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Zhang et al. Satell Navig            (2021) 2:11                                         Page 6 of 10












































              Fig. 2  Estimates of P1 (red lines) and P2 (green lines) receiver code biases and their ionosphere-free (gold line) and GF (blue line) combination on
              an epoch-by-epoch basis at stations NOT1 and MEDI for two consecutive days



            of nanoseconds. In this test the most signifcant change
            occurs at station MTDN on day 005 in 2018, with a peak-
            to-peak range of about 30 ns for the variation of P1 and
            P2 code biases as well as their ionosphere-free combi-
            nations. Tis is bound to bring disastrous efects on the
            estimated parameters, especially for ambiguity param-
            eters, ionospheric STEC retrieval and receiver clock of-
            sets, refer to Eq. (11).
              It can be seen from Eq. (7) that the GF and ionosphere-
            free combinations of receiver code biases both enter
            ambiguity parameters when conducting the original
            PPP. Te time-varying receiver code biases will there-
            fore impair the ambiguity estimation performance and
            make them not constant because of the incorrect func-  Fig. 3  Estimated ambiguity parameters of L1 frequency at station
            tional model. Let us take station MTDN associated with   MTDN using the original PPP model. Diferent colors correspond to
            the largest variation of receiver code biases as an exam-  diferent satellites
            ple. Figures 3 and 4 show the estimated ambiguities of L1
            frequency based on the original PPP and MPPP models,
            respectively.                                     distribution (see Fig.  5) owing to the efect of receiver
              With the original PPP model, ambiguity estimates are   code biases.
            subject to variations, not constant (see Fig. 3). Further-  Tis will inevitably induce leveling errors in the STEC
            more, the residuals obtained do not follow the normal   estimation. In contrast, with the MPPP model (see Fig. 4)
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