On the Information Dilution Theorem and Its Application to Attitude Determination

Abstract

The information dilution theorem (IDT), as presented in the literature, shows the difference between the least squares (LS) estimate of the state of an ordinary linear system and the estimate of the state of the same system when a bias is added to it. In the formulation of the IDT it is tacitly assumed that each of the estimators uses the corresponding correct model. However, contrary to the claim that the outcome of the theorem explains certain empirical results in attitude determination, it is shown in this work that this is not the case. A more complete formulation of the pertinent estimation problem is presented and results are derived which show that, unlike the conclusion of the IDT, the answer to the question which estimator is preferred is not unique. This work presents the conditions under which those empirical results could be more completely explained. The analytic development is accompanied by two space-related examples which demonstrate the analytic conclusions.