Correcting for Bias in Mahalanobis and Log-Likelihood Estimates

Mahalanobis and log-likelihood estimates are used extensively in tracking systems, but are affected by residual bias and by uncertainty in covariance matrices. This paper provides a formal framework that, to some extent, justifies covariance inflation techniques and allows existing fudge factor thresholds to be interpreted in terms of residual bias covariance matrices and covariance matrix uncertainty.