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Efficient Covariance Encoding
March 2012
James R. Van Zandt, The MITRE Corporation
ABSTRACT
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.
Additional Search Keywords
covariance encoding, eigenvalues, Euler angles, Bhattacharyya distance, scalar measures, logarithmic encoding, Cholesky factor, networked tracking systems
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