is the ionosphere-free combination of the B1C pilot component (C1P) and the B2a pilot component (C5P), and the BDS DCB precision products released by IGS is used to eliminate the delay of pseudo-ranges at different frequency points. Equation (2) can be described as [10]: P ,r IF r k12 DCBkk12 P P2 3 (3) 12 c dt dT m ZWD 1 13 r s 11 DCB PP In (3), k12 1575.42 1176.45 is a factor related to frequency, the DCB C P C I PP 56 . The same principle, the ionospherePP 16 , and 13 the DCB C P C I 23 free combination of carrier phase observation equation [11] is shown in (4): L ,r IF fL fL ff 22 12 22 11 22 (4) In this paper, the algorithm of Kalman filtering is used to estimate the parameter, the observation and state equations can be expressed using (5) [12]: k = k kk k X Xw L HX v kk k ,1 1 k 1 where Xk is the state variable at time k, Φk,k-1 sition matrix from time k-1 to time k, wk (5) of the system, Lk is the observation vector at time k, Hk coefficient matrix of the observation equation, and vk is the state tranis the noise vector is the is the observation noise. The process noise and observation noise of the system have the following statistical properties: E w Cov w w E w w Q E v Cov w v E w vT , kj k 0, k , k , j k j k 0, Cov v v E v v Rkj k k 0 j T k j kj T (6) where V is the observation residual vector, H is the coefficient matrix, l is observed minus computed, the state vector X includes receiver position coordinate increment ( ,, xy z NN1 are the carrier phase m IF 12 ,, IF12 ambiguity. The state vector X is shown in (10) [12], [13]: 12 X x y z cdt ZWD N N 1 m , , , r , , ,, IF12 IF ),cdtr is the receiver clock bias correction, ZWD is the zenith tropospheric wet delay, and (10) Fig. 2 shows the principle of BDS-3 PPP time comparison [11], [16], and the model correction algorithms are listed in Table 1. The BDS PPP time comparison method can be described as follows: the local reference time frequency signal of station A is T1ref is T2ref , the local reference time frequency signal of station B , and the common reference time is IGST: 1 t T IGSTref A t T IGSTref 2 B (11) (12) Here, t A is the time difference between T1ref and IGST, t B is the time difference between T2ref and IGST. Therefore, the time difference between station A and station B is derived from (11) minus (12): The Q and Rare the variance matrices of system noise and observation noise, respectively, and it is assumed to be known with white noise. The δkj kj is the Kronecker function, and 1 kj kj . The state transition matrix can be express as: 4 4 44 kk 0I4 4 44 /1 II dt (7) where I is the diagonal matrix, and dtis time interval between adjacent epochs. The coefficient matrix can be expressed as: 32 t ref ref A B (1 t T IGST T IGST T IGST T IGST t ) ( 2 Testing and Analysis The BDS-3 new signal PPP time comparison was studied based on the observation data (NTSC and TP) obtained July 3-6, 2020. The BDS receiver was connected to the 1 PPS and 10 MHz signals from a local laboratory. The laboratory had suitable environmental conditions where the temperature and humidity are kept at about 23 °C and 45%, respectively, for a long time. Meanwhile, the BDS precise orbit and clock products published by GFZ were used. Based on the algorithm and principle introduced previously, the receiver short-baseline and high-precision IEEE Instrumentation & Measurement Magazine August 2022 12 AB ref ref ) (13) 2 where ax ,ay r where Pr,IF H a a a MF a a a MF xy z xy z i ii 1 11 1 11 aaa MFi 0 0 (8) xyz 1 xyz 1 xy z xy z n nn n nn 0 1 0 0 a a a MF a a a MF 1 1 ,as n 0 0 n 0 0 are the cosines of the satellite-ground direction. Based on (3) and (4), it is assumed that m satellites are observed at the time t, and observation equations are established. The error equation is shown in (9): V =HX l (9) 0 0 0 0 1 0 0 aaa MFi i ii 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0

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