A screeding machine for screeding an uncured concrete surface, said screeding machine comprising: a screed head assembly comprising a grade setting device and a vibrating member, wherein said screed head assembly is movable over the concrete surface via said screeding machine; a pair of elevation sensors disposed at opposite ends of said screed head assembly, wherein said elevation sensors sense an elevation of the respective end of said screed head assembly relative to a reference plane established at the concrete surface; an angle sensor disposed at said screed head assembly, wherein said angle sensor senses a pitch angle of said screed head assembly and/or a roll angle of said screed head assembly, and wherein said angle sensor captures angle sensor data indicative of the sensed pitch angle and/or roll angle; a gyroscope sensor disposed at said screed head assembly, wherein said gyroscope sensor senses roll rotational velocity of said screed head assembly about a lateral axis of said screed head assembly that extends fore-aft of said screed head assembly and/or a pitch rotational velocity of said screed head assembly about a longitudinal axis of said screed head assembly that extends across said screed head assembly, such that roll and/or pitch rotational velocity is detected about one or both of the two orthogonal axes of the screed head assembly, and wherein said gyroscope sensor captures gyroscope sensor data indicative of the sensed roll and/or pitch rotational velocity; a control, wherein said control, responsive to signals from said elevation sensors, controls said screed head assembly to set the grade of the uncured concrete; wherein said control processes gyroscope sensor data and angle sensor data to determine the pitch angle and/or roll angle of the screed head assembly, and wherein said control controls the screed head assembly based on signals from one or both of said elevation sensors and the determined pitch angle and/or roll angle of the screed head assembly; wherein, responsive to one of said elevation sensors being compromised so as to not properly sense the elevation of its respective end of said screed head assembly, and responsive to processing of angle sensor data captured by said angle sensor and gyroscope sensor data captured by said gyroscope sensor, said control determines whether the angle sensor data is compromised; and wherein, responsive to determination that the angle sensor data is compromised, said control processes the gyroscope sensor data to determine the pitch angle and/or roll angle of the screed head assembly, and wherein said control controls the screed head assembly based on signals from an uncompromised elevation sensor of said elevation sensors and based on the pitch angle and/or roll angle of the screed head assembly determined using the gyroscope sensor data. a screed head assembly comprising a grade setting device and a vibrating member, wherein said screed head assembly is movable over the concrete surface via said screeding machine; a pair of elevation sensors disposed at opposite ends of said screed head assembly, wherein said elevation sensors sense an elevation of the respective end of said screed head assembly relative to a reference plane established at the concrete surface; an angle sensor disposed at said screed head assembly, wherein said angle sensor senses a pitch angle of said screed head assembly and/or a roll angle of said screed head assembly, and wherein said angle sensor captures angle sensor data indicative of the sensed pitch angle and/or roll angle; a gyroscope sensor disposed at said screed head assembly, wherein said gyroscope sensor senses roll rotational velocity of said screed head assembly about a lateral axis of said screed head assembly that extends fore-aft of said screed head assembly and/or a pitch rotational velocity of said screed head assembly about a longitudinal axis of said screed head assembly that extends across said screed head assembly, such that roll and/or pitch rotational velocity is detected about one or both of the two orthogonal axes of the screed head assembly, and wherein said gyroscope sensor captures gyroscope sensor data indicative of the sensed roll and/or pitch rotational velocity; a control, wherein said control, responsive to signals from said elevation sensors, controls said screed head assembly to set the grade of the uncured concrete; wherein said control processes gyroscope sensor data and angle sensor data to determine the pitch angle and/or roll angle of the screed head assembly, and wherein said control controls the screed head assembly based on signals from one or both of said elevation sensors and the determined pitch angle and/or roll angle of the screed head assembly; wherein, responsive to one of said elevation sensors being compromised so as to not properly sense the elevation of its respective end of said screed head assembly, and responsive to processing of angle sensor data captured by said angle sensor and gyroscope sensor data captured by said gyroscope sensor, said control determines whether the angle sensor data is compromised; and wherein, responsive to determination that the angle sensor data is compromised, said control processes the gyroscope sensor data to determine the pitch angle and/or roll angle of the screed head assembly, and wherein said control controls the screed head assembly based on signals from an uncompromised elevation sensor of said elevation sensors and based on the pitch angle and/or roll angle of the screed head assembly determined using the gyroscope sensor data.