  We present a comprehensive framework for fusing measurements from multiple
and generally placed accelerometers and gyroscopes to perform inertial
navigation. Using the angular acceleration provided by the accelerometer array,
we show that the numerical integration of the orientation can be done with
second-order accuracy, which is more accurate compared to the traditional
first-order accuracy that can be achieved when only using the gyroscopes. Since
orientation errors are the most significant error source in inertial
navigation, improving the orientation estimation reduces the overall navigation
error. The practical performance benefit depends on prior knowledge of the
inertial sensor array, and therefore we present four different state-space
models using different underlying assumptions regarding the orientation
modeling. The models are evaluated using a Lie Group Extended Kalman filter
through simulations and real-world experiments. We also show how individual
accelerometer biases are unobservable and can be replaced by a six-dimensional
bias term whose dimension is fixed and independent of the number of
accelerometers.
