Inertial measurement apparatus arranged to be carried by a carrier vehicle, the apparatus comprising: a chassis , a turntable mounted on the chassis to turn about an axis of rotation (Z) normal to a surface of the turntable , and a first inertial measurement unit that is mounted on said surface of the turntable and that is connected to an electronic control unit connected to a motor for driving the turntable to control turning of the turntable , the first inertial measurement unit comprising three rate gyros and three accelerometers arranged on the axes of a first measurement reference frame (R1); the apparatus being characterized in that it comprises a second inertial measurement unit secured to the chassis and comprising three rate gyros and three accelerometers arranged on the axes of a second measurement reference frame (R2), and in that the control unit is arranged: • from a fixed initial angular position of the turntable , to cause the turntable to turn periodically through one revolution with symmetrical go and return movements in order to return the turntable to the fixed initial position; • over a predetermined duration, to calculate the acceleration of the carrier vehicle from: · accelerometer and gyro measurements of the first inertial measurement unit while the turntable is stationary; and · accelerometer and gyro measurements of the second inertial measurement unit while the turntable is moving; and • to reconstitute an inertial reference frame for each inertial measurement unit from the accelerometer measurements and the gyro measurements measured by said measurement unit during the predetermined duration and to compare the two inertial reference frames in order to determine an orientation difference between them and to take account of this orientation difference when calculating the acceleration on switching from using gyro measurements of the first measurement unit to using gyro measurements of the second measurement unit , and vice versa. • from a fixed initial angular position of the turntable , to cause the turntable to turn periodically through one revolution with symmetrical go and return movements in order to return the turntable to the fixed initial position; • over a predetermined duration, to calculate the acceleration of the carrier vehicle from: · accelerometer and gyro measurements of the first inertial measurement unit while the turntable is stationary; and · accelerometer and gyro measurements of the second inertial measurement unit while the turntable is moving; and · accelerometer and gyro measurements of the first inertial measurement unit while the turntable is stationary; and · accelerometer and gyro measurements of the second inertial measurement unit while the turntable is moving; and • to reconstitute an inertial reference frame for each inertial measurement unit from the accelerometer measurements and the gyro measurements measured by said measurement unit during the predetermined duration and to compare the two inertial reference frames in order to determine an orientation difference between them and to take account of this orientation difference when calculating the acceleration on switching from using gyro measurements of the first measurement unit to using gyro measurements of the second measurement unit , and vice versa. <EOS>