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Positioning with one inertial measurement unit and one ranging sensor iscommonly thought to be feasible only when trajectories are in certain patternsensuring observability. For this reason, to pursue observable patterns, it isrequired either exciting the trajectory or searching key nodes in a longinterval, which is commonly highly nonlinear and may also lack resilience.Therefore, such a positioning approach is still not widely accepted inreal-world applications. To address this issue, this work first investigatesthe dissipative nature of flying robots considering aerial drag effects andre-formulates the corresponding positioning problem, which guaranteesobservability almost surely. On this basis, a dimension-reduced wrigglingestimator is proposed accordingly. This estimator slides the estimation horizonin a stepping manner, and output matrices can be approximately evaluated basedon the historical estimation sequence. The computational complexity is thenfurther reduced via a dimension-reduction approach using polynomial fittings.In this way, the states of robots can be estimated via linear programming in asufficiently long interval, and the degree of observability is thereby furtherenhanced because an adequate redundancy of measurements is available for eachestimation. Subsequently, the estimator's convergence and numerical stabilityare proven theoretically. Finally, both indoor and outdoor experiments verifythat the proposed estimator can achieve decimeter-level precision at hundredsof hertz per second, and it is resilient to sensors' failures. Hopefully, thisstudy can provide a new practical approach for self-localization as well asrelative positioning of cooperative agents with low-cost and lightweightsensors.

SRIBO: An Efficient and Resilient Single-Range and Inertia Based Odometry for Flying Robots