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# Examples of multi-frequency Cycle-Slip Detectors

Fundamentals
Title Examples of multi-frequency Cycle-Slip Detectors
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011

With two frequency signals (or multifrequency in general) it is possible to build combinations of measurements to enhance the cycle-slip detection reliability. The target is to remove the geometry, which is the largest varying effect [footnotes 1], the clocks and the other non-dispersive delays, and ionospheric delays, as well.

Two kinds of examples of detectors are presented: Detectors based in carrier phase measurements only, and detectors based in code and carrier phase data. In the first type, carrier phase measurements of signals in two different frequencies are subtracted in order to remove the geometry and all non-dispersive effects. This provides a very precise test signal (multipath and noise less than one centimetre), although affected by the ionospheric refraction. But this effect varies as a smooth function and it can be modelled by a low degree polynomial fit. Nevertheless, high ionospheric activity conditions can degrade the performance of this detector, mainly with a low sampling rate data (i.e., $\displaystyle{ \Delta t \geq 30 }$ seconds).

As the cycle-slips can occur in each of both signals independently, two independent combinations must be use to assure that all possible jumps are being taken into account. In this way, the simultaneous use of two independents detectors protects against situations where the combination of $\displaystyle{ \Delta N_1 }$ and $\displaystyle{ \Delta N_2 }$ cycle slips would produce inappreciable jumps in the geometry free combination [footnotes 2].

The second type of detectors' example is based in the Melbourne-Wübbena combination of code and carrier phase measurements [Blewitt, 1990] [1]. This combination cancels not only the non-dispersive effects, but also the ionospheric refraction. Nevertheless, the resulting test signal (i.e., Melbourne-Wübbena combination) is affected by the code multipath, which can reach up to some meters. The impact of this noise is partially reduced by the increased ambiguity spacing of the Wide-lane combination of carrier phases, on one hand, and the noise reduction due to the narrow-lane combination of code measurements, on the other hand (both of them involved in the Melbourne-Wübbena combination). Nevertheless, and in spite of these benefits, its performance is worse than the carrier-phase based detector and it is as a secondary test.

## Notes

1. ^ .The range $\displaystyle{ R }$ varies up to hundreds of meters meters in one second.
2. ^ For instance, with GPS signals, $\displaystyle{ \Delta N_1/\Delta N_2=9/7 }$ or $\displaystyle{ 18/14 }$ or $\displaystyle{ 68/53 }$\dots produces jumps of few millimetres in the geometry free combination. In particular no jump happens when $\displaystyle{ \Delta N_1/\Delta N_2=77/60 }$, but this event produces a jump of $\displaystyle{ 17 \lambda_W \simeq 15 }$ meters in the wide lane combination.

## References

1. ^ [Blewitt, 1990] Blewitt, G., 1990. An automatic editing Algorithms for GPS data. Geophysical Research Letters. 17(3), pp. 199-202.