## 1 Introduction  
Vehicle positioning with global navigation satellite system (GNSS) in urban areas is challenging for the reason that satellite signals often suffer from power attenuation and multipath. As the pilot signal is transmitted with the origin data signal in the new GNSS such as the European Galileo and the modernization of the US Global Positioning System (GPS) [1; 2; 3], the limitation of the coherent integration length brought by the unknown phase inversion no longer exists. As a result, it is possible to further improve the GNSS receiver sensitivity in urban area. However, for the traditional closed-loop tracking approach, the integration length cannot be extensively extended since closed loop is a feedback system and long integration length will break the loop stability. Moreover, it has been verified that lengthening the integration time has little improvement for the sensitivity of the closed-loop tracking [4]. In addition, for multipath mitigation, specially designed methods are also needed. The block processing based open-loop tracking technique has been proposed to efficiently overcome the limitations of the traditional closed-loop sequential tracking technique for GNSS receivers [5]. The basic process of open loop tracking is detailed in [6]. As it is an open-loop system, open-loop signal tracking is absolutely stable and the power accumulation length can be greatly expanded which will tremendously improve the signal receiving sensitivity [7; 8]. Moreover, the sensitivity will be further improved by the introduction of the pilot channel which eliminates the restriction to lengthen the coherent integration length [9]. Additionally, the time-frequency two-dimension correlation result of the open-loop tracking technique makes it convenient to distinguish the line-of-sight (LOS) signal and multipath signal accurately in the harsh urban environments [10; 11]. The open-loop tracking method can also detect and lock the signal quickly since it combines the acquisition and tracking stage. As a result, high dynamic signal tracking and limb scan signal tracking can be achieved by it as well [12; 13; 14]. Hence, the open-loop signal tracking method realized by batch correlators has been applied to vehicle positioning in urban areas [15; 16]. In the method, by lengthening the integration time, the sensitivity is improved so that the weak signal in urban area can be detected. With the help of the time-frequency image, the LOS signal is picked out and multipath is mitigated. In order to further keep the LOS signal peak away from multipath peaks, the strategy to choose the most accurate peak instead of the dominate peak among the correlation results is proposed [17]. In [18], amplitude threshold is used to categorize the LOS signal, multipath and noise to keep the correctness of peak detection. The time to position is shortened by the single stage quickly signal locking. However, including the traditional scheme that computes the correlation results with real correlators and the interpolation based correlation calculation method in [6], the pseudo ranges of all the previously designed open loop methods are measured by discrete code search grids with fixed empirical width. No previous study has focused on the impacts of the grid size on the measurement accuracy of open-loop tracking. In fact, the measuring accuracy is probably distorted by the inapposite grid sizes. If the grid is too small, the LOS signal energy that adjacent search grids contain is close to each other so that the most accurate peak is difficult to be distinguished from its adjacent ones and false peak detection will tremendously destroy the accuracyespecially when signal power is low. While, for large grid size, it is easy to detect the correct peak but the relatively large grid size brings large uncertainty for the measurement estimation. Although early minus late discriminator (EMLD) is introduced to eliminate the uncertainty [8,19], the measurement accuracy will still be highly degraded when signal power decreases.