7.3.5 Getting Started: Pre- & Initial Processing Steps

DETECTION AND REPAIR OF CYCLE SLIPS

Although triple-difference solutions are tolerant of cycle slips, double-difference solutions cannot tolerate cycle slips (see the Table in section 6.3.7), hence all data must be "cleaned" before reaching this stage of the adjustment.

Cycle slips occur when the continuous tracking of a satellite is interrupted by an obstruction, or the antenna being moved too fast, or faulty signal processing within the receiver, or even when the ionospheric activity is too high (WANNINGER, 1993). They cause the integrated carrier phase count to become "corrupted" once signal lock-on is reacquired on the satellite. Cycle slips generally occur at a receiver tracking a satellite and rarely are there slips on all satellites at the same time. Slips can occur independently on L1 and L2. It is a characteristic of cycle slips that all observations taken after the cycle slip has occurred are shifted by the same integer number of cycles (section 6.2.1).

The detection and repair of cycle slips is therefore an important pre-processing step. It can also be a labour intensive and time consuming process if the data is noisy, has gaps and has many slips on more than one satellite at a time. Automatic procedures are generally used for standard GPS surveying applications addressed by commercial processing software.

Several techniques have been developed to perform this task. Cycle slip detection is easier than its correction, and the difficulty is a function of: the positioning mode, the baseline length, the type of data available, the antenna dynamics, etc., hence the following comments can be made:

• Cycle slip detection/correction of dual-frequency data is easier than for single frequency data (section 6.4.1 and section 8.4.1).
• Cycle slip detection/correction of differenced data is easier than for one-way (undifferenced) phase data, because of the elimination of the clock biases.
• Cycle slip detection/correction of static data is easier than the case of kinematic data.
• Cycle slip detection/correction of short baseline data (<30km) is easier than for long baseline data.
• Cycle slip detection/correction of data in the post-mission mode is easier than for the case of real-time data processing.

All cycle slip procedures are dependent on the (implicit or explicit) analysis of the residual pattern of the data from epoch to epoch. Hence they are dependent on how well the rate-of-change of phase can be predicted from epoch to epoch. Rate-of-change of phase is a function of the rate-of-change of the receiver-satellite geometric range, as well as the other biases. The ease with which the rate-of-change of phase can be predicted is a function of:

• The data collection rate -- the higher the rate (the shorter the time between observations) the easier it is to predict the phase/range change from one epoch to the other.
• How well the errors and biases in the observation model have been accounted for. For example, the atmospheric refraction (particularly the ionosphere in the case of single frequency observations) and multipath, and receiver and/or satellite clock biases -- this is best accomplished through data differencing.
• Whether the GPS receiver is stationary or moving -- the phase "jump" between epochs may be due to antenna motion rather than a cycle slip.
• How good the apriori coordinates of the baseline stations are -- these must be known to the few decimetre level to ensure that cycle slips are not masked by baseline errors.
• The baseline length -- the longer the baseline the more difficult it is to detect cycle slips as they are masked by residual biases due to the decorrelated atmospheric biases, and the impact of orbit errors.

In general, the cycle slip detection methods can be classified as follows, and the various test observables include the single- and double-differenced data, the raw undifferenced phase data, linear combinations of L1 and L2 phase data, and combinations of phase and pseudo-range data:

