Traditionally, inertial measurement unit (IMU)-based human joint angle estimation techniques are evaluated for general human motion where human joints explore all of their degrees of freedom. Pure human walking, in contrast, limits the motion of human joints and may lead to unobservability conditions that confound magnetometer-free IMU-based methods. This work explores the unobservability conditions emergent during human walking and expands upon a previous IMU-based method for the human knee to also estimate human hip angles relative to an assumed vertical datum. The proposed method is evaluated (N=12) in a human subject study and compared against an optical motion capture system. Accuracy of human knee flexion/extension angle (7.87∘ absolute root mean square error (RMSE)), hip flexion/extension angle (3.70∘ relative RMSE), and hip abduction/adduction angle (4.56∘ relative RMSE) during walking are similar to current state-of-the-art self-calibrating IMU methods that use magnetometers. Larger errors of hip internal/external rotation angle (6.27∘ relative RMSE) are driven by IMU heading drift characteristic of magnetometer-free approaches and non-hinge kinematics of the hip during gait, amongst other error sources. One of these sources of error, soft tissue perturbations during gait, is explored further in the context of knee angle estimation and it was observed that the IMU method may overestimate the angle during stance and underestimate the angle during swing. The presented method and results provide a novel combination of observability considerations, heuristic correction methods, and validation techniques to magnetic-blind, kinematic-only IMU-based skeletal pose estimation during human tasks with degenerate kinematics (e.g., straight line walking).