## 1 Introduction  
With the rapid development of Global Navigation Satellite System (GNSS), real-time precise point positioning (RT PPP) with integer ambiguities resolution is possible thanks to the real-time precise orbits, clocks, and code/phase biases products of satellites, provided freely by the Center National d'Etudes Spatiales (CNES) [1]. These real-time products in the CLK93/CLK92 stream have been broadcasted by the CNES real-time analysis center since 14/09/2014 [2]. Based on these products, the integer property of user ambiguities can be recovered to improve positioning accuracy and reliability. However, ambiguities and other parameters (e.g., tropospheric delay) need a few hours to achieve the proper convergence, even with good satellite geometries and observation quality [3]. Therefore, how to reduce the RT PPP convergence time has become one of the key issues for further improving RT PPP performance [4]. Three different methods have been proposed to reduce the convergence time in RT PPP. One is to fix ambiguity parameters to integer values. Many researchers have demonstrated that ambiguity resolution can improve the PPP in terms of both precision and convergence performance [5; 6; 7]. The second method is to utilize multi-frequency and/or other GNSS constellation observations [8; 9; 10]. With the application of observations from multi-frequency or other satellite positioning systems, the PPP convergence time can be reduced due to high measurement redundancy and improved degrees of freedom [11]. The third method is to apply RT ionospheric or tropospheric correction products [7; 12; 13]. Accuracy better than 10 cm can be achieved in a few minutes with dual-frequency signals by using precise ionospheric and tropospheric correction products [13]. Compared to the other two methods, ionospheric products are the more effective in terms of reducing the convergence time [14]. Thanks to the standardized RT message of Vertical Total Electron Content (VTEC) models in CLK93/CLK92 stream from CNES [15], the convergence time of RT PPP can be reduced significantly by using an uncombined functional model with RT ionospheric correction products [3]. When RT ionospheric products are applied as an extra constraint in the RT PPP, proper and precise variances of the raw observations and ionospheric constraint are important as they involve the processing of measurements of different types whose quality is different in terms of residual errors. Currently, a priori variances are mainly used to determine the weights of observation and ionospheric constraint in the whole process of data processing. However, this method may not be precise, especially when the accuracy of ionospheric products is uncertain, and it will lead to unreliable positioning results. To address this issue, a weighting approach is proposed by combining a weight factor searching algorithm with a moving-window average filter. Weight factors are utilized to adjust the priori variances of ionospheric constraint and the moving-window average filter is introduced to improve the precision and reliability of the weight factors. In this paper, we adopt this method in the Precise Point Positioning With Integer and Zero-difference Ambiguity Resolution Demonstrator (PPP-WIZARD) by the CNES. Both static and kinematic experiments in single-frequency and dual-frequency cases are conducted to assess the performance of the new weighting approach. The results indicate that this new method can significantly reduce convergence time and improve reliability of positioning solutions in RT PPP. The rest of the paper is organized as follows: Firstly, the uncombined functional model with ionospheric constraint for GPS/GALILEO RT PPP is presented. Secondly, the RT ionospheric products from CNES are compared with post-processing GIM (global ionospheric map) products from CODE (Center for Orbit Determination in Europe) agencies. Afterwards, the weight factors searching algorithm with a moving-window average filter is proposed.