Invariant Extended Kalman Filter for Low-Cost Foot-Mounted Inertial Pedestrian Navigation

This paper presents an observer approach for a low-cost foot-mounted inertial pedestrian navigation. The approach is based on the theory of invariant observer design, which enables the observer to estimate the navigation state with high accuracy even in the presence of noise and uncertainties. The navigation state is modeled as an element of the matrix Lie group of double direct isometries, SE
2
(3), which is a mathematical representation of the space such as position, velocity and attitude, in which the pedestrian moves. The model includes accelerometers and rate-gyros biases, which are commonly found in low-cost inertial sensors. Next, the design matrix based on the Invariant Extended Kalman Filter (IEKF) framework is derived. The proposed system is designed to operate using only Zero Velocity Updates (ZVU) as the aiding information, which is then shown to be left-invariant measurements.