A Precise Weighting Approach with Application to Combined L1/B1 GPS/BeiDou Positioning

The BeiDou system has been providing a regional navigation service since 27 December 2012. The Global Navigation Satellite System (GNSS) user community will benefit from combined Global Positioning System (GPS)/BeiDou positioning due to improved positioning accuracy, reliability and availability. But to achieve the best positioning solutions, precise weights of the GPS and BeiDou observations are important since this involves the processing of measurements from two different satellite systems with different quality. Currently, a priori variances are typically used to determine the weights of different types of observations. However, such an approach may not be precise since many un-modelled errors are not accounted for. The Helmert variance component estimation method is more appropriate in this case to determine the weights of GPS and BeiDou observations. This requires high redundant observations in order to obtain reliable solutions, which will be a concern in the case of insufficient numbers of visible satellites. To address this issue, a weighting approach is proposed by a combination of the Helmert method and a moving-window average filter. In this approach, the filter is applied to combine all epoch-by-epoch weight estimates within a time window. As a result, more precise and reliable weights for GPS and BeiDou observations can be obtained at every epoch. Both static and kinematic tests in open sky and under tree environments are conducted to assess the performance of the new weighting approach. The results indicate significantly improved positioning accuracy.