A Study on GPS/GLONASS Multiple Reference Station Techniques for Precise Real-Time Carrier Phase-Based Positioning

Real-time high precision GPS/GLONASS surveying and navigation applications have been constrained to the short-range case due to the presence of distancedependent biases in the between-receiver singledifferenced observables. Over the past few years, the use of a GPS/GLONASS reference station network approach, to extend the inter-receiver distances (user-to-reference receiver separation), has shown great promise. In order to account for the distance-dependent residual biases, such as the atmospheric biases and orbit errors, several techniques have been developed. They include the Linear Combination Model, Distance-Based Linear Interpolation Method, Linear Interpolation Method, Lower-Order Surface Model, and Least–Squares Collocation. All of these methods aim to model (or interpolate) the distancedependent biases between the base station(s) and the user receiver with the support of a multiple reference station network. In this paper, the interpolation methods related to these techniques are reviewed in detail. The advantages and disadvantages of each of these techniques are discussed. On an epoch-by-epoch and satellite-by-satellite basis, all of the abovementioned methods use a n-1 independent error vector generated from a n reference station network to model the distance-dependent biases at the user station. General formulas for all of the methods involve the computation of the n-1 coefficients first, and then form a n-1 linear combination with a n-1 error vector from the reference stations to mitigate the spatially correlated errors for the user station(s). Test data from GPS reference stations was used to evaluate the performance of the proposed methods. The numerical results show that all of the proposed implementations of the multiple reference station approach can significantly reduce the distance-dependent biases associated with carrier phase and pseudo-range measurements at the GPS user station. The performance of all the methods is similar. INTRODUCTION Over the past few years, the concept of using reference station networks for real-time kinematic GPS positioning has been promoted strongly by several investigator groups. The basic idea is that, with the pre-determined coordinates of reference stations and fixed GPS carrier phase ambiguities, the so-called 'correction terms' for the atmopsheric biases and orbit errors can be generated to support carrier phase-based medium RTK positioning. See, for example, Gao et al. (1997), Han & Rizos (1996); Raquet (1997); Wanninger (1995); Wubbena et al. (1996). A detailed review of the various multi-reference station network approachs can be found in Fotopoulos & Cannon (2001). After the double-differenced ambiguities associated with the reference receivers have been fixed to their correct values (for more details concerning this issue see, e.g. Gao et al., 1997; Schaer et al., 1999; Colombo et al., 1999; Chen et al., 2000; Dai et al., 2001a), the doubledifferenced GPS/GLONASS residuals can be generated. The spatially correlated errors to be interpolated could be the pseudo-range and carrier phase residuals for the L1, L2 frequencies, or other linear combinations. One core issue for multi-reference techniques is how to interpolate the distance-dependent biases generated from the network for the user's location? Over the past few years, in order to interpolate (or model) the distancedependent residual biases, several interpolation methods have been proposed. They include Linear Combination Model (Han & Rizos, 1996; 1997), Distance-Based Linear Interpolation Method (Gao et. al, 1997; 1998), Linear Interpolation Method (Wanniger, 1995; Wübbena et al., 1996), Lower-Order Surface Model (Wübbena et al., 1996; Fotopoulos & Cannon, 2000), and Least– Squares Collocation (Raquet, 1997; Marel, 1998). It should be emphasized that the Virtual Reference Station (VRS) method is an implementation of the multipel reference station approach, and all of the aforementioned interpolation methods can be applied. In this paper, the aforementioned interpolation methods are reviewed in detail. The advantages and disadvantages of each of these techniques are discussed. An underlying common formula for all of the interpolation methods has been identified. Their performances will be demonstrated through case study examples of GPS (and GLONASS) reference station networks. EXISTING INTERPOLATION METHODS Linear Combination Model (LCM) A linear combination of single-differenced observations was proposed by Han & Rizos (1996, 1997) to model the spatially correlated biases (i.e. orbit bias ∆dρ i , ionospheric bias i ion d , ∆ and tropospheric bias i trop d , ∆ ), and to mitigate multipath φ i mp d , ∆ and noise ∑ ∆ ⋅ = n