Instrument for measuring an aircraft's roll, pitch, and heading by matching position changes along two sets of axes

An instrument for indirectly measuring the attitude of a moving aircraft includes three accelerometers, a GPS radio receiver, an electronic estimating module, and an electronic output module. The three accelerometers indicate three accelerations of the aircraft respectively along three aircraft body axes. The GPS radio receiver receives from GPS satellites the position and velocity of the aircraft along an earth fixed axis. The electronic estimating module estimates a vector such that a series of aircraft position changes along the three body axes that are caused by the measured accelerations, times the vector, approximately matches a corresponding series of position changes along the earth fixed axis as given by the receiver. The electronic output module generates a visual display of the roll, pitch, or heading of the aircraft by performing trigonometric functions on the vector.