Kalman Filtering for Relative Inertial Navigation of Uninhabited Air Vehicles

An extended Kalman filter is derived for estimating the relative position and attitude of a pair of uninhabited air vehicles, designated leader and follower. All leader states are assumed known, while the relative states are estimated using line-of-sight measurements between the vehicles along with angular rate and acceleration measurements of the follower. Noise is present on all measurements, while biases are present only on the latter two. Line-of-sight measurements are generated using visual navigation beacons. The global attitude is parameterized using a quaternion, while the local attitude error is given by a three-dimensional attitude representation. The quaternion normalization constraint is maintained using a multiplicative error quaternion. Simulation results show that the relative states and measurement biases converge within their respective covariance bounds. The number of visual navigation beacons is shown to affect estimator convergence in the presence of initial condition errors.