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Abstract

Single-frequency precise point positioning (SFPPP) is widely applied in the engineering field due to its low cost and portability, among which the extended Kalman filter (EKF) is commonly used to obtain final results. However, single-frequency observation is vulnerable to various errors. On the one hand, the state parameter weight matrix will be ill-conditioned due to large process noise and initial variance of the estimated parameters. On the other hand, the observation weight matrixis also ill-conditioned since the noise of pseudorange observations is much higher than that of phase observations. In addition, the condition number of normal matrix will jump in case of cycle slip, new emerging satellite, and signal outage. To reduce the condition number of normal matrix, a regularized Kalman filter (RKF) algorithm using support for maximum variance is proposed. Through experiments of dynamic and static observation data, it is found that the convergence time will be shortened and the accuracy will be improved by RKF. Compared with the SFPPP using EKF, static positioning accuracy with centimeter-level (1.4, 0.9, 3.5) cm and kinematic positioning accuracy with decimeter-level (15.7, 12.4, 31.8) cm could can be achieved for the east, north, and up components, with an improvement of （33%, 35%, 43%） and (35%, 37%, 24%), respectively, in the static and kinematic scenarios. The analyses provided new insight into the caculation of SFPPP by proposing and verifying the ill-conditioned normal matrix of SFPPP by EKF as well as demonstrated the suitability of the RKF method for this purpose.