An accurate estimation of pipe attributes, pose of pipeline inspection gauge (PIG), and downstream pipeline topology is essential for successful in-line inspection (ILI) of underground compressible gas pipelines. Taking a 3D point cloud of light detection and ranging (LiDAR) or time-of-flight (ToF) camera as the input, in this paper, we present the simultaneous pipe-attribute and PIG-pose estimation (SPPE) approach that estimates the optimal pipe-attribute and PIG-pose parameters to transform a 3D point cloud onto the inner pipe wall surface: major- and minor-axis lengths, roll, pitch, and yaw angles, and 2D deviation from the center of the pipe. Since the 3D point cloud has all spatial information of the inner pipe wall measurements, this estimation problem can be modeled by an optimal transformation matrix estimation problem from a PIG sensor frame to the global pipe frame. The basic idea of our SPPE approach is to decompose this transformation into two sub-transformations: The first transformation is formulated as a non-linear optimization problem whose solution is iteratively updated by the Levenberg–Marquardt algorithm (LMA). The second transformation utilizes the gravity vector to calculate the ovality angle between the geometric and navigation pipe frames. The extensive simulation results from our PIG simulator based on the robot operating system (ROS) platform demonstrate that the proposed SPPE can estimate the pipe attributes and PIG pose with excellent accuracy and is also applicable to real-time and post-processing non-destructive testing (NDT) applications thanks to its high computational efficiency.