  In the rapidly evolving fields of virtual and augmented reality, accurate
spatial audio capture and reproduction are essential. For these applications,
Ambisonics has emerged as a standard format. However, existing methods for
encoding Ambisonics signals from arbitrary microphone arrays face challenges,
such as errors due to the irregular array configurations and limited spatial
resolution resulting from a typically small number of microphones. To address
these limitations and challenges, a mathematical framework for studying
Ambisonics encoding is presented, highlighting the importance of incorporating
the full steering function, and providing a novel measure for predicting the
accuracy of encoding each Ambisonics channel from the steering functions alone.
Furthermore, novel residual channels are formulated supplementing the
Ambisonics channels. A simulation study for several array configurations
demonstrates a reduction in binaural error for this approach.
