A new generalized residual multiple model adaptive estimator of parameters and states

This article 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 the traditional Kalman filter residual and the “post-fit” Kalman filter residual which is calculated after measurement incorporation. This new modified MMAE is termed a Generalized Residual Multiple Model Adaptive Estimator (GRMMAE). A derivation is provided for the hypothesis conditional probability formula which the GRMMAE uses to calculate probabilities that each elemental filter 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 linear combination of the two. The original GRMMAE design goal was to choose the GRMMAE design parameter which caused the fastest GRMMAE convergence to the correct hypothesis. However, this article demonstrates that the GRMMAE design parameter can lead to ββ-dominance, a negative performance effect in the GRMMAE. That fact is a key result of this research as other researchers have previously suggested that the use of post-fit residuals may be advantageous in certain MMAE applications. This article demonstrates the ββ-dominance effect and recommends that post-fit residuals not be used in an MMAE.