Suboptimal robust estimation for signal plus noise models

This paper considers the general problem of estimating the parameters of a deterministic signal in additive i.i.d noise. We develop an estimator for the signal parameters with no a priori knowledge of the noise distribution. The estimator is based on the theory of M-estimation, we replace the true score function by a weighted linear combination of basis functions. Minimising the mean square error between the true score function and the influence function leads to a simple least squares solution for the weights. A theoretical study shows that there is always a gain in performance by doing so. Several computer simulations are presented to illustrate the performance of the proposed adaptive procedure.