Задача оцінювання векторних однорідних випадкових полів

Key Points

• The goal is to optimally estimate linear functionals based on observations from noisy vector homogeneous random fields.
• Developed formulas for calculating mean square error of estimates.
• Derived spectral characteristics of optimal linear estimates under spectral determinacy.
• Assumed known spectral densities of the fields.
• Provided explicit formulas for mean square error for optimal estimators.
• Characterized spectral properties that enhance estimation accuracy.
• Enabled precise optimizations in the context of homogeneous random fields.