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.

中文翻译：

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信息稀释定理及其在态度确定中的应用

文献中介绍的信息稀释定理（IDT）显示了普通线性系统状态的最小二乘法（LS）估计与同一系统的状态估计之间的差异。 。在制定IDT时，默认假定每个估计量都使用相应的正确模型。但是，与声称定理的结果解释了姿态确定中的某些经验结果的说法相反，这项工作表明事实并非如此。给出了有关估计问题的更完整表述，并得出了结果，结果表明，与IDT的结论不同，首选估计器的问题的答案不是唯一的。这项工作提出了可以更完整地解释这些经验结果的条件。分析的发展伴随着两个与空间有关的例子，这些例子证明了分析结论。