Toward Developing an Indoor Localization System for MAVs Using Two or Three RF Range Anchors: An Observability Based Approach

This study performs a nonlinear observability analysis on radio frequency (RF) range assisted inertial navigation system (INS) for localizing quadrotor micro-aerial vehicles (MAV) in indoor environments. The objective is to use fewer number of RF range nodes as possible to support the efficient scalability of the localization system. The proposed INS formulation incorporates the effect of aerodynamic drag forces, which allows this novel INS to operate without having to use a velocity sensor. The nonlinear observability analysis is carried out for two distinct cases where the range is measured between the MAV and RF anchors placed at known locations. The first case uses three anchors, and for the second case, the analysis is repeated for two range anchors. For each case, different scenarios are considered to identify unobservable conditions of the proposed INS, and the corresponding unobservable modes for those scenarios are determined. These unobservable modes are validated through numerical simulation. The analysis facilitates the range assisted localization of MAVs when there are less than the typical four range configuration and allows planning of the trajectory of the MAV while preserving the observability of the INS. The main contributions of this paper are as follows: 1) nonlinear observability analysis of a range assisted INS for quadrotor MAV with three or two range measurements, 2) theoretical derivation of unobservable trajectories and corresponding unobservable modes, 3) numerical validation of the unobservable modes and experimental validation of the proposed INS performance.