In GNSS positioning, the cycle slips are the most detrimental for estimating ________.
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Recall that the carrier phase integer ambiguity is defined as a constant whole number of cycles for an unbroken tracking arc, and think about what happens to that count when the receiver briefly loses and reacquires lock.
Step 1: Write the carrier phase observation equation. The carrier phase pseudorange model can be written as $\Phi = \rho + c(dt_r - dt_s) - I + T + \lambda N + \epsilon$, where $\rho$ is the geometric range, $dt_r$ and $dt_s$ are the receiver and satellite clock errors, $I$ and $T$ are the ionospheric and tropospheric delays, $\lambda$ is the carrier wavelength, and $N$ is the integer ambiguity, the unknown whole number of wavelengths present when tracking began.
Step 2: See what a cycle slip changes in this equation. As long as the receiver keeps continuous lock on a satellite, $N$ stays fixed for that entire pass and is estimated once using many epochs of data, later fixed to an integer using methods such as LAMBDA. A cycle slip is an abrupt jump of the tracked cycle count by some integer amount $\Delta N$, so after the slip the observation carries $N + \Delta N$ instead of $N$. Every phase measurement taken after that point is biased by $\lambda \Delta N$, which for the GPS L1 wavelength of about 19 centimeters can amount to tens of centimeters or several meters even for a small slip of one or two cycles.
Step 3: Compare with the other listed error sources. Receiver clock error $dt_r$ is common to all satellites in view and is solved for directly as one extra unknown in the position solution, it never disturbs $N$. Multipath adds a bounded, non integer, slowly time varying bias of a few centimeters at most on phase data, again leaving $N$ untouched. The delay terms $I$ and $T$ vary smoothly with satellite elevation and atmospheric state and are modeled or estimated as continuous quantities, they never appear as a discrete jump in cycle count. Only a cycle slip changes the integer term $N$ itself in a discontinuous way.
Step 4: Consequence for the position solution. Since centimeter level GNSS positioning is achievable only once $N$ is correctly fixed, an undetected slip either forces the ambiguity resolution process to restart or produces a position error equal to the slip size times the wavelength, until the slip is flagged using detection techniques such as the Melbourne-Wubbena combination or a phase versus code comparison, and the ambiguity is re-estimated. This makes the cycle slip the error type that most severely affects estimation of the integer ambiguity.
