Design and Error Analysis of Accelerometer-Based Inertial Navigation Systems

We examine the feasibility of designing an accelerometer-based (or gyroscope-free) inertial navigation system that uses only accelerome-ters to compute the linear and angular motions of a rigid body. The accelerometer output equation is derived to relate the linear and an-gular motions of a rigid body relative to a fixed inertial frame. A suf-ficient condition is given to determine if a configuration of accelerom-eters is feasible. If the condition is satisfied, the angular and linear motions can be computed separately using two decoupled equations of an input-output 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 sys-tem equations for a special cube configuration for which the angular acceleration is expressed as a linear combination of the accelerometer outputs. The effects of accelerometer location and orientation errors are analysed. Algorithms that identify and compensate these errors are developed. Keywords gyroscope-free, configuration of accelerometers, feasibility, input-output dynamical system realisation, error sensitivity analysis.