Generalized damped LAMBDA method and the application in long baseline real-time positioning

In long baseline real-time positioning, strong correlation between adjacent observations resulting in ill-conditioned normal equation which is adverse to fast integer solution of carrier phase ambiguity. In this contribution, a generalized damped least-squares ambiguity decorrelation adjustment (LAMBDA) method was be proposed based on traditional LAMBDA method and the solution expression for carrier phase ambiguity in single epoch also be derived. This method uses the prior information of coordinates and carrier phase ambiguity to improve the ill-condition of the normal equation and the solution accuracy of floating ambiguity, which is helpful for the fast integer ambiguity solution. Two long baselines (266 km and 456 km) measured data were used to verify. Compared with the traditional method, the ambiguity fixed rate of the improved method was increased by 28.8%. When the amplification factor c=0, the generalized damped LAMBDA method was equivalent to the traditional damped LAMBDA method. Four long baseline real-time data streams from the Australian continuous operation reference system (CORS) network were selected for testing. The experimental results show that multi-system real-time positioning accuracy was better than 2 cm in the horizontal direction and 4 cm in the elevation direction with a baseline length of less than 1 000 km. The generalized damped LAMBDA method has certain application reference value for long baseline real-time positioning.