Robust estimation with parametric score function estimation

Robust estimation of signal parameters in the additive noise model has become an important problem. Its relevance can be attributed to the realisation that impulsive noise is present in communications channels. The approach to robust estimation taken here follows the M-estimation concept of robust statistics, except the score function is modeled as a linear combination of bases and is estimated from the observations. The asymptotic covariance of the M-estimates is derived and both the small and large sample performance is investigated. By imposing suitable constraints when estimating the score function small sample performance is improved with minimal large sample loss.