  Foot-mounted inertial sensors become popular in many indoor or GPS-denied
applications, including but not limited to medical monitoring, gait analysis,
soldier and first responder positioning. However, the foot-mounted inertial
navigation relies largely on the aid of Zero Velocity Update (ZUPT) and has
encountered inherent problems such as heading drift. This paper implements a
pedestrian navigation system based on dual foot-mounted low-cost inertial
measurement units (IMU) and inter-foot ultrasonic ranging. The observability
analysis of the system is performed to investigate the roles of the ZUPT
measurement and the foot-to-foot ranging measurement in improving the state
estimability. A Kalman-based estimation algorithm is mechanized in the Earth
frame, rather than in the common local-level frame, which is found to be
effective in depressing the linearization error in Kalman filtering. An
ellipsoid constraint in the Earth frame is also proposed to further restrict
the height drift. Simulation and real field experiments show that the proposed
method has better robustness and positioning accuracy (about 0.1-0.2% travelled
distance) than the traditional pedestrian navigation schemes do.
