kalman filter, particle filter, and least squares are investigated for a transient heat transfer problem in which a high heat flux concentrated 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. 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 one-way ultrasonic pulse time of flight measurements are presented. Comparisons of heating source localization measurement models are conducted where ultrasonic pulse time of flight readings provide the measurement update to the extended Kalman filter, particle filter, and least squares. Two different measurement models are compared: (1) directly using the one-way ultrasonic pulse time of flight as the measurement vector and (2) indirectly obtaining distance from the one-way ultrasonic pulse time of flight and then using these obtained distances as the measurement vector. For the direct model, the Jacobian required by the extended Kalman filter and least squares is obtained numerically using finite differences and a finite element forward conduction solution. For the indirect model, the derivatives with respect to the state variables are obtained in closed form. Heating source localization results and convergence behavior are compared for the three inverse methods and the two measurement models. The extended Kalman filter, least squares, and particle filter methods using the one-way ultrasonic pulse time of flight measurement model (direct model) produced similar results when considering accuracy of converged solution, ability to converge to the correct solution, and smoothness of convergence behavior. The results provide quantified justification for moving forward with development of an extended Kalman filter-based localization solution.