Page 183 - 卫星导航2021年第1-2合期
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Zhang et al. Satell Navig            (2021) 2:11                                       Page 7 of 10





                                                              where the variations of receiver code biases become esti-
                                                              mable, the ambiguity estimates converge to constant rea-
                                                              sonably and the residuals of code observations follow the
                                                              normal distribution (see Fig. 6).
                                                                At this stage it is proved that MPPP model can get
                                                              correct ambiguity estimates and reasonable code obser-
                                                              vation residuals. In the following sections the improve-
                                                              ments in STEC retrieval and timing based on the MPPP
                                                              model will be investigated.

                                                              Retrieval of STEC parameter
                                                              As mentioned earlier, also see Ciraolo et al. (2007), if the
                                                              short-term variability of receiver DCBs is not properly
              Fig. 4  Estimated ambiguity parameters of L1 frequency at station
              MTDN using the MPPP model. Diferent colors correspond to diferent   managed,  it  can  have  signifcant  impact  on  the  STEC
              satellites                                      results. In order to evaluate the performance of the MPPP
                                                              in retrieving STEC, we compared the DSTECs obtained
                                                              by the original and modifed PPP models was compared
                                                              with those derived by using the GF carrier phase obser-
                                                              vations to minimize any impact from multipath or code
                                                              biases. Te corresponding results are shown in Fig.  7,
                                                              where diferent colors represent diferent satellites.
                                                                It can be clearly seen that the STECs retrieved by the
                                                              MPPP (right column) are more accurate and stable than
                                                              those  by  the  original  PPP  model  (left  column).  Table  2
                                                              summarizes the Root-Mean-Square (RMS) values for the
                                                              original PPP-DSTEC as well as MPPP-DSTEC. Note that
                                                              the most obvious improvement of 96% occurs at station
                                                              MTDN, which also has the signifcant variations of code
                                                              biases on P1 and P2 as shown in Fig. 1. Te other three
                                                              stations (ALIC, NOTI and MEDI) also show consider-
                                                              able improvements. Considering the fact that the MPPP
                                                              results are free of the efects due to variability of code
              Fig. 5  P1 (magenta dots) and P2 (green dots) residuals of code   biases, we can thus interpret the diferences as the errors
              observations at station MTDN using the original PPP model
                                                              to which the original PPP results are subject.

                                                              Timing
                                                              Generally, the colored signature of the code noise is an
                                                              interfering factor for the medium and long-term (from
                                                              some hours to some days) stability of receiver clock solu-
                                                              tions (Martínez-Belda  et  al.  2011;  Martinez-belda  et  al.
                                                              2012). Te MPPP (see Eq.  10) can theoretically elimi-
                                                              nate the efect caused by the time-varying receiver code
                                                              biases. To validate its efectiveness, the data at station
                                                              NOT1 on day 001 in 2018 and station MEDI on day 009
                                                              in 2018 were used. Figure 8 shows the Allan deviation of
                                                              receiver clock ofsets at station NOT1 and MEDI, respec-
                                                              tively, which are both connected to the external Hydro-
                                                              gen atomic clock.
                                                                Te blue lines and red lines represent the Allan devia-
                                                              tion of the PPP-derived and MPPP-derived receiver
              Fig. 6  P1 (magenta dots) and P2 (green dots) residuals of code   clock ofsets, respectively. It can be clearly seen that
              observations at station MTDN using the MPPP model
                                                              the frequency stability of the MPPP-derived solu-
                                                              tions  is  improved  signifcantly  relative  to  the  original
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