  This paper proposes a novel Gap Reduced Minimum Error Robust Simultaneous
(GRMERS) estimator for resource-constrained Nano Aerial Vehicle (NAV) that
enables a single estimator to provide simultaneous and robust estimation for a
given N unstable and uncertain NAV plant models. The estimated full state
feedback enables a stable flight for NAV. The GRMERS estimator is implemented
utilizing a Minimum Error Robust Simultaneous (MERS) estimator and Gap Reducing
(GR) compensators. The MERS estimator provides robust simultaneous estimation
with minimal largest worst-case estimation error even in the presence of a
bounded energy exogenous disturbance signal. The GR compensators reduce the gap
between the graphs of N linear plant models to decrease the estimation error
generated by the MERS estimator. A sufficient condition for the existence of a
simultaneous estimator is established using LMIs and robust estimation theory.
Further, MERS estimator and GR compensator design are formulated as non-convex
tractable optimization problems and are solved using the population-based
genetic algorithms. The performance of the GRMERS estimator consisting of MERS
estimator and GR compensators from the population-based genetic algorithms is
validated through simulation studies. The study results indicate that a single
GRMERS estimator can produce state estimates with reduced errors for all flight
conditions. The results indicate that the single GRMERS estimator is robust
than the individually designed H inifinity filters.
