A dynamics based method for accelerometer-only navigation of a spinning projectile

Abstract

A method of navigating a gun-launched, spinning projectile using only accelerometers is presented. A linear combination of the outputs of a general configuration of at least 12 accelerometers is shown to provide measurements of angular acceleration and angular rate products of the form w2/i and wiwj. These measurements are used in the development of a 12 state, extended Kalman filter to estimate position, velocity, attitude, and angular rate, with twelve additional states included to estimate accelerometer biases. Assumptions about the dynamic behavior of the vehicle are used to assist in attitude estimation. These assumptions come in two parts. First, that the nose of the vehicle remains pointed along the air-relative velocity vector during flight. Second, that the vehicle lateral angular rates have a secular component due to the vehicle pitching over during flight to maintain this alignment. A digital filter is used to isolate the secular pitch-over component of the estimated rate in an intermediate, non-rolling frame. These dynamics-based estimates are then incorporated as measurements in the navigation filter. A configuration of 12 accelerometers arranged on the faces of a 10 cm cube is used in a six degree of freedom simulation to navigate a projectile spinning at 2 Hz. The navigation filter is shown to reliably estimate angular rates with biases as large as 1 g. Bias state estimation is also shown to compensate for instrument misalignments up to 1 degree. Using the dynamics-based measurements, the navigation filter successfully estimates projectile roll attitude to within 20 degrees for instrument random walk errors up to 2.5 milli-g/[square root] Hz.