Square-Root Algorithms for Model Sensitivity Analysis.

Abstract : The Morf-Kailath discrete square-root filtering algorithms are extended to incorporate sensitivity information with respect to the assumed model and statistics is available, considered to be the actual model. The sensitivity analysis is carried out by computing the so-called variance ratios that can be obtained by a second set of orthogonal transforms. These operations can be performed either in covariance or information filter form, as the actual filters. This leads to four basic variants for the propagation of the variance ratios. These ideas can also be applied to other related areas such as smoothing and the dual control problems, where it is of interest to study the sensitivity of the total cost with respect to different models and weights of the cost.