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Du et al. Satell Navig             (2021) 2:3                                           Page 15 of 22





            Table 3  Excluded measurements with diferent FDE methods compared with simulated faults in measurements
            Numbers of epoch   Measurements      Simulated    Excluded measurements
            with 1‑s interval  with simulated outliers  outliers (m)
                                                              Simple FDE            Advanced FDE  Chi‑square test
                                                                                                  based FDE
            2137              G03 L1             ‑1.0061      G03 L1                G03 L1        G03 L1
                              G31 L1             ‑0.6252      G31 L1                G31 L1        G31 L1
            2145              G01 L1             ‑0.8257      G01 L1                G01 L1        G01 L1
                              G31 L1             ‑0.5368      G31 L1                G31 L1        G31 L1
            2146              G03 L1             ‑0.4397      G03 L1                G03 L1        G03 L1
                              G23 L1             ‑0.2917      –                     G23 L1        G23 L1
                                                              Wrong exclusion:
                                                              L1: G09, G18, E26, E07, E27
                                                              L2: G09, G23, G18
                                                              L5: G09, E26, E27, E07
            2182              G03 L1             0.4673       G03 L1                G03 L1        G03 L1
            2264              G16 L1             0.5393       G16 L1                G16 L1        G16 L1
                              G31 L1             ‑0.3877      G31 L1                G31 L1        G31 L1
            2550              G03 L1             0.2335       –                     G03 L1        G03 L1
                              G22 L1             0.4185       G22 L1                G22 L1        G22 L1
                                                              Wrong exclusion:
                                                              L1: G14, G18, G23, E07, E27
                                                              L2: G03, G18, G22, G23
                                                              L5: G03, E27
            2580              G22 L1             ‑0.5009      G22 L1                G22 L1        G22 L1
                              G23 L1             0.5970       G23 L1                G23 L1        G23 L1
                                                              Wrong exclusion: G09 L1
            2854              G09 L1             0.5608       G09 L1                G09 L1        G09 L1
                              G16 L1             0.8676       G16 L1                G16 L1        G16 L1
            2870              G09 L1             ‑0.0654      –                     –             –
                              G26 L1             0.0930       G26 L1                G26 L1        G26 L1
            2911              G09 L1             ‑0.5632      G09 L1                G09 L1        G09 L1
                              G22 L1             ‑0.4518      G22 L1                G22 L1        G22 L1























                                                               Fig. 3  Fault detection tests, i.e. checking if the absolute post‑ft
              Fig. 2  PPP positioning errors (after convergence) in the case of faulty   residuals are less than empirical thresholds, for code and carrier‑phase
              measurements, with no FDE applied. Note that faults may cause   measurements with PPP‑Wizard; the fault detection test was
              positioning errors larger than the shown 0.2 m maximum  preformed group by group for diferent signals and constellations;
                                                               threshold values were set to 10 m and 0.05 m for code and
                                                               carrier‑phase, respectively. Scatters with diferent colours represent
                                                               diferent satellites
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