# Statistical Multipath Model Based on Experimental GNSS Data in Static Urban Canyon Environment
## 1 Introduction  
The high-precision differential technique of global navigation satellite system (GNSS) has prompted the development of applications such as unmanned aerial vehicles (UAVs), autonomous land vehicle driving, and precise farming. The differential positioning technique can remove most of the errors, such as satellite ephemeris and clock, ionosphere, and troposphere, by using spatial or temporal correlations between the mobile receiver and the reference station. However, multipath is an exceptional interference because of its dependency on specific environments. Unfortunately, there is no method that can solve the multipath problem completely, especially in a severe multipath environment, such as an urban canyon area. Therefore, multipath is the last major error source that may prevent high accuracy in some circumstances. An important multipath error elimination strategy is to design a suitable filtering according to multipath statistical features [1]. A similar example is the application of a mobile correspondence satellite, for which a land mobile channel model has been fully studied [2; 3]. Research on the GNSS signal's multipath statistical model is also necessary and important. However, there are a few reasons that make establishing the GNSS multipath models difficult. First, the GNSS signal is extremely weak when it arrives at the surface of the earth, which makes the reception and the analysis of the multipath more difficult. Second, the blend of the multipath signal and the line-of-sight (LOS) signal makes it more difficult to separate each component ray, especially when we are more interested in the near multipath, which lies within the one-chip extension. Third, the variety of application environmentsmakes studying the multipath channel more difficult. Therefore, it is not easy to make significant progress in a short time. Over the past several decades, researchers worldwide have made much progress in characterizing multipath signals. Normally, the study methods can be divided into two types. One type of method uses a ray tracing technique to precisely calculate all possible multipath signals for a specific environment. This type is very suitable for studying multipath characteristics under specific carriers, such as fighter and warship, since the 3-dimensional structure model of carriers can be built relatively precise [4]. The ray tracing technique is also proposed to study the code phase and carrier phase characteristics of multipath propagation, and the accuracy of the method is verified by real data [5; 6]. Some algorithms are proposed to improve the positioning performance by using a 3D model [7]. However, it is very difficult to build a precise 3D model for a large-scale environment and use the ray tracing method, without even mentioning the many computations required. The practical applications of these approaches have many limitations, such as the fact that the surrounds need to be kept static. Thus, there is a need for new approaches to be proposed. Another type of method uses signal estimations on sampled real multipath signals to directly study the characteristics of multipath parameters for interested environments. Since multipath code error is periodic for the static receiver, the error model is often used to mitigate the multipath error of pseudorange [8; 9]. These research studies only consider the estimation error of the delay lock loop, which is caused by the static reflectors [10]. However, it is more important to analyze the detailed characteristics of a multipath caused by the environment, such as time delay, power attenuation, and fading frequency. To solve this problem, some theoretical models have been proposed to characterize near-surface reflectometry [11; 12]. In addition, the German Aerospace Center (DLR) group emits impulse signals from a Zeppelin in different environments, and the impulse response data are sampled and recorded for analysis by multipath channel modelling [13].