## 1 Introduction  
Global Navigation Satellite Systems (GNSSs) have been extensively adopted to provide accurate and continuous positioning, navigation and timing (PNT) services on a global scale. Among GNSSs,China's BeiDou Navigation Satellite System (BDS) has achieved its regional coverage and it has been providing PNT services over China and its surrounding areas since the end of 2012 [1,2]. The regional BDS constellation is comprised of five geo-stationary Earth orbit (GEO) satellites, five inclined geosynchronous orbit (IGSO) satellites and four medium Earth orbit (MEO) satellites and will evolve into a constellation with 5 GEOs + 3 IGSOs + 27 MEOs by 2020 to realize its global service [3,4]. A GNSS receiver senses the carrier's position information, whose precision can be significantly improved with a multitude of carrier phase based techniques among which the real time kinematic (RTK) algorithm is known for its real-time and high-precision features. Compared with single point positioning using only pseudorange measurements, RTK utilizes the signal carrier phase information which is more precise than the pseudorandom code measurements and has the potential to diminish the position error to centimeter level [5]. Another feature is its use of real-time broadcast satellite navigation messages other than post-processed precise ephemeris products frequently adopted in non-real-time applications including relative static positioning that requires higher precision and precise point positioning (PPP). However, RTK requires a higher quality and a larger number of received navigation signals than pseudorange-based positioning methods to guarantee its high-precision and continuous performance which limits its availability and reliability. With the combination of GPS and BDS, the number of satellites available for users is increased, which has a potential to improve the positioning precision and availability for RTK. Motivated by the fast development of BDS, recent research works have begun to study the feasibility and methods to exploit the ability of BDS for real time high-precision positioning. The contribution in [6] utilized simulated single-epoch measurements to evaluate the RTK performance on BDS multi-frequency signals. The raw measurement characteristics are analyzed and the single point and short baseline relative positioning results were demonstrated in [7]. Another study in [8] focused on the measurement quality of BDS GEO and IGSO satellites and compared the single point and relative positioning performance between BDS and GPS. The research of [9] illustrated the RTK performance improvement of a combination of BDS and GPS over a single system with a single-epoch ambiguity resolution method. Work in [10] analyzed the single-baseline observation model and assessed the relative positioning performance of GPS+BDS with also a single-epoch ambiguity resolution. In this work, we first analyze the measurement model of double-differenced (DD) carrier phases and pseudoranges based on which a Kalman filtering model that utilizes previous and current measurement information to estimate the carrier phase float ambiguities is proposed. This model can process carrier phase and pseudorange measurements from a sole constellation of BDS or GPS. We adapt the original model to the dual-constellation case and use measurements from both systems as input to the Kalman filter to estimate all float ambiguities and their variances, and then we resolve the integer ambiguities of the two constellations simultaneously. Due to the larger number of visible satellites than either single constellation, this combined method has the potential to increase the availability of RTK. We also propose an implementation scheme with details including filter parameter setting, satellite rising/setting handling, baseline resolution, _etc._, which is rarely found in previous literature, and realize it with Matlab code to process the double-differenced measurements from the two systems with different signal frequencies and time frames.