Assessment of Measuring Orthometric Height With Multi-GNSS Undifferenced Time–Frequency Signals

Abstract

The traditional approach to measuring orthometric height has numerous limitations. It suffers from error accumulation, involves time-consuming and labor-intensive procedures, exhibits low efficiency, and faces challenges in cross-sea transfers. In contrast, by exploiting the principle of general relativity, using precision global navigation satellite system (GNSS) time-frequency signals for orthometric height determination can surmount these problems. This research employs the multi-GNSS undifferenced carrier phase time-frequency signal for orthometric height determination and constructs a model for undifferenced multi-GNSS carrier phase time-frequency comparison to determine orthometric height and transfer. Moreover, the study delves into simulation methods for precise clock offsets and multi-GNSS observations. Simulation experiments between China and USA are conducted to verify GNSS time-frequency signals’ efficacy in cross-sea orthometric height transfer. The experimental results indicate that the frequency stability of multi-GNSS undifferenced time-frequency comparisons can reach approximately $2\times 10^{-{17}}$ , with the bias and uncertainty of orthometric height transfer about 2.0 cm and 0.2 m, respectively. Considering the accuracy of multi-GNSS carrier phase observations and the cost of improving clock performance, a clock with frequency stability around sub- $10^{-{17}}$ offers significant advantages for multi-GNSS time-frequency signals in orthometric height transfer. As clock performance improves and miniaturization trends continue, the accuracy of multi-GNSS time-frequency signals for determining orthometric height is expected to reach centimeter or even millimeter levels, further advancing the accurate unification of the global vertical height datum.