An Efficient UD Factorization Implementation of Kalman Filter for RTK Based on Equivalent Principle

Real-time kinematic (RTK) is a technique frequently utilized to provide real-time highly precise positioning services for mobile Internet-of-Things (IoT)-embedded terminals from intelligence appliances and smartphones to autonomous drones and self-driving vehicles. To fully utilize hardware resources, the internal GNSS chips or modules equipped in IoT terminals should satisfy the traits of energy efficiency and low computational complexity. As the number of global navigation satellite system (GNSS) increases, the continuous accumulation of high-dimensional rounding errors, the rough system model, and seriously distorted observations will result in divergence and considerable processing burden in the conventional Kalman filter (KF) process. Computational efficiency is significant in the reduction in the power consumption and intensifies the positioning performance of GNSS receivers. Here, a new filter strategy based on UD factorization, where U stands for the unit upper-triangular factor and D indicates the diagonal factor, is proposed for RTK positioning to enhance the numerical stability and reduce the computational effort. The equivalent principle was applied to turn double-difference (DD) observations into zero-difference (ZD) observations. Then, the UD-factorization-based Kalman filter (UD-KF) is proposed as a way to sequentially provide accurate real-time estimations of the filter states and variance-covariance (VC) matrix. Both static and dynamic tests were carried out with single-frequency data from a GPS to evaluate the performance of UD-KF. The results of the zero-baseline test show that UD-KF can obtain smaller RMS of the estimated parameters as the noise of DD observations was twice that of the ZD observations. A short baseline test showed that, compared to the regular filter approach with DD observations, UD-KF achieved a shorter computation time with a higher data utilization rate for both filtering and fixing stages, with an average improvement of 32% and 18%. Finally, a dynamic test showed that the UD-KF can avoid the undesirable effect of satellite changes. Therefore, compared to KF with DD observations, the UD-KF with equivalent ZD observations can enhance the robustness as well as improve the positioning accuracy of RTK positioning.