Intelligent polynomial curve fitting for time-domain triggered inertial devices

A method of blended-polynomial curve fitting is employed to improve performance of time domain triggered inertial devices. In such devices, a spring-mass system is perturbed to oscillate sinusoidally. This sinusoidal motion of the mass (the carrier) is perturbed by the time varying motion caused by inertial accelerations (the signal). When the mass passes several predefined locations, a trigger accurately measures the time of crossing. For each half-oscillation period, the overall motion of the mass is mapped by fitting a high order polynomial function to the triggering data. An analytic approximation of the motion of the mass is then obtained for all time by smoothly blending neighboring and overlapping polynomial fits together. If the carrier frequency is known, the inertial acceleration signal can be isolated from the overall polynomial fit by intelligently choosing the times to out-sample data. A 10 second real-time simulation is performed: having up to ±10 g inertial accelerations resulting in roughly 1 km of displacement. The average error magnitude is shown to be less than 1 μg, and the error in the navigational position estimate is 36.94 μm per 1 km of travel, or roughly 3 parts in 10⁸ using a timing uncertainty of 10 ps.