Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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Kalman filtering and multiple model adaptive estimation MMAE methods have been applied by researchers in several engineering disciplines to a multitude of problems featuring a linear or mildly nonlinear model based on finite-dimensional differential or difference equations perturbed by random inputs. However, many real-world systems are more naturally modeled using an infinite-dimensional continuous-time linear systems model, such as those most naturally modeled as partial differential equations or time-delayed differential equations along with a possibly infinite-dimensional measurement model. The Kalman filtering technique was extended to encompass infinite-dimensional continuous-time systems with sampled-data measurements and a technique to approximate an infinite-dimensional continuous-time system model with an essentially equivalent finite-dimensional discrete-time model upon which a filtering algorithm could be based was developed. The tools developed during this research were demonstrated using an estimation problem based on a stochastic partial differential equation with an unknown noise environment.
- Theoretical Mathematics
- Electricity and Magnetism