Design of gyroscope-free navigation systems

We examine the feasibility of designing a gyroscope-free inertial navigation system (INS) that uses only accelerometers to compute the linear and angular motions of a rigid body. The accelerometer output equation is derived to relate the linear and angular motions of a rigid body relative to a fixed inertial frame. A sufficient condition is given to determine if a configuration of accelerometers is feasible. If the condition is satisfied, the angular and linear motions can be computed separately using two decoupled equations of an input-output (I/O) dynamical system; a state equation for angular velocity and an output equation for linear acceleration. This simple computation scheme is derived from the corresponding dynamical system equations for a special cube configuration for which the angular acceleration is expressed as a linear combination of the accelerometer outputs.