# Performance Enhancement of Consumer-Grade MEMS Sensors through Geometrical Redundancy
## 6 Conclusions  
A method based on redundant configuration for the performance improvement in terms of bias instability and bias drift of low-cost of consumer-grade MEMS inertial measurement units has been presented hereinafter; attention has been mainly focused on bias with respect to scale factor, since the former is more relevant for this category of sensors [5]. The method has been assessed by means of a proper prototype of redundant IMU. In particular, the IMU has been implemented by arranging six SensorTile(tm) boards by STMicroelectronics on the faces of a cube. Each SensorTile(tm) is equipped with an inertial sensor (referred to as iNemo) consisting of 16-bit triaxial gyroscope and triaxial accelerometer exchanging raw measures with a concentrator. According to the proposed method, the first contribution to performance enhancement is brought by (i) aligning raw measures coming from each sensor with respect to a reference frame, (ii) averaging for each sensing axis, and (iii) exploiting a GNSS-aided Kalman filter to estimate position, velocity and attitude. To further improve the performance of the redundant configuration, values of entries of the process noise covariance matrix of the Kalman filter are obtained through an Allan variance approach. According to the authors' best knowledge, this is the first application of multiple Allan variance estimation for redundant configurations of inertial sensors. The corresponding improvement can easily be appreciated, since errors reduction with respect to the best single sensor ranged within 25% up to 80%. Moreover, initial estimates of bias for both accelerations and angular rates are achieved through the application of a ZUPT filter in a stationary condition. Method performance has been assessed by comparing its position, velocity, and attitude estimates, obtained during an urban car test, with those granted by a commercial tactical-grade IMU, STIM300 by SensoNor. As far as heading is concerned, differences as low as 0.025 rad have been evaluated for vehicles navigation on a straight lane; corresponding values for a single-sensor navigation are much greater than 1 rad. Similar results have been achieved for pitch and roll. As for position, the performance has been expressed in terms of RMSE of the EVM of the differences of the position estimated by means of the proposed prototype and that granted by the reference. RMSE values equal to 0.89 m have been experienced for the whole car test when the update rate of the GNSS measures was equal to 1 Hz; the performance got worse in the presence of GNSS outages, reaching values of 5.25 m for an update period of the GNSS equal to 10 s.  
Similar solutions have already been presented in the literature. As an example, a cubic sensor configuration has been proposed in [40] to make accurate measurements of angular velocity using a set of 12 dual-axis accelerometers. Moreover, a redundant configuration of six-axis MEMS gyroscopes as described in [41] to achieve accurate attitude estimates; to this aim, expensive navigation grade gyroscopes (with a bias instability equal to 0.02 \({}^{\circ}\)/h) have been exploited. On the contrary, the proposed method consists of 12 consumer-grade triaxial sensors (six accelerometers and six gyroscopes), which allows us to realize at almost the same size a complete navigation system capable of improving the overall performance of the single sensors up to the tactical grade. The proposed method, leveraging the main features of MEMS sensors, is tailored for the implementation of an integrated navigation system for small and light unmanned vehicles, both terrestrial and aerial. However, it can be easily applied also to most performing IMU, even though the performance improvement would not be sustainable from an economic point of view. Finally, the method can be extended by considering regular polyhedrons characterized by a higher number of faces (dodecahedron and icosahedron);