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Table 1 Relations between the BLUEs related to the joint estimation, the OSP-based estimation, and the differential estimation

From: On a unified framework for linear nuisance parameters

Models BLUEs Equality conditions
Original Model in (1) Joint estimator in (2) [I L 0 L×M ]a, \(\mathbf {P}_{\mathbf {G}}^{\perp }\triangleq \mathbf {I}_{N}-\mathbf {G} \mathbf {G}^{\dagger }\)
OSP Model Type I in (4) OSP estimator type I in (6) \(\mathbf {P}_{\mathbf {G}}^{\perp T} \mathbf {P}_{\mathbf {G}}^{\perp }=\mathbf {P}_{\mathbf {G}}^{\perp }\)
OSP Model Type II in (7) OSP estimator type II in (9) \(\mathbf {U}_{n}\mathbf {U}_{n}^{T}=\mathbf {P}_{\mathbf {G}}^{\perp }\)
Differential Model in (19) Differential estimator in (22) \(\mathbf {P}^{T}\mathbf {P}=\mathbf {P}_{\mathbf {G}}^{\perp }\)
or the Whitened One in (20)   
  1. a [I L 0 L×M ] is used for extracting \(\hat {\mathbf {x}}_{\text {jls}}\) in (22)