Design of kinematic DGNSS filters with consistent error covariance information

Consistent and realistic error covariance information is important for position estimation, error analysis, fault detection, and integer ambiguity resolution for the applications of global navigation satellite systems. In designing a position domain carrier-smoothed-code filter where incremental carrier-phases are used for time-propagation, formulation of consistent error covariance information is not easy due to correlation of successive propagation noises. To provide consistent and correct error covariance information, two recursive filter algorithms are proposed based on carrier-smoothed-code techniques: the stepwise optimal position projection filter, and the stepwise unbiased position projection filter. A Monte Carlo simulation result shows that the proposed filter algorithms actually generate consistent error covariance information and the neglecting of carrier-phase noise induces optimistic error covariance information. It is also shown that the stepwise unbiased position projection filter is attractive since its performance is good and its computational burden is moderate.