Interrelationship of single-filter and multiple-model adaptive algorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model.