A Cascading Approach for Multi-Frequency Widelanes and Extra-Widelanes Carrier Phase Integer Ambiguity Resolution

Precise Point Positioning (PPP) in Global Navigation Satellite Systems (GNSS) relies on the resolution of carrier phase ambiguities to achieve high-precision positioning. Usually, ambiguity resolution has relied on widelane or Melbourne-Wübbena combinations of two frequencies. However, with the development of new generation satellite constellations and the advent of multi-frequency GNSS signals, the potential for utilizing more than two signals in ambiguity resolution has emerged. Studies have explored this potential using various systems such as GPS, Beidou, and Galileo, which employ up to four frequencies. Despite their benefits, ionosphere-free integer phase combinations often suffer from large noise amplification factors or result in small wavelengths. Conversely, traditional widelane combinations, while maintaining a reasonable noise amplification factor, tend to amplify ionospheric delays, which can be difficult to estimate with the necessary precision. In this paper, we propose a novel method that optimizes the use of code, carrier-phase and Doppler measurement at multiple frequencies to enhance ambiguity resolution in PPP. Our approach mitigates the limitations of existing combinations by balancing noise amplification and ionospheric delay effects; and allows instantaneous extra-widelanes fixation, and very fast widelanes fixations.