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# Carrier-smoothing of code pseudoranges

Fundamentals | |
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Title | Carrier-smoothing of code pseudoranges |

Author(s) | J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. |

Level | Advanced |

Year of Publication | 2011 |

The noisy (but unambiguous) code pseudorange measurements can be smoothed with the precise (but ambiguous) carrier phase measurements. A simple algorithm (the Hatch filter) is given as follows:

Let's and the code and carrier measurement of a given satellite at the time . Thence, the smoothed code can be computed as:

- The algorithm is initialised with:

where, when and when

This algorithm must be initialised every time that a carrier phase cycle-slip occurs.

The previous algorithm can be interpreted as a real-time alignment of the carrier phase to the code measurement. That is:

where the mean bias ^{[footnotes 1]} between the code and carrier phase is estimated in real time and used to align the carrier phase with the code.

For more information, please go to the article:

## Notes

- ^ The mean value of a set of measurements can be computed recursively as: . The equation (2) is a variant of previous expression, that provides an estimate of a moving average over a samples window. Notice that, when , the weighting factors and are used instead of and .