## 1 Introduction  
With precise satellite orbit and clock corrections, precise point positioning (PPP) can provide decimeter- to centimeter-level kinematic positioning results directly referenced to the global reference frame. Such positioning does not require a dense reference network and has proven to be a powerful tool in a number of applications, such as those pertaining to geophysics and meteorology [1; 2]. Integer carrier-phase ambiguity resolution (IAR) is important to shorten the initialization time and improve the precision of traditional PPP. In contrast to relative positioning, because only one receiver is involved in PPP, the uncalibrated phase delay (UPD) will be absorbed by the ambiguity estimates, which makes it impossible to fix the ambiguities to integers [3]. UPDs must therefore be separated from precise satellite clock products and applied in PPP to fix the ambiguities. [PERSON] et al. [4] proposed a phase-only method for PPP-IAR. [PERSON] et al. [5] estimated the single-difference between-receiver wide-lane (WL) and narrow-lane (NL) frequency code biases (FCBs), achieving PPP-IAR over a global network. Later, [PERSON] et al. [6] and [PERSON] et al. [7] used satellite clock estimates to absorb the un-differenced (UD) NL FCBs. In contrast, [PERSON] et al. [8] delivered all UD ambiguity estimates that contain the FCBs to users for PPP ambiguity resolution. The traditional PPP model requires a few tens of minutes to get the first ambiguity-fixed solution [9]. In Network Real-Time Kinematic (NRTK) positioning, because atmospheric delays can be modeled precisely, rapid ambiguity resolution can be achieved. [PERSON] et al. [10] showed that if one uses precise atmospheric delays to augment PPP IAR,instantaneous PPP IAR can be also achieved. Even for Galileo and BeiDou, which do not have complete constellations, initial results of PPP-IAR have already been obtained, in [11; 12]. Additionally, [PERSON] et al. [13] showed that using GPS + BeiDou can significantly improve the fixing percentage of GPS-only PPP. Meanwhile, Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS), which was declared fully operational globally with 24 satellites at the end of 2011, still faces obstacles to realizing PPP-IAR, owing to its frequency-division-multiple-access signals. Currently, the 24-satellite constellation of GLONASS uses 14 frequency channels, and only satellites at antipodal slots of an orbital plane can share the same frequency. Commonly tracked GLONASS satellites thus have slightly different frequencies, which produces both inter-frequency code bias (IFCB) and inter-frequency phase bias (IFPB) [14; 15; 16]. Generally, GLONASS IFPB is a linear function of frequency, which can be calibrated with the model given in [16] or estimated in real time [17]. The IFCB behaves abnormally, varying not only with receiver type but also possibly antennas, domes, and firmware. Currently, there is no general model to correct IFCB [18; 19; 20; 21; 15]. Although IFCBs have little effect on short-baseline differential ambiguity resolution [16; 20; 22], they totally undermine ambiguity resolution in PPP, because PPP relies on the Hatch-Melbourne-Wubbena (HMW) combination [23; 24; 25] of code and carrier phase observations to resolve WL ambiguity. The presence of IFCB results in a biased WL ambiguity estimation, thereby causing PPP ambiguity resolution to fail. [PERSON] et al. [26] used a network of homogeneous receivers to perform GLONASS UPD estimation and PPP-IAR, obtaining a preliminary result for GLONASS-only static PPP. [PERSON] [27] formed an ionosphere-free combination with wavelength \(\sim\)5 cm for GLONASS PPP ambiguity resolution. However, very limited improvements were achieved in shortening the initialization time for kinematic PPP-IAR, owing to the relatively short wavelength. [PERSON] and [PERSON] [15] proposed the use of a precise ionospheric model to directly fix WL ambiguity with the WL combination of L1 and L2 carrier-phase observations.