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Light Detection and Ranging (LiDAR) based Simultaneous Localization and Mapping (SLAM) has drawn increasing interests in autonomous driving. However, LiDAR-SLAM suffers from accumulating errors which can be significantly mitigated by Global Navigation Satellite System (GNSS). Precise Point Positioning (PPP), an accurate GNSS operation mode independent of base stations, gains more popularity in unmanned systems. Considering the features of the two technologies, LiDAR-SLAM and PPP, this paper proposes a SLAM system, namely P3-LOAM (PPP based LiDAR Odometry and Mapping) which couples LiDAR-SLAM and PPP. For better integration, we derive LiDAR-SLAM positioning covariance by using Singular Value Decomposition (SVD) Jacobian model, since SVD provides an explicit analytic solution of Iterative Closest Point (ICP), which is a key issue in LiDAR-SLAM. A novel method is then proposed to evaluate the estimated LiDAR-SLAM covariance. In addition, to increase the reliability of GNSS in urban canyon environment, we develop a LiDAR-SLAM assisted GNSS Receiver Autonomous Integrity Monitoring (RAIM) algorithm. Finally, we validate P$^3$-LOAM with UrbanNav, a challenging public dataset in urban canyon environment. Comprehensive test results prove that P3-LOAM outperforms benchmarks such as Single Point Positioning (SPP), PPP, LeGO-LOAM, SPP-LOAM, and loosely coupled navigation system proposed by the publisher of UrbanNav in terms of accuracy and availability.