A Closed-Form Analytical Estimation of Vertical Displacement Error in Pedestrian Navigation

We present an analytical expression for estimating the position error in the vertical direction in pedestrian navigation using an Inertial Measurement Unit (IMU) aided by an altimeter. The analytical expression is found to be directly proportional to the altimeter resolution, the square root of the altimeter sampling rate, IMU Velocity Random Walk (VRW), and a ratio of time intervals in the stance phase and the swing phase during the gait cycle, and inversely proportional to the square root of IMU sampling rate. The analytical analysis was verified by numerical simulations and supported by experimental results. The numerical simulation of the ZUPT-augmented navigation aided by an altimeter was conducted based on a mathematically simulated foot motion trajectory. Experiments were implemented on a foot-mounted platform containing IMUs and altimeters. The results from both simulations and experiments matched our analytical prediction, with an error less than 20%.