12. Absolute Code Biases Based on the Ambiguity-Free Linear Combination—DCBs Without TEC

Absolute code biases and associated DCBs determined using absolute code biases are called “absolute” because they do not require TEC information to estimate them and are defined against the IGS Clock Convention (“P₃ clocks”).

Differential code biases (DCBs) are typically determined by co-estimating the first-order ionosphere effect using the geometry-free linear combination of code measurements from two different GNSS frequencies. We develop ambiguity-free linear combinations based on the dual- or triple-frequency GPS carrier-phase and code measurements on only one GPS frequency. In this way, we can estimate code biases on a single GPS frequency. Since the datum of the GPS satellite clock corrections is defined by the ionosphere-free linear combination of the P-code measurements on L₁ and L₂ we can estimate these single-frequency code biases as “absolute biases” using the geometry-free approach. Our ambiguity-free linear combination removes single-frequency ambiguities, but it requires the estimation of one wide-lane ambiguity with a very long wavelength, a wavelength that is significantly greater than the size of the code biases. In addition, by forming single-differences between two GNSS satellites using measurements from one station, one can separate satellite-based from station-based code biases. We show the relationship between the code biases and the narrow-lane biases in the Melbourne-Wübbena linear combination and DCBs. The same approach is extended to other multi-GNSS code observables.

Absolute code biases defined for single-frequency observables can be used to combine carrier-phase and code measurements consistently in a multi-GNSS environment and to define carrier-phase ambiguities and ionospheric effects in an “absolute sense”. Absolute code biases can provide a datum for estimated global ionosphere maps and for all calibration of multi-GNSS code measurements (e.g., group delays). We show here absolute code bias in P₁ and C₅ code GPS measurements on L₁ and L₂ carrier-phases and present calibration of ¼-ambiguities associated with L₅. We discuss absolute code biases in the light of the S-curve bias and group delay variation maps for GNSS satellites. We show how, by introducing absolute code biases, we can consistently define a datum for GNSS satellite clock parameters and ionosphere maps in a multi-frequency GNSS environment. Galileo and future GNSS will introduce wide-band signals that will lead to low code noise (in the cm-range). Specifically, the Galileo E5 wide-band signal (nominal bandwidth of 51.15 MHz) and the AltBOC modulation will offer code noise at cm-level. The same approach could be applied to Galileo using wide-band signals as reference signals to determined absolute code biases.