The estimation of robot pose and pipe diameter is an essential task for reliable in-line inspection (ILI) operations and the accurate assessment of pipeline attributes. This paper addresses the problem of robot pose and pipe diameter estimation for natural gas pipelines based on 3D time-of-flight (ToF) sensors. To tackle this challenge, we model the problem as a non-linear least-squares optimization that fits 3D ToF sensor measurements in its local coordinates to an elliptic cylindrical model of the pipe inner surface. We identify and prove that the canonical ellipse-based estimation method (C-EPD), which uses a canonical residual function, suffers from bias in diameter estimation due to its asymmetry to depth errors. To overcome this limitation, we propose the robust and unbiased estimation of pose and diameter (RU-EPD) approach, which employs a novel error-based residual function. The proposed function is symmetric to depth errors, effectively reducing estimation bias. Extensive numerical simulations and prototype pipeline experiments demonstrate that RU-EPD outperforms C-EPD, achieving an at least six times lower estimation bias and a 2.5 times smaller estimation error range in pipe diameter and about a 2 times smaller estimation error range in pose estimation.

In-line inspection (ILI) is essential for maintaining the integrity of natural gas pipelines. In ILI, pipeline inspection gauges (PIGs) autonomously navigate through pipelines under real-time and resource-constrained conditions to measure pipeline irregularities. Elbow and T-junction detection and estimation (ETDE) play a critical role in enabling PIG navigation to avoid speed excursions which prevent effective data collection or even damage the PIG and pipelines. Existing approaches are often computationally intensive, incomplete, or late estimations, making them unsuitable for real-time operation in such environments. This paper proposes a real-time elbow and T-junction detection and estimation (RT-ETDE) framework that efficiently detects elbows and T-junctions and estimates their critical parameters for PIG navigation using 3D point clouds. Our framework relies on intelligent point cloud partition and feature extraction together with simple geometric solutions which greatly reduce computational complexity. Furthermore, several real-time adaptation techniques are introduced to ensure real-time operation. Experimental results on a prototype pipeline demonstrate that the RT-ETDE framework consistently detects elbows and T-junctions while achieving a 10 Hz frame rate on a real PIG processing unit, validating its suitability for next-generation pipeline inspection systems.