Algorithm for carrier-adjusted DGPS positioning and some numerical results

This paper derives a DGPS positioning algorithm, referred to as the algorithm for carrier-adjusted DGPS positioning. This algorithm can be applied by a DGPS user when code and carrier observations are available and when the dynamic behaviours of both mobile positions and receiver-clock biases can and cannot be modelled. Since the algorithm directly uses code and carrier observations, the stochastic model of observations has a simple structure and can be easily specified. When the dynamic behaviour of mobile positions can be modelled, the algorithm can provide recursive solutions of the positions, on the other hand, when the behaviour cannot be modelled, it can provide their instantaneous solutions. Furthermore, the algorithm can integrate with a real-time quality-control procedure so that the quality of the position estimates can be guaranteed with a certain probability. Since in the use of the algorithm there always exist redundant observations unless the position parameters are inestimable, the quality control can even be performed when only four satellites are tracked. Using the algorithm and real GPS data collected at a 100-km baseline, this contribution investigates how DGPS positioning accuracies vary with the type of observables used at reference and mobile stations, and how important it is to choose an elevation-dependent standard deviation for code observations in DGPS data reduction. It was found that using carrier observations along with code observations is more important at the reference station than at the mobile station. Choosing an elevation-dependent standard deviation for code observations can result in better positioning accuracy than choosing a constant standard deviation for code observations. For the 100-km baseline, half-metre single-epoch positioning accuracy was achieved when dual-frequency data was used at both reference and mobile stations. The positioning accuracy became better than 0.75m when the types of observable used at the mobile station were replaced by L1 code and carrier. Received: 9 April 1996 / Accepted: 6 February 1997