# Detecting and Mitigating Attacks on GPS Devices
## 6 Countermeasures and Their Comparison
### Countermeasures for GPS-Denied Environment--Alternate Positioning
#### 6.3.1 IMU-Based Approaches
The authors of [113] proposed an approach that employs an array of six commercial-grade inertial sensors arranged in a cube containing triaxial gyros, accelerometers, and magnetometers. This approach aims to compensate for individual sensor bias using mutual calibration. This mutual calibration is accomplished by calculating average values across all sensors for each spatial axis. This approach was demonstrated in a vehicle-based experimental testbed with reported average position accuracy within 1.1 m. The multi-IMU approach outperformed GPS-based positioning during experimentation, providing an average position accuracy within 3.52 m. The authors of [113] continued their work in [114], focusing on the accuracy of attitude determination in UAS applications. They again used their multi-IMU system with six IMUs in a cubic configuration and focused on assessing the accuracy of roll, pitch, and heading. The reported root mean square error (RMSE) was extremely low, with heading, pitch, and roll errors reported as 0.032, 0.012, and 0.023 radians, respectively. The authors of [115] proposed a multi-IMU redundancy approach, where they fused measurements from five different IMUs using a feedback-federated Kalman filter with attitude estimation using the Bortz equation, resulting in the best performance of all methods considered. This approach achieved very low errors in estimating the test platform's roll, pitch, and yaw compared with ground truth. These various research efforts established the feasibility of using multi-IMU approaches in terms of achievable performance. The major challenge with these approaches is the higher cost and required sensor hardware, which may be prohibitive for some systems. The research presented in these papers has one primary limitation: they all evaluate their solutions in well-controlled vehicle-based or small UAS-based systems in seemingly benign environments. One main limitation of IMUs is that inertial sensors are extremely sensitive to environmental and platform factors, such as temperature, pressure, mechanical vibration, and electrical system noise, in the case of magnetometers. Many unmanned systems will be expected to operate in harsh environments that may produce fluctuations in these parameters and significant system vibration, which complicates effective IMU calibration. The mutual self-calibration approach proposed in [113] is promising since it may solve this problem; however, additional experiments and analyses are required to determine performance under harsh conditions. Most IMU-related research focuses on multi-sensor fusion and using additional sensors to improve IMU-based positioning performance. The underlying concept of these approaches is that IMUs can provide very accurate positioning solutions for limited periods of time due to error accumulation. Additional sensors are used to periodically achieve an accurate ground-truth position estimate that can be used to reset the IMU-based method. The IMU-based method then needs to simply maintain accuracy until the next ground-truth solution can be achieved via the other sensors. A common approach is using a hybrid IMU-GNSS approach with GPS-provided ground truth to reset inertial accumulation errors, with the IMU maintaining positioning during GPS intermittent outages. This approach does not work in the GPS-denied environment; another sensor is required to provide this ground-truth IMU reset function. The authors of [116] proposed an inertial navigation algorithm that incorporates sensor outputs from accelerometers, gyroscopes, magnetometers, Pitot tubes, and air vanes; however, a stated goal of their approach was to facilitate the fusion of their proposed inertial filter with visual odometry methods. Several papers have proposed using magnetometer sensor outputs to improve IMU performance. The authors of [117] proposed to fuse inertial and magnetometer sensors using a Kalman filter to improve performance.