Microelectromechanical system (MEMS) gyroscopes have advantageous properties for orientation sensing and navigation as they are small, low cost, and consume little power. However, the significant noise at low frequencies results in large orientation errors as a function of time. Controlled physical rotation of the gyroscope can be used to remove the constant part of the gyro errors and reduce low-frequency noise. As adding motors for this would increase the system cost, it would be advantageous to attach gyros to a rotating platform that is already built in the vehicle. In this paper, we present theory and results for novel navigation systems where an inertial measurement unit (IMU) is attached to the wheel of a ground vehicle. The results show that a low-cost MEMS IMU can provide a very accurate navigation solution using this placement option.