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Table 3 Estimated receiver clock, DCB, IFB, and ionospheric delay parameters from various BDS PPP models

From: PPP models and performances from single- to quad-frequency BDS observations

Model

Receiver clock (\(d\bar{t}_{r}\))

DCB (DCB)

IFB (ifb)

Ionospheric delay (\(\tau\))

SF1

\(dt_{r} + d_{r,j}\)

Null

Null

\(\tau\)

SF2

\(dt_{r} + d_{r,j} /2 + b_{r,j} /2\)

Null

Null

Null

SF3

\(dt_{r} + d_{r,j}\)

Null

Null

\(\tau\)

DF1

\(dt_{r} + d_{r,(1,2)}\)

Null

Null

\(\tau \text{ + }\beta_{1,2} \cdot DCB_{r,(1,2)}\)

DF2

\(dt_{r} + d_{r,(1,2)}\)

Null

Null

Null

DF3

\(dt_{r} + d_{r,j} /2 + b_{r,j} /2\)

\(DCB_{r,(1,2)}\)

Null

Null

DF4

\(dt_{r} + d_{r,(1,2)}\)

Null

Null

\(\tau\)

TF1

\(dt_{r} + d_{r,(1,2)}\)

Null

\(\beta_{ 1, 2} /\beta_{ 1,3} \cdot DCB_{r,(1,2)} - DCB_{r,(1,3)}\)

\(\tau \text{ + }\beta_{1,2} \cdot DCB_{r,(1,2)}\)

TF2

\(dt_{r} + d_{r,(1,2)}\)

Null

\(\beta_{ 1, 2} \cdot DCB_{r,(1,2)} - \beta_{ 1,3} \cdot DCB_{r,(1,3)}\)

Null

TF3

\(dt_{r} + d_{r,(1,2,3)}\)

Null

\(d_{r,(1,2)} - d_{r,(1,2,3)}\)

Null

TF4

\(dt_{r} + d_{r,(1,2)}\)

\(DCB_{r,(1,2)}\)

\(\beta_{ 1, 2} /\beta_{ 1,3} \cdot DCB_{r,(1,2)} - DCB_{r,(1,3)}\)

\(\tau\)

QF1

\(dt_{r} + d_{r,(1,2)}\)

Null

1. \(\beta_{ 1, 2} /\beta_{ 1,3} \cdot DCB_{r,(1,2)} - DCB_{r,(1,3)}\)

2. \(\beta_{ 1, 2} /\beta_{ 1, 4} \cdot DCB_{r,(1,2)} - DCB_{r,(1, 4)}\)

\(\tau \text{ + }\beta_{1,2} \cdot DCB_{r,(1,2)}\)

QF2

\(dt_{r} + d_{r,(1,2)}\)

Null

\(d_{r,( 3, 4)} - d_{r,(1,2)}\)

Null

QF3

\(dt_{r} + d_{r,(1,2,3,4)}\)

Null

\(d_{r,(1,2)} - d_{r,(1,2,3,4)}\)

Null

QF4

\(dt_{r} + d_{r,(1,2)}\)

\(DCB_{r,(1,2)}\)

1. \(\beta_{ 1, 2} /\beta_{ 1,3} \cdot DCB_{r,(1,2)} - DCB_{r,(1,3)}\)

2. \(\beta_{ 1, 2} /\beta_{ 1, 4} \cdot DCB_{r,(1,2)} - DCB_{r,(1, 4)}\)

\(\tau\)

  1. where dtr is the raw receiver clock offset, dr,j and br,j denote the receiver pseudorange and carrier phase hardware delay on the jth frequency. \(d_{r,(m,n)} = \alpha_{m,n} \cdot d_{r,m} + \beta_{m,n} \cdot d_{r,n}\). \(d_{r,(1,2,3)} = e_{1} \cdot d_{r,1} + e_{2} \cdot d_{r,2} + e_{3} \cdot d_{r,3}\). \(d_{r,(1,2,3,4)} = e_{1}^{\prime } \cdot d_{r,1} + e_{2}^{\prime } \cdot d_{r,2} + e_{3}^{\prime } \cdot d_{r,3} + e_{4}^{\prime } \cdot d_{r,4}\)