# Performance Enhancement of Consumer-Grade MEMS Sensors through Geometrical Redundancy
## 1 Introduction  
Micro Electro-Mechanical Sensors for inertial measurements, such as gyros and accelerometers, are of high interest in the development of modern vehicles. Compact, lightweight, reliable, and affordable solutions are needed to develop autonomous transport platforms, such as Unmanned Aircraft Systems, Unmanned Ground Vehicles, and Autonomous Underwater Vehicles [1, 2, 3]. New needs are also determined for platforms with human passengers on-board, such as Urban Air Mobility aircraft, Autonomous Cars, and Autonomous Ships [4, 5, 6]. Typically, MEMS inertial sensors are included in integrated navigation packages with one or more aiding systems to control the intrinsic inertial measurement drift by means of sensor data fusion [7, 8]. Improved technical solutions are made available by fast-developing innovation frameworks, such as Internet of Things IoT and Industry Automation [9]. These solutions include a large number of electronic components used for indoor and outdoor navigation that can be used as aiding sensors, such as Radio-Frequency positioning systems, air data sensors, logs, altimeters, depth sensors, echo sounders, ultrasonic sensors, and several types of imaging cameras. They are all compact electronic components that can be integrated with MEMS inertial sensors to realize small and lightweight units that can be installed on advanced transport platforms. MEMS sensors still have some significant limitations. Actually, gyros are more critical than accelerometers since their overall accuracy is poor with respect to advanced solutions, such as optical and mechanical ones. In particular, the bias instability can be very large. Consumer-grade MEMS gyros can be affected by a bias instability in the order of 50 degreesper hour or more [9], while advanced sensors can reach tactical grade levels with a bias instability in the order of \(10^{-1}\) degrees per hour [10]. Tactical grade is defined as the condition when the gyro can measure the Earth rate, i.e., 15 degrees per hour; this term allows for performing autonomous initialization of heading by gyrocompassing [11]. The bias instability of gyros is the most important error term that defines the overall performance of an Inertial Measurement Unit. It can be divided into two contributions, such as bias thermal drift and bias drift [5]. The first contribution can be reduced by means of calibration [12]; the negative effects of the second one are controlled by means of sensor data fusion. Typically, it is considered as an additional state parameter with respect to navigation errors to form Augmented-state Extended Kalman Filters [5]. In this framework, MEMS gyro bias drift shall be reduced as much as possible to keep the overall error within acceptable performance levels. If no single sensor is available with satisfactory bias performance, the use of redundancy is an option to realize proper solutions. It is worth noting that using MEMS gyros instead of optical ones results in a very large gain in terms of space, weight, power consumption, and costs. For this reason, part of the gain can be sacrificed to increase the number of sensors, thus also increasing the accuracy of navigation state estimates by integrating the measurements of redundant gyros and accelerometers. Redundancy can be considered as a special form of sensor data fusion, where the integrated measurement comes all from sensors of the same type. The benefits of redundancy are not just related to accuracy. Redundancy can also be effective in increasing the overall reliability, integrity, and robustness of the system [5]. For instance, redundant sensor configurations provide graceful degradation of accuracy in case of single-sensor failure [13]. The availability of rapid-prototyping electronic boards, such as those provided by STMicroelectronics(tm) [14], permits us to perform a fast arrangement of prototypical redundant units to test the effectiveness of redundant solutions for advanced transport systems applications.