Question 5 of 8: The Cycle Slip Phenomenon and Its Consequences

Question 5: The Cycle Slip Phenomenon and Its Consequences (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

What a cycle slip is. A carrier-phase observation consists of two parts: a fractional phase that the receiver measures directly and continuously, and an integer number of whole cycles — the ambiguity \(N\) — that the receiver counts by keeping an unbroken lock on the signal since the start of tracking. A cycle slip is a sudden discontinuity in that integer count: the receiver momentarily loses phase lock and, when it resumes, the accumulated cycle count is off by an integer number of wavelengths, while the fractional phase remains correct. The observation therefore jumps by an integer number of cycles at the instant of the slip and stays biased by that same integer thereafter.

Causes. Cycle slips arise whenever the tracking loop loses the signal, even briefly: obstruction of the line of sight (trees, buildings, bridges, the operator’s body), low signal-to-noise ratio at low elevation, strong ionospheric scintillation, severe multipath, high receiver dynamics, or receiver-firmware failures. They are common in kinematic work through obstructed environments and are the reason continuous tracking cannot always be assumed.

Consequences in data processing. Because the whole precision of carrier-phase positioning depends on the integer ambiguity being a single known constant, an undetected cycle slip is serious:

• The affected phase observations are biased by an integer number of wavelengths (\(\approx 19\) cm per cycle on L1), so the computed baseline/coordinates are wrong — a precise but incorrect result.
• The single constant ambiguity is broken into two unknowns — one before and one after the slip — adding an unknown to the adjustment (in Q6’s bookkeeping, continuous tracking is what kept each ambiguity constant).
• In real-time kinematic work a slip can cause loss of the fixed solution and force re-initialization (re-fixing the ambiguities), interrupting production.

Detection and repair. Slips are detected by testing quantities that should vary smoothly: differences of the phase between epochs (and their higher-order differences), the phase-minus-code combination, the geometry-free (ionospheric) combination \(L_1-L_2\), the Melbourne–Wübbena wide-lane combination, or triple differences (which show a slip as a single outlier epoch). Once located, a slip is repaired by estimating the integer jump \(\Delta N\) and adding it back to all subsequent observations, restoring the single constant ambiguity; if it cannot be repaired reliably, a new ambiguity parameter is introduced from the slip epoch onward.