Integer Ambiguity Resolution for Frequency-Varying Carrier Phase Signals: Theory and Numerical Results

Abstract

The carrier phase signals are considered the key observations in global navigation satellite systems (GNSS) and several other high-precision interferometric measurement systems. Such ultra precise measurements are, however, not fully exploited when the integerness of their ambiguous cycles, the so-called ambiguities, is discarded in the estimation process. Provided that integer-estimable functions of the phase ambiguities are properly identified, integer ambiguity resolution (IAR) can be utilized to benefit the associated parameter solutions. For the GNSS code division multiple access systems whose transmitters broadcast carrier phase signals on identical frequencies, such integer-estimable functions are the well-known double differenced ambiguities. This is, however, not the case with frequency-varying carrier phase signals as broadcast by, e.g., the GLONASS satellites, Low-Earth-Orbiting communication satellites, or cellular long-term evolution transmitters. The present contribution aims to introduce algorithmic tools with which one can identify integer-estimable ambiguity functions, thereby bringing the observation equations of frequency-varying carrier phase measurements into the form to which IAR is applicable. Simulated results demonstrate, depending on the measurements’ precision and the number of epochs involved, that successful ambiguity resolution is possible and beneficial to high-precision parameter estimation even when one works with ‘frequency-varying’ carrier phase data.