Cycle Slip Detection in Observations Using Dual-Frequency Combination

In GNSS (Global Navigation Satellite System) data processing, cycle slips are integer cycle count discontinuities that occur in carrier phase observations. Cycle slips significantly impact positioning accuracy and therefore require effective detection and repair. The dual-frequency combination method is a common approach for cycle slip detection, which utilizes combinations of carrier phase observations from two different frequencies to amplify the effects of cycle slips, making them easier to identify.

### Principles of Dual-Frequency Combination Observations Dual-frequency GNSS receivers can simultaneously receive signals from both L1 and L2 frequency bands, with their carrier phase observations denoted as φ₁ and φ₂ respectively. Since signals at different frequencies experience different ionospheric delays during propagation, we can construct specific linear combinations, such as wide-lane combinations or geometry-free combinations, to amplify the impact of cycle slips.

Wide-Lane Combination The wide-lane combination forms a new observable through linear combination of φ₁ and φ₂, resulting in a longer wavelength (approximately 86 cm), making cycle slips easier to detect. The formula is: [ phi_{text{w}} = phi_1 - phi_2 ] If a cycle slip occurs, the variation in the wide-lane combination will be significantly larger than normal observation fluctuations.

Geometry-Free Combination This combination eliminates geometric distance effects between satellites and receivers, preserving only ionospheric delay and noise terms, and can be used for cycle slip detection: [ phi_{text{gf}} = phi_1 - frac{f_1}{f_2} phi_2 ] Since ionospheric delays typically change slowly, abrupt changes in observations often indicate cycle slips.

### MATLAB Implementation Approach The general steps for implementing dual-frequency cycle slip detection in MATLAB include:

Data Preprocessing Read GNSS observation data files (such as RINEX format), extract carrier phase observations φ₁ and φ₂ from L1 and L2 frequency bands, and perform necessary quality control (e.g., removing invalid data). This can be implemented using MATLAB's file reading functions and data filtering techniques.

Combination Observation Calculation Compute time series for wide-lane or geometry-free combinations, and perform differencing operations (such as epoch-to-epoch differencing) to amplify cycle slip effects. Key MATLAB functions include array operations for combination calculations and diff() for differencing.

Cycle Slip Detection Threshold Method: Set appropriate thresholds - if the differenced combination observations exceed the threshold, a cycle slip is detected. Implementation requires logical indexing and threshold comparison operations. Polynomial Fitting Method: Use low-order polynomial fitting on combination observations - epochs with excessive residuals may indicate cycle slips. This can be implemented using polyfit() and polyval() functions. Sliding Window Statistical Method: Calculate mean and standard deviation within a sliding window - points outside certain confidence intervals are marked as cycle slips. MATLAB's movmean() and movstd() functions are useful here.

Result Visualization Plot combination observations and their difference sequences, and highlight detected cycle slip points using markers or other visualization techniques. MATLAB's plotting functions like plot(), scatter(), and annotation tools are essential for this step.

### Experimental Data Validation Validate algorithm effectiveness using actual observation data (such as static or dynamic GNSS data), analyze detection sensitivity of different combination methods, and compare applicability of different threshold or statistical methods. MATLAB's data analysis工具箱 provides robust tools for statistical validation.

### Extended Considerations How to optimize cycle slip detection performance in high-dynamic environments or low signal-to-noise ratio conditions using dual-frequency combination methods? Can integration with other methods (such as Doppler integration, signal strength) improve cycle slip detection reliability? How to combine detected cycle slips with repair methods (such as ambiguity reinitialization)?

Implementing dual-frequency cycle slip detection in MATLAB enables intuitive validation of algorithm feasibility and provides reliable data preprocessing support for high-precision GNSS positioning applications. The implementation typically involves creating modular functions for each processing step and developing a comprehensive testing framework.