Sect_6.2.11

6.2.11 Measurement Biases and Errors

CARRIER PHASE CYCLE SLIPS

Signal reception by a GPS receiver can be interrupted by: (a) the shadowing, or large acceleration of the antenna, both are particularly a problem in the case of kinematic positioning; or (b) during a severe signal disturbance such as due to ionospheric activity and multipath interference; or (c) low signal-to-noise ratio. After the signal tracking interruption, the ambiguity n_jⁱ has a different value than before.

How is the measurement affected? As indicated in Figure 1 below, the integrated carrier phase measurement at time T_j involving satellite i and receiver j consists of the three components:

The fraction of a cycle, for example 0.25cyc (0.0475m on L1), denoted by _fjⁱ(T_j) in eqn (6.2-17).
The arbitrarily assigned integer ambiguity at signal lock-on, for example 106000000cyc, denoted by n_jⁱ in eqn (6.2-17).
A count of the whole cycles by the receiver, for example 1000cyc, denoted by C_R(T_j) in eqn (6.2-17).

Figure 1. Components of the integrated carrier phase measurement.

Following a loss-of-lock, on resumption of tracking to the satellite, the accurate fractional part of the carrier phase can be measured again, however, the integer part ( n_jⁱ + C_R(T_j) ) will no longer provide the correction to the fractional phase measurement that yields the true satellite-receiver range. In essence, the "zero-crossing" measurement of C_R(T_j) has not "kept up" with the actual change in satellite-receiver range. Therefore, to account for this "jump" in the integrated carrier phase in the interval between the epoch before loss-of-lock, and when the signal is again acquired (Figure 2 below), the unknown ambiguity term must be assigned a new value n_j^i* (= n_jⁱ + S(T_e) ) in the mathematical model (eqn (6.2-17)). The term S(Te) is a cycle slip that has occurred at epoch T_e (the epoch when signal tracking resumed), and is a constant additional term that affects all observations after epoch T_e (Figure 2).

Figure 2. A "jump" the sequence of carrier phase measurements due to the occurrence of a cycle slip.

In practice, cycle slips are usually detected and repaired in a data pre-processing step (section 7.3.5). Many techniques have been developed to perform this task dependent such things as: the positioning mode being used, the baseline length, the type of data available, the antenna dynamics, etc. The following comments can be made regarding this process:

Cycle slip detection is easier than its correction, especially if the slip is "large" (say, greater than about 10 cycles).
However, cycle slip correction involves the determination of the exact number of slipped carrier cycles at epoch T_e. This is very difficult in one-way carrier phase observations because of the presence of biases, in particular the clock biases.
Cycle slip correction is easier when the clock biases have been eliminated during between-receiver and/or between-satellite differencing (section 6.3.2).
Cycle slip correction of dual-frequency data is easier than for single frequency data.
Cycle slip correction of static data is easier than the case of kinematic data.
Cycle slip correction of data in the post-mission mode is easier than for the case of real-time data processing.

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