  Positioning with one inertial measurement unit and one ranging sensor is
commonly thought to be feasible only when trajectories are in certain patterns
ensuring observability. For this reason, to pursue observable patterns, it is
required either exciting the trajectory or searching key nodes in a long
interval, which is commonly highly nonlinear and may also lack resilience.
Therefore, such a positioning approach is still not widely accepted in
real-world applications. To address this issue, this work first investigates
the dissipative nature of flying robots considering aerial drag effects and
re-formulates the corresponding positioning problem, which guarantees
observability almost surely. On this basis, a dimension-reduced wriggling
estimator is proposed accordingly. This estimator slides the estimation horizon
in a stepping manner, and output matrices can be approximately evaluated based
on the historical estimation sequence. The computational complexity is then
further reduced via a dimension-reduction approach using polynomial fittings.
In this way, the states of robots can be estimated via linear programming in a
sufficiently long interval, and the degree of observability is thereby further
enhanced because an adequate redundancy of measurements is available for each
estimation. Subsequently, the estimator's convergence and numerical stability
are proven theoretically. Finally, both indoor and outdoor experiments verify
that the proposed estimator can achieve decimeter-level precision at hundreds
of hertz per second, and it is resilient to sensors' failures. Hopefully, this
study can provide a new practical approach for self-localization as well as
relative positioning of cooperative agents with low-cost and lightweight
sensors.
