Disclosed is a positioning system including: several inertial measurement units; at least one common sensor, providing a measurement of a positioning parameter of a system; for each inertial measurement unit, a navigation filter configured to: a) determine an estimate of the positioning parameter, on the basis of an inertial signal provided by the inertial measurement unit; and to b) correct the estimate, as a function of the measurement and of a correction gain that is determined on the basis of an augmented variance higher than the variance of a measurement noise of a common sensor; and—at least one fusion module determining a mean of the estimates, the mean being not reinjected at the input of the navigation filters. Also disclosed is an associated positioning method.