Implicit Kalman filter for position estimation with visual and inertial sensor fusion

In mobile robotics, position-sensing is crucial to a robot. We investigate a type of online position estimations based on visual and inertial sensor fusion. Being different from the traditional state estimation, our position estimation is a linear state estimation with implicit observation equations. To this end, an implicit Kalman filter is proposed and designed in details for this position estimation. Furthermore, a state augmentation method is employed in which the accelerometer bias is taken as a state of the filter to compensate for its effect to the position estimation results. Simulation results show that the implicit Kalman filter is convergent, and the effect of the accelerometer bias is eliminated from the position estimation.