Range-based collaborative relative navigation for multiple unmanned aerial vehicles using consensus extended Kalman filter

Precise relative navigation between unmanned aerial vehicles (UAVs) in a GNSS-denied environment is a critical technology enabling collaborative missions. Range-based relative navigation allows other onboard optical sensors to be used for missions instead of for tracking other formation members. However, range-based relative navigation suffers from a well-known ambiguous solution problem. Approaches developed in previous studies include the use of one or more anchors, optical-flow measuring velocity, or multiple range sensors to solve the observability of the estimated states. In this study, a novel range-based collaborative relative navigation algorithm for multiple fixed-wing UAVs is proposed by integrated ranging-sensor with other commonly used onboard sensors such as low-cost IMUs, where anchor, optical-flow measurement or multi ranging sensor is not required. A relative motion estimation model is established in a floating horizontal frame; the sensor biases are augmented in the model to solve the colored noise problem. The observability of the estimated states is analyzed, and the observable criteria to guide the flight are obtained by introducing the Lie derivative criteria. The relative position vector must not be a constant in both direction and distance, and non-rectilinear trajectory is also required to obtain observability. A decentralized estimation strategy based on a consensus extended Kalman filter is designed for the system, with several physical constraints on the estimation in constructing the consensus to improve the observability. The proposed algorithm is tested and verified using standard Monte Carlo simulations. The simulation results indicate that the full state is observable if the observable criteria are satisfied. The sensitivity of the relative localization accuracy to the sensors and motion is presented and discussed. It is shown that the uncertainties from ranging-sensors and IMUs contribute more to the performance of the estimation. The estimated uncertainties of the sensor biases are also promising, and can potentially be used to improve the absolute navigation of UAVs.