• Use of a low-order polynomial to fit the time series of the tested observable -- the residual after fitting is screened for the cycle slip. This is the most commonly used method.
• Use of a Kalman filter (section 7.4.1) to forward predict the phase observable -- the difference between the predicted and measured test observable is used for cycle slip detection. Often used with kinematic phase data.
• Use of a first, second, third and even fourth between-epoch differences to highlight any anomalous single epoch slips -- at some level of differencing the resulting values are almost a constant, and any slips are amplified. This is illustrated in Table below.
• Use of a precise pseudo-range data allows the ambiguity to be independently determined at each epoch, at some level of accuracy (section 6.4.1 and section 8.4.1) -- any variation in the value of the ambiguity from epoch to epoch can be construed as a cycle slip. A common strategy for kinematic data and precise static GPS geodesy, as both applications use top-of-the-range receivers able to measure all observables (section 4.3.1).
• Use of dual-frequency phase and/or pseudo-range data to independently determine the ambiguity at each epoch -- any variation in the value of the ambiguity from epoch to epoch can be construed as a cycle slip. This is particularly appropriate for kinematic data where "on-the-fly" ambiguity resolution techniques are used (section 8.3.1).
• Use of external data within an integrated system such as when GPS is combined with an Inertial Navigation System (INS) -- the INS can measure change in position of the antenna very precisely and this can be compared to that implied by the phase measurements. This is particularly appropriate for real-time kinematic airborne GPS applications.
  

First, second and third between-epoch differences.

Single Epoch Observable	First Differences (across two epochs)	Second Differences (across two 1st diffs)	Third Differences (across two 2nd diffs)
ji(e-2) ji(e-1) ji(e) ji(e+1) ji(e+2)	ji(e-2,e-1) ji(e-1,e) ji(e,e+1) ji(e+1,e+2)	2Ii(e-2,e-1,e) 2Ii(e-1,e,e+1) 2Ii(e,e+1,e+2)	3Ii(e-2,e-1,e,e+1) 3Ii(e-1,e,e+1,e+2)

Note that only large cycle slips are likely to show up in the one-way residuals (because of the unpredictable size of the receiver and satellite clock's erratic behaviour), whereas all cycle slips should be visible in the double-differences (see Figure 1a below). Figure 1b illustrates the residuals after between-epoch differencing. Note the "outlier" effect illustrated in the Table in section 6.3.7.

Figure 1. Cycle slip signature in double-differenced phase (a "jump" - (a)) and triple-differenced phase data (an "outlier" - (b)) series.

Cycle slip detection and repair procedures therefore consist essentially of the following steps:

• Identifying a baseline and observable (undifferenced or differenced) to be processed.
• Obtaining good apriori coordinates of the baseline stations using, for example, a cycle slip tolerant triple-difference solution. If a triple-differenced observable is constructed from a phase observation contaminated by a cycle slip it could be detected in the residuals after adjustment, as the large residual (a multiple of the wavelength) would be located at the epoch at which the cycle slip had occurred. It's magnitude may be subsequently determined through an appropriate screening strategy.
• The change in one-way residuals from epoch to epoch can indicate the location of a cycle slip. This change may be modelled by a polynomial or determined from successive between-epoch differences as illustrated in above table . Alternatively, the range-rate estimated from pseudo-range data can be used to repair the "big" slips, leaving the "fine" detection for a subsequent step involving either single- or double-differences.
• Changes in single-difference residuals may then be scanned. Using some criteria, a "jump" in the residuals can be identified and the slip repaired. This step does not usually unambiguously determine the value of the cycle slip at the one cycle level (approximately 20cm).
• Changes in the double-difference residuals are much smoother than in the case of single-differenced or one-way phase data, as all the clock errors have been eliminated. Hence the precise value of the cycle slip can be determined, and the data repaired. Note however that the repair is to the double-difference and not to the particular receiver-satellite observation that was the source of the slip in the first place.
• If dual-frequency data is scanned, the process may be repeated on the L2 observable, or linear combinations of the L1 and L2 observable, as discussed below.

If scanning dual-frequency observations, this process would take place independently on L1 and L2, as well for certain linear combinations of L1 and L2 data (section 6.4.1, section 8.4.1, and HOFMANN-WELLENHOF et al, 1998, for further details). It may also be necessary to screen for "half-cycle" slips on L2 if "squaring" receivers have been used.

The "clean" double-differenced data is now ready for the main processing step.

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© Chris Rizos, SNAP-UNSW, 1999