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Table 3 Total noise level \(\sigma_{{{\text{TC}}2}}\) and success rate under different given ionospheric biases of 10 cm, 20 cm and 100 cm, respectively

From: Improved precise positioning with BDS-3 quad-frequency signals

Combination schemes

\(\mu_{{\left( {a,b,c,d} \right)}} + \mu_{{\left( {i,j,k,h} \right)}}\)

\(\sigma_{\text{TCN}}\) (in cycle)

Success-rate (%)

Phase

Code

\(\delta_{\iota }\) = 10

\(\delta_{\iota }\) = 20

\(\delta_{\iota }\) = 100

\(\delta_{\iota }\) = 10

\(\delta_{\iota }\) = 20

\(\delta_{\iota }\) = 100

\(\phi_{{\left( {1, - 1,0,0} \right)}}\)

\(p_{{\left( {1,1,1,1} \right)}}\)

0.2864

0.0389

0.0390

0.0412

100.00

100.00

100.00

\(\phi_{{\left( {0,0,1, - 1} \right)}}\)

\(p_{{\left( {1,1,1,1} \right)}}\)

− 0.3675

0.0834

0.0856

0.1398

100.00

100.00

100.00

\(\phi_{{\left( {0,1, - 4,3} \right)}}\)

\(p_{{\left( {1,1,1,1} \right)}}\)

6.9574

0.1137

0.1314

0.3947

100.00

100.00

86.88

\(\phi_{{\left( {1, - 1,0,0} \right)}}\)

\(p_{{\left( {1,1,1,0} \right)}}\)

0.1536

0.0395

0.0395

0.0402

100.00

100.00

100.00

\(\phi_{{\left( {0,0,1, - 1} \right)}}\)

\(p_{{\left( {0,0,1,1} \right)}}\)

0

0.1124

0.1124

0.1124

100.00

100.00

100.00

\(\phi_{{\left( {0,1, - 4,3} \right)}}\)

\(p_{{\left( {1,1,0,0} \right)}}\)

6.6710

0.1140

0.1303

0.3799

100.00

100.00

89.55

\(\phi_{{\left( { - 2,3, - 2,1} \right)}}\)

\(p_{{\left( {1,1,1,0} \right)}}\)

0.0882

0.1967

0.1969

0.2031

98.90

98.89

98.63