Conditions for Error-Free Best Linear Unbiased Estimation Without Prior

Generally, estimates are subject to errors. For a general linear data model, we study conditions for guaranteed error-free best linear unbiased estimation (BLUE) without prior information in this article. A necessary and sufficient condition for error-free BLUE estimation is presented. So are a sufficient condition in three equivalent forms and a necessary condition. To illustrate these conditions, more specific data models are considered. For the case of two measurement noises with the same dimension, their linear correlation can be measured by the generalized Pearson correlation coefficient. Under perfect correlation, a more specific sufficient condition for error-free BLUE estimation fusion is provided. As another special case, distributed fusion of two local estimates is discussed. The relationship of these results are also analyzed. Besides, the results of perfect correlation help explain why a strong linear correlation may relate to an accurate fused estimate. An illustrative example verifies these findings.