Using the bootstrap for robust detection in array signal processing

A critical problem in many signal processing applications is the determination of the correct model order for example, the number of multipath components in a received communication signal. One approach to detect the model order is to use the distribution of the criterion function of the estimator applied to find interesting parameters. Unfortunately, the nominal distribution of such a criterion function relies heavily on a correct model of the observed signal. In practice, with modeling errors present, the distribution is unknown. For robust detection based on the criterion function of a certain class of estimators, a two-step procedure is proposed. First, an alternative representation of the residuals is found using a predictor. Second, using bootstrap resampling, a parameter is estimated from the new residuals. This parameter transforms the criterion function to pivotal form. Numerical experiments show robustness to a range of possible modeling errors. An example from real measured array data is included.