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Table 1 Constraints on atmospheric delays and their estimable forms in the code-plus-phase ionosphere-float, ionosphere-weighted, and ionosphere-fixed models

From: PPP–RTK functional models formulated with undifferenced and uncombined GNSS observations

Model Parameter Constraint Estimable form
Ionosphere-float Troposphere None \(\tau_{r}\)
Ionosphere None \(\overline{l}_{r}^{s} = l_{r}^{s} - d_{{,{\rm GF}}}^{s} + d_{{r,{\rm GF}}}\)
Ionosphere-weighted Troposphere \(m_{1}^{s} = \cdots = m_{n}^{s}\) \(\tilde{\tau }_{r} = \tau_{r} - \tau_{1} \,\)
Ionosphere \(0 = l_{r}^{s} - l_{1}^{s}\) \(\tilde{l}_{r}^{s} = l_{r}^{s} - d_{{,{\rm GF}}}^{s} + d_{{1,{\rm GF}}}\)
Ionosphere-fixed Troposphere \(m_{1}^{s} \tau_{1} = \cdots = m_{n}^{s} \tau_{n} = \tau^{s}\) None
Ionosphere \(l_{1}^{s} = \cdots = l_{n}^{s} = l^{s}\) \(\overline{\overline{l}}^{s} = l^{s} - d_{{,{\rm GF}}}^{s} + d_{{1,{\rm GF}}}\)