## 1 Introduction
The trade-off between the quality of performances and the complexity of calculations needs to be seriously concerned. Solving WGDOP algorithm in a short time is critical for real-time applications. Good measurements, as well as WGDOP algorithm, are key factors that determine the characteristics of wireless positioning systems. When the measurements have different error variances or come from integrated positioning systems, the WGDOP minimum criterion can be used to select the appropriate measurement units to reduce the positioning error. This can present challenges to real time practical applications. The WGDOP calculation using the matrix inversion method is a time and power consuming procedure, and fast calculation of WGDOP is most concerned. WGDOP decreases as the number of satellites increases. Thus, the all-in-view method is adopted by reference [16] and the optimal WGDOP value was obtained through computing all-in-view satellites. With the development of electronics technology, receivers can track many satellites simultaneously and use all the visible satellites to position to improve the accuracy. If the processing capability of the receiver is powerful and the number of visible satellites is not large, the all-in-view method is a good choice to improve the positioning accuracy. However, it takes a considerable computation time. There will be 70-90 satellites in the sky at the same time when Glonass and Galileo reach full operation capability [26], and the visible satellite number can reach 30 in any moment. It thus will become very difficult for people to use the all-in-view procedure for location estimation in the future. Nowadays, due to the vibrant developments of GPS embedded systems, most smart phones and other wearable electronic devices are already equipped with GPS. Despite the performance increases, these devices still possess limited battery capacities and fast calculation capability. Since the battery life and the processing delay are the main limitations on the performance of mobile phones, GPS service should be provided under the condition of high processing ability and low power dissipation. Hence, for the location-estimating applications, how to derive WGDOP efficiently from a large of measurements sent from different satellites is a critical challenge. Due to the limited resources associated with many mobile devices and the very large number of visible satellites, selecting the desired data from a limited number of suitable satellites is a possible solution [26]. Interpreting the original and complicated WGDOP algorithm as a set of simple approximations greatly reduces the computational complexity. By restricting the scale of measurements, the mobile phones can not only reduce the processor load, but also effectively increase the charged period of batteries. Furthermore, the saved memory space can be used to run other programs. This paper considers all positioning systems, that is WGDOP can select any suitable measurement units, such as satellites, BSs, or wireless sensors. A smaller WGDOP value is obtained with more usable measurement units. In [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], the authors focus on improving the GPS positioning accuracy by WGDOP concepts. Selecting four from 30 satellites would give 27,405 possible subsets. The conventional method for calculating WGDOP is to use the matrix inversion method, which requires a large amount of computation. In order to avoid complicated matrix inversion operations, we presented a novel architecture based on resilient back-propagation (Rprop) to obtain the approximate WGDOP for location estimation in [27]. However, machine learning techniques require computational resources to train a model, which needs troublesome processes and consumes more time. Furthermore, machine learning techniques offer only approximations to the target values. This method suffers from the approximation error and inaccuracy incurred by approximating the inverse matrix in calculating WGDOP.