Modified Multiple Model Adaptive Estimation (M3AE) for Simultaneous Parameter andState Estimation

摘要

In many estimation problems, it is desired to estimate system states andparameters simultaneously. However, inherent to traditional estimation architectures of the past, the designer has had to make a trade-off decision between designs intended for accurate state estimation versus designs concerned with accurate parameter estimation. This research develops one solution to this trade-off decision by proposing a new architecture based on Kalman filtering (KF) and Multiple Model Adaptive Estimation (MMAE) techniques. This new architecture, the Modified-MMAE (M3AE), exploits the benefits of an MMAE designed for accurate parameter estimation, and yet performs at least as well in state estimation as an MMAE designed for accurate state estimation. The M3AE accomplishes the simultaneous estimation task by providing accurate state estimates from a single KF designed to accept accurate parameter estimates from the MMAE. Additionally, an M3AE approximate covariance analysis capability is developed, giving the designer a valuable design tool for analyzing and predicting M3AE performance before actually implementing the M3AE and conducting a time-consuming full-scale Monte Carlo performance analysis. Finally, the M3AE architecture is applied to two existing research examples to demonstrate the performance improvement over that of conventional MMAEs. The first example involves a simple second-order mechanical translational system, in which the system's natural frequency is the uncertain parameter. The second example involves a 13-state nonlinear integrated Global Positioning System/Inertial Navigation System (GPS/INS) system, in which the variance of the measurement noise affecting the GPS outputs, is the uncertain parameter.