Extra-wide-lane real-time kinematic (ERTK) is a technique that makes full use of extra-wide-lane (EWL) observations to realize instantaneous precise positioning. Beyond the previous study by using triple-frequency signals, the hexa- and penta-frequency signals, referred to as hyper-frequency signals in this study, are currently available for Beidou-3 and Galileo systems, respectively, which will be definitely beneficial to ERTK. In this study, the advantages and performance of hyper-frequency ERTK (HERTK) are profoundly addressed. The mathematical model of generalized HERTK is deduced with canonical formulae to show how model parameters profit from additional signals and high-precision EWL/WL observations. Specifically, the optimal linear combinations of hyper-frequency signals are determined in terms of ionosphere-weighted and ionosphere-float models. The precision gains of both position and ambiguity parameters are numerically demonstrated for single- and multi-epoch, accompanied by a comprehensible explanation of the hyper-frequency enhancement mechanism. The performance of HERTK is evaluated with three long baselines from 248.4 to 511.0 km. The results show that the HERTK achieves instantaneous decimeter-level solutions without the need for complicated narrow-lane (NL) ambiguity resolution (AR). Furthermore, centimeter HERTK can be realized by only accumulating NL phase data over approximately 20 epochs, which essentially leverages the more precise between-epoch information to smooth the noisy solutions. Besides the smoothed positions, the precision of NL ambiguity is also significantly improved, thus enabling rapid and reliable NL AR for long baselines. Higher accuracy of 1–2 cm solutions is achieved within 10–30 epochs.
Li et al. (2026) studied this question.