| This dissertation develops a modification to the standard Multiple Model Adaptive Estimator (MMAE) which allows the use of a new “generalized residual” in the hypothesis conditional probability calculation. The generalized residual is a linear combination of traditional Kalman filter residuals and “post-fit” Kalman filter residuals which are calculated after measurement incorporation. This modified MMAE is termed a Generalized Residual Multiple Model Adaptive Estimator (GRMMAE). The dissertation provides a derivation of the hypothesis conditional probability formula which the GRMMAE uses to calculate probabilities that each elemental filter in the GRMMAE contains the correct parameter value. Through appropriate choice of a single scalar GRMMAE design parameter, the GRMMAE can be designed to be equivalent to a traditional MMAE, a post-fit residual modified MMAE, or any number of yet unused MMAEs. The original GRMMAE design goal was to choose the GRMMAE design parameter which caused the fastest GRMMAE convergence to the correct hypothesis. However, this dissertation demonstrates that the GRMMAE design parameter can lead to β-dominance, a negative performance effect in the GRMMAE. This is a key contribution of this research as other researchers have previously suggested that the use of post-fit residuals may be advantageous in certain MMAE applications. This dissertation directly addresses the use of post-fit residuals by those researchers and demonstrates that, for their application, equivalent performance is achieved using a traditional MMAE. |
