Efficient Covariance Encoding

We describe, optimize, and compare covariance encoding schemes. Several current systems encode three dimensional covariances in terms of their eigenvalues and Euler angles. We generalize this method to n dimensions. We precondition covariances to ensure that reconstructed matrices will be positive definite. We propose a new scalarmeasure ofmerit for covariance encodings, the Bhattacharyya distance. We compare the schemes in terms of the encoding error and the encoding length in bits. We recommend using enough bits to make the encoding error small compared to the error described by the covariance itself. The most efficient scheme uses logarithmic encoding of the variances and linear encoding of the Cholesky factor of the correlation matrix